Polygonal Shapes
Figure 5.1: hierarchical map of the set of functions in qmsh for creating abstract polygonal shapes.
BOX-2D : Generate 2D Rectangle
→ 'instantiates an axis-aligned 2D rectangular polygonal shape'
Classification:→ { instantiative, convex, orthogonal, cyclic };
Alias & Synonyms:→ { box, box_2D, rect, rectangle, rect_2D, rectangle_2D };
Invocation Options:prefix G2 box ( D size )prefix G2 box ( D width, D height )prefix G2 box ( D x, D y, D width, D height )Input Arguments:•
D x :
default = width * -0.5 : the minimum x-axis position of the box - a positive or negative decimal.•
D y :
default = height * -0.5 : the minimum y-axis position of the box - a positive or negative decimal.•
D width :
default = 1.0 : the width of the box - or its extent/span along the x-axis - a positive decimal greater than zero.•
D height :
default = 1.0 : the height of the box - or its extent/span along the y-axis - a positive decimal greater than zero.•
D size :
default = 1.0 : a uniform scale factor used to construct the box - a positive decimal greater than zero.→ [ width, height, size ] > 0
Vertex Count:→ |V| = 4Practical Examples:return box(); // returns the default zero-argument unit box
return box(2); // returns a uniform box, origin-centered and with a width and height of 2 units
return box(5,1.25); // returns a non-uniform rectangular box, origin centered - with a width and height of (respectively) 5 and 1.25 units
return box(-1,-1,0.25,0.5); // returns a non-uniform rectangular box, with minimum position equal to [-1,-1], a width of 0.25 units and a height of 0.5 units
Additional Notes: B-BOX-2D : Generate 2D Beveled-Rectangle
→ 'instantiates a beveled-corner 2D rectangular polygonal shape'
Classification:→ { instantiative, convex, cyclic };
Alias & Synonyms:→ { b_box, b_box_2D, b_rect, b_rectangle, b_rect_2D, b_rectangle_2D, bevel_box, bevel_box_2D, bevel_rect, bevel_rectangle, bevel_rect_2D, bevel_rectangle_2D, ... (+24) };
Invocation Options:prefix G2 bbox ( D bevel )prefix G2 bbox ( D size, D bevel )prefix G2 bbox ( D width, D height, D bevel )prefix G2 bbox ( D x, D y, D width, D height, D bevel )Input Arguments:•
D x :
default = width * -0.5 : the minimum x-axis position of the bbox - a positive or negative decimal.•
D y :
default = height * -0.5 : the minimum y-axis position of the bbox - a positive or negative decimal.•
D width :
default = 1.0 : the width of the bbox - or its extent/span along the x-axis - a positive decimal greater than zero.•
D height :
default = 1.0 : the height of the box - or its extent/span along the y-axis - a positive decimal greater than zero.•
D bevel :
default = 0.125 : the beveling/chamfering distance/radius to apply to the corners of the bbox - a positive decimal - greater than zero and less than the mimimum of the bbox's width, height or uniform size divided by two.•
D size :
default = 1.0 : the uniform scale factor used to construct the bbox - a positive decimal greater than zero.→ [ width, height, size, bevel ] > 0
→ [ width, height, size ] > ( bevel * 2 )
Vertex Count:→ |V| = 8Practical Examples:return bbox(); // returns the default zero-argument unit bbox
return bbox(0.25); // returns a unit-size bbox with a bevel of 0.25 units applied to its corners
return bbox2D(2,1,0.05); // return a rectangular bbox with a width of 2 units, a height of 1 unit and a bevel distance of 0.05 units
return bbox(-1,-1,0.25,0.5,0.0125); // returns a rectangular bbox with minimum position [-1,-1], a width and height of 0.25 and 5 and a bevel of 0.0125 units applied to each corner
Alias Formation Rules:Additional Notes: R-BOX-2D : Generate 2D Rounded-Rectangle
→ 'instantiates a rounded-corner 2D rectangular polygonal shape'
Classification:→ { instantiative, convex, cyclic };
Alias & Synonyms:→ { r_box, r_box_2D, r_rect, r_rectangle, r_rect_2D, r_rectangle_2D, rnd_box, rnd_box_2D, rnd_rect, rnd_rectangle, rnd_rect_2D, rnd_rectangle_2D, ... (+12) };
Invocation Options:prefix G2 rbox ( D radius, I steps )prefix G2 rbox ( D size, D radius, I steps )prefix G2 rbox ( D width, D height, D radius, I steps )prefix G2 rbox ( D x, D y, D width, D height, D radius, I steps )Input Arguments:•
D x :
default = width * -0.5 : the minimum x-axis position of the rbox - a positive or negative decimal.•
D y :
default = height * -0.5 : the minimum y-axis position of the rbox - a positive or negative decimal.•
D width :
default = 1.0 : the width of the rbox - or its extent/span along the x-axis - a positive or decimal greater than zero.•
D height :
default = 1.0 : the height of the rbox - or its extent/span along the y-axis - a positive or decimal greater than zero.•
D radius :
default = 0.125 : the the rounding radius to apply to the corners of the rbox - a positive decimal greater than zero and less than the minimum of the rbox's width, height or uniform size dividded by two.•
I steps :
default = 8 : the nubmer of rounding discretisation steps to apply to the corners of the rbox - a positive integer greater than or equal to 1.•
D size :
default = 1.0 : the uniform scale factor used to construct the rbox - a positive decimal greater than zero.→ [ width, height, size, radius ] > 0
→ steps >= 1
→ [ width, height, size ] > ( radius * 2 )
Vertex Count:→ |V| = ( ( steps + 1 ) * 4 )Practical Examples:return rbox(); // returns the default zero-argument unit rbox
return rbox(0.25,4); // returns a unit-size rbox with a rounding radius of 0.25 units applied to its corners - with 4 discretisation steps per corner
return rbox(5,0.25,1); // returns a uniform rbox with a width and height of 5 units, a round radius of 0.25 units and a single discretisation step applied per corner
return rbox2D(2,1,0.05,16); // return a rectangular rbox with a width of 2 units, a height of 1 unit, a round radius of 0.05 units and 16 steps per corner
return rbox(-1,-1,0.25,0.5,0.0125,8); // returns a rectangular rbox with minimum position [-1,-1], a width and height of 0.25 and 5, a radius of 0.0125 units applied to each corner and 8 steps per corner
Alias Formation Rules:Additional Notes: CIRCLE : Generate 2D Circle
→ 'instantiates a 2D circular polygonal shape'
Classification:→ { instantiative, convex, cyclic };
Alias & Synonyms:→ { circle };
Invocation Options:prefix G2 circle ( D radius )prefix G2 circle ( D radius, I segments )prefix G2 circle ( D ox, D oy, D radius, I segments )Input Arguments:•
D ox :
default = 0 : the x-axis central position of the circle - the origin x component.•
D oy :
default = 0 : the y-axis central position of the circle - the origin y component.•
D radius :
default = 0.5 : the radius of the circle - a positive non-zero decimal.•
I segments :
default = 32 : the number of discretisation steps used to construct the circle - a positive integer greater than or equal to 3.→ radius > 0
→ segments >= 3
Vertex Count:→ |V| = segmentsPractical Examples:return circle(); // returns the default zero-argument unit circle
return circle(2); // returns a circle centered at the origin with a radius of 2 units (i.e. a diameter of 4 units) and the default (32) discretisation steps
return circle(0.5,8); // returns a circle centered at the origin with a radius of 0.5 units (diameter 1 unit) and 8 discretisation steps
return circle(-1,-1,3,16); // returns an offset circle (centered at [-1,-1]) with a radius of 3 units (diameter 6 units) and 16 discreisation steps
Additional Notes: OVAL : Generate 2D Oval
→ 'instantiates a 2D elliptic (non-uniformly scaled circle) polygonal shape defined by an axis-aligned box'
Classification:→ { instantiative, convex, cyclic };
Alias & Synonyms:→ { oval, ellipse };
Invocation Options:prefix G2 oval ( D width, D height )prefix G2 oval ( D width, D height, I segments )prefix G2 oval ( D x, D y, D width, D height, I segments )Input Arguments:•
D x :
default = width * -0.5 : the minimum x-axis position of an axis-aligned bounding-box used to define the oval.•
D y :
default = height * -0.5 : the minimum y-axis position of an axis-aligned bounding-box used to the oval.•
D width :
default = 1.0 : the width of the oval - or the extent of its defining axis-aligned bounding-box along the x-axis - a positive non-zero decimal.•
D height :
default = 0.5 : the height of the oval - or the extent of its defining axis-aligned bounding-box along the y-axis - a positive non-zero decimal.•
I segments :
default = 32 : the number of discreisation steps used to construct the oval - a positive integer greater than or equal to 3.→ [ width, height ] > 0
→ segments >= 3
Vertex Count:→ |V| = segmentsPractical Examples:return oval(); // returns the default zero-argument unit oval
return oval(3,1); // returns an oval centered at the origin with a width of 3 units, height equal to 1 unit and the default (32) circular steps.
return oval(5,20,4); // returns an oval centered at the origin with a width and height of 5 and 20 units and 4 circular steps.
return oval(-10,-2,4,2,64); // returns an offset oval with miminum aabb position equal to [-10,-2], a width and height of 4 and 2 units and 64 circular steps.
Additional Notes: ARC : Generate 2D Arc
→ 'instantiates a 2D circular arc polygonal shape'
Classification:→ { instantiative, convex, cyclic };
Alias & Synonyms:→ { arc };
Invocation Options:prefix G2 arc ( I segments, D start_angle, D end_angle )prefix G2 arc ( D radius, I segments, D start_angle, D end_angle )prefix G2 arc ( D ox, D oy, D radius, I segments, D start_angle, D end_angle )Input Arguments:•
D ox :
default = 0 : the origin x-axis position of the arc - its center or pivot - a decimal number.•
D oy :
default = 0 : the origin y-axis position of the arc - its center or pivot a decimal number.•
D radius :
default = 0.5 : the radius of the arc - a positive non-zero deecimal number.•
I segments :
default = 24 : the number of circular discretisation steps used to construct the arc - a positive integer greater than or equal to 2.•
D start_angle :
default = 0 : the starting angle for the arc's sweep specified in degrees.•
D end_angle :
default = 270 : the ending angle for the arc's sweep specified in degrees.→ radius > 0
→ segments >= 2
→ start_angle != end_angle
→ |( end_angle - start_angle )| < 360
Vertex Count:→ |V| = ( segments + 1 )Practical Examples:return arc(); // returns the default zero-argument unit arc
Additional Notes: PIE : Generate 2D Pie
→ 'instantiates a 2D pie segment polygonal shape'
Classification:→ { instantiative, cyclic };
Alias & Synonyms:→ { pie };
Invocation Options:prefix G2 pie ( I segments, D start_angle, D end_angle )prefix G2 pie ( D radius, I segments, D start_angle, D end_angle )prefix G2 pie ( D ox, D oy, D radius, I segments, D start_angle, D end_angle )Input Arguments:•
D ox :
default = 0 : the origin x-axis position of the pie - its center or pivot - a decimal number.•
D oy :
default = 0 : the origin y-axis position of the pie - its center or pivot - a decimal number.•
D radius :
default = 0.5 : the radius of the pie - a positive non-zero decimal number.•
I segments :
default = 24 : the number of circular steps used to construct the pie - a positive integer greater than or equal to 1.•
D start_angle :
default = 0 : the starting angle for the pie's sweep specified in degrees.•
D end_angle :
default = 270 : the ending angle for the pie's sweep specified in degrees.→ radius > 0
→ segments >= 1
→ start_angle != end_angle
→ |( end_angle - start_angle )| < 360
Vertex Count:→ |V| = ( segments + 2 )Practical Examples:return pie(); // returns the default zero-argument unit pie
Additional Notes: ARCH : Generate 2D Archway
→ 'instantiates a 2D circular archway polygonal shape'
Classification:→ { instantiative, convex, cyclic };
Alias & Synonyms:→ { arch, archway };
Invocation Options:prefix G2 arch ( D radius, D length )prefix G2 arch ( D radius, D length, I steps )prefix G2 arch ( D radius, D y, D length, I steps )Input Arguments:•
D radius :
default = 0.5 : the radius of the circular portion of the arch - a non-zero positive decimal.•
D y :
default = -0.5 : the lowest y-axis position of the arch - or its ground position.•
D length :
default = 0.5 : the length of the upright portion of the arch - i.e. the height of its verticals - a positive non-zero decimal.•
I steps :
default = 32 : the number of semi-circular steps used to construct the arch - a positive integer greater than or equal to 1.→ [ radius, length ] > 0
→ steps >= 1
Vertex Count:→ |V| = ( steps + 1 + 2 )Practical Examples:return arch(); // returns the default zero-argument unit arch
Additional Notes: CAP-2D : Generate 2D Capsule
→ 'instantiates a 2D capsule polygonal shape'
Classification:→ { instantiative, convex, cyclic };
Alias & Synonyms:→ { cap_2D, capsule_2D };
Invocation Options:prefix G2 cap2D ( D radius, D length )prefix G2 cap2D ( D radius, D length, I steps )prefix G2 cap2D ( D radius, D x1, D y1, D x2, D y2, I steps )Input Arguments:•
D radius :
default = 0.25 : the radius of the semi-circular portions of the capsule - a non-zero positive decimal.•
D length :
default = 0.5 : the length of the straight porition of the capsule - a non-zero positive decimal.•
D x1 :
default = length * -0.5 : the x-axis component of the first vertex in a line defining the spine of the capsule.•
D y1 :
default = 0 : the y-axis component of the first vertex in a line defining the spine of the capsule.•
D x2 :
default = length * 0.5 : the x-axis component of the second vertex in a line defining the spine of the capsule.•
D y2 :
default = 0 : the y-axis component of the second vertex in a line defining the spine of the capsule.•
I steps :
default = 32 : the number of semi-circular steps used to construct the capsule - a positive integer greater than or equal to 1.→ [ radius, length ] > 0
→ steps >= 1
→ ( x1, y1 ) != ( x2, y2 )
→ |( x2, y2 ) - ( x1, y1 )| > 0
Vertex Count:→ |V| = ( ( steps + 1 ) * 2 )Practical Examples:return cap2d(); // returns the default zero-argument unit cap2d
Additional Notes: TRIANGLE : Generate 2D Triangle
→ 'instantiates a 2D triangular polygonal shape'
Classification:→ { instantiative, convex, cyclic };
Alias & Synonyms:→ { tri, triangle };
Invocation Options:prefix G2 tri ( D radius )prefix G2 tri ( D ax, D ay, D bx, D by, D cx, D cy )Input Arguments:•
D radius :
default = 0.5 : the radius of the origin centered equilateral triangle - a positive decimal greater than zero.•
D ax :
the x-axis component of the first vertex coordinate position in the triangle.•
D ay :
the y-axis component of the first vertex coordinate position in the triangle.•
D bx :
the x-axis component of the second vertex coordinate position in the triangle.•
D by :
the y-axis-component of the second vertex coordinate position in the triangle.•
D cx :
the x-axis component of the third vertex coordinate position in the triangle.•
D cy :
the y-axis component of the third vertex coordinate position in the triangle.→ radius > 0
→ ( ax, ay ) != ( bx, by ) != ( cx, cy )
Vertex Count:→ |V| = 3Practical Examples:return tri(); // returns the default zero-argument unit tri
Additional Notes:The triangle function provides two complementary overloads. The unary overload returns an origin-centered equilateral triangle - whilst the hexad overload (which accepts vertex-position data) can return any valid 2D triangle be it right-angled, scalene or obtuse.
QUADRILATERAL : Generate 2D Quadrilateral
→ 'instantiates a 2D quadrilateral polygonal shape'
Classification:→ { instantiative, cyclic };
Alias & Synonyms:→ { quad, quadrilateral };
Invocation Options:prefix G2 quad ( D ax, D ay, D bx, D by, D cx, D cy, D dx, D dy )Input Arguments:•
D ax :
the x-axis component of the first vertex coordinate position in the quadrilateral.•
D ay :
the y-axis component of the first vertex coordinate position in the quadrilateral.•
D bx :
the x-axis component of the second vertex coordinate position in the quadrilateral.•
D by :
the y-axis component of the second vertex coordinate position in the quadrilateral.•
D cx :
the x-axis component of the third vertex coordinate position in the quadrilateral.•
D cy :
the y-axis component of the third vertex coordinate position in the quadrilateral.•
D dx :
the x-axis component of the fourth vertex coordinate position in the quadrilateral.•
D dy :
the y-axis component of the fourth vertex coordinate position in the quadrilateral.→ ( ax, ay ) != ( bx, by ) != ( cx, cy ) != ( dx, dy )
Vertex Count:→ |V| = 4Practical Examples:return quad(); // returns the default zero-argument unit quad
Additional Notes: PARALLELOGRAM : Generate 2D Parallelogram
→ 'instantiates a 2D parallelogram specified by 3 points which define the first two edges'
Classification:→ { instantiative, convex, cyclic };
Alias & Synonyms:→ { pgram, plgram, parallelogram };
Invocation Options:prefix G2 pgram ( D ax, D ay, D bx, D by, D cx, D cy )Input Arguments:•
D ax :
the x-axis component of the first vertex coordinate position in the parallelogram.•
D ay :
the y-axis component of the first vertex coordinate position in the parallelogram.•
D bx :
the x-axis component of the second vertex coordinate position in the parallelogram.•
D by :
the y-axis component of the second vertex coordinate position in the parallelogram.•
D cx :
the x-axis component of the third vertex coordinate position in the parallelogram.•
D cy :
the y-axis component of the third vertex coordinate position in the parallelogram.→ ( ax, ay ) != ( bx, by ) != ( cx, cy )
Vertex Count:→ |V| = 4Practical Examples:return pgram(); // returns the default zero-argument unit pgram
Additional Notes: SQUARE : Generate 2D Square
→ 'instantiates a four (4) sided regular 2D polygon centered at the origin (0,0)'
Classification:→ { instantiative, convex, cyclic };
Alias & Synonyms:→ { square, reg_4, regular_4, reg_poly_4, regular_polygon_4 };
Invocation Options:prefix G2 square ( D radius )prefix G2 square ( D vx, D vy )Input Arguments:•
D radius :
default = 0.5 : the radius of the origin centered square - a positive non-zero decimal.•
D vx :
the x-axis component of the first vertex coordinate position in the square.•
D vy :
the y-axis component of the first vertex coordinate position in the square.→ radius > 0
→ |( vx, vy )| > 0
Vertex Count:→ |V| = 4Practical Examples:return square(); // returns the default zero-argument unit square
return square(1.25); // returns a regular square with a radius of 1.25 units
return square(3,4); // returns a regular square with a radius of 5 units - i.e. the square-root of (3*3)+(4*4) - and initial vertex located at coordinate position [3,4] units.
Additional Notes: PENTAGON : Generate 2D Pentagon
→ 'instantiates a five (5) sided regular 2D polygon centered at the origin (0,0)'
Classification:→ { instantiative, convex, cyclic };
Alias & Synonyms:→ { pentagon, reg_5, regular_5, reg_poly_5, regular_polygon_5 };
Invocation Options:prefix G2 pentagon ( D radius )prefix G2 pentagon ( D vx, D vy )Input Arguments:•
D radius :
default = 0.5 : the radius of the origin centered pentagon - a positive non-zero decimal.•
D vx :
the x-axis component of the first vertex coordinate position in the pentagon.•
D vy :
the y-axis component of the first vertex coordinate position in the pentagon.→ radius > 0
→ |( vx, vy )| > 0
Vertex Count:→ |V| = 5Practical Examples:return pentagon(); // returns the default zero-argument unit pentagon
return pentagon(1.25); // returns a regular pentagon with a radius of 1.25 units
return pentagon(3,4); // returns a regular pentagon with a radius of 5 units - i.e. the square-root of (3*3)+(4*4) - and initial vertex located at coordinate position [3,4] units.
Additional Notes: HEXAGON : Generate 2D Hexagon
→ 'instantiates a six (6) sided regular 2D polygon centered at the origin (0,0)'
Classification:→ { instantiative, convex, cyclic };
Alias & Synonyms:→ { hexagon, reg_6, regular_6, reg_poly_6, regular_polygon_6 };
Invocation Options:prefix G2 hexagon ( D radius )prefix G2 hexagon ( D vx, D vy )Input Arguments:•
D radius :
default = 0.5 : the radius of the origin centered hexagon - a positive non-zero decimal.•
D vx :
the x-axis component of the first vertex coordinate position in the hexagon.•
D vy :
the y-axis component of the first vertex coordinate position in the hexagon.→ radius > 0
→ |( vx, vy )| > 0
Vertex Count:→ |V| = 6Practical Examples:return hexagon(); // returns the default zero-argument unit hexagon
return hexagon(1.25); // returns a regular hexagon with a radius of 1.25 units
return hexagon(3,4); // returns a regular hexagon with a radius of 5 units - i.e. the square-root of (3*3)+(4*4) - and initial vertex located at coordinate position [3,4] units.
Additional Notes: SEPTAGON : Generate 2D Septagon
→ 'instantiates a seven (7) sided regular 2D polygon centered at the origin (0,0)'
Classification:→ { instantiative, convex, cyclic };
Alias & Synonyms:→ { septagon, reg_7, regular_7, reg_poly_7, regular_polygon_7 };
Invocation Options:prefix G2 septagon ( D radius )prefix G2 septagon ( D vx, D vy )Input Arguments:•
D radius :
default = 0.5 : the radius of the origin centered septagon - a positive non-zero decimal.•
D vx :
the x-axis component of the first vertex coordinate position in the septagon.•
D vy :
the y-axis component of the first vertex coordinate position in the septagon.→ radius > 0
→ |( vx, vy )| > 0
Vertex Count:→ |V| = 7Practical Examples:return septagon(); // returns the default zero-argument unit septagon
return septagon(1.25); // returns a regular septagon with a radius of 1.25 units
return septagon(3,4); // returns a regular septagon with a radius of 5 units - i.e. the square-root of (3*3)+(4*4) - and initial vertex located at coordinate position [3,4] units.
Additional Notes: OCTAGON : Generate 2D Octagon
→ 'instantiates an eight (8) sided regular 2D polygon centered at the origin (0,0)'
Classification:→ { instantiative, convex, cyclic };
Alias & Synonyms:→ { octagon, reg_8, regular_8, reg_poly_8, regular_polygon_8 };
Invocation Options:prefix G2 octagon ( D radius )prefix G2 octagon ( D vx, D vy )Input Arguments:•
D radius :
default = 0.5 : the radius of the origin centered octagon - a positive non-zero decimal.•
D vx :
the x-axis component of the first vertex coordinate position in the octagon.•
D vy :
the y-axis component of the first vertex coordinate position in the octagon.→ radius > 0
→ |( vx, vy )| > 0
Vertex Count:→ |V| = 8Practical Examples:return octagon(); // returns the default zero-argument unit octagon
return octagon(1.25); // returns a regular octagon with a radius of 1.25 units
return octagon(3,4); // returns a regular octagon with a radius of 5 units - i.e. the square-root of (3*3)+(4*4) - and initial vertex located at coordinate position [3,4] units.
Additional Notes: NONAGON : Generate 2D Nonagon
→ 'instantiates a nine (9) sided regular 2D polygon centered at the origin (0,0)'
Classification:→ { instantiative, convex, cyclic };
Alias & Synonyms:→ { nonagon, reg_9, regular_9, reg_poly_9, regular_polygon_9 };
Invocation Options:prefix G2 nonagon ( D radius )prefix G2 nonagon ( D vx, D vy )Input Arguments:•
D radius :
default = 0.5 : the radius of the origin centered nonagon - a positive non-zero decimal.•
D vx :
the x-axis component of the first vertex coordinate position in the nonagon.•
D vy :
the y-axis component of the first vertex coordinate position in the nonagon.→ radius > 0
→ |( vx, vy )| > 0
Vertex Count:→ |V| = 9Practical Examples:return nonagon(); // returns the default zero-argument unit nonagon
return nonagon(1.25); // returns a regular nonagon with a radius of 1.25 units
return nonagon(3,4); // returns a regular nonagon with a radius of 5 units - i.e. the square-root of (3*3)+(4*4) - and initial vertex located at coordinate position [3,4] units.
Additional Notes: DECAGON : Generate 2D Decagon
→ 'instantiates a ten (10) sided regular 2D polygon centered at the origin (0,0)'
Classification:→ { instantiative, convex, cyclic };
Alias & Synonyms:→ { decagon, reg_10, regular_10, reg_poly_10, regular_polygon_10 };
Invocation Options:prefix G2 decagon ( D radius )prefix G2 decagon ( D vx, D vy )Input Arguments:•
D radius :
default = 0.5 : the radius of the origin centered decagon - a positive non-zero decimal.•
D vx :
the x-axis component of the first vertex coordinate position in the decagon.•
D vy :
the y-axis component of the first vertex coordinate position in the decagon.→ radius > 0
→ |( vx, vy )| > 0
Vertex Count:→ |V| = 10Practical Examples:return decagon(); // returns the default zero-argument unit decagon
return decagon(1.25); // returns a regular decagon with a radius of 1.25 units
return decagon(3,4); // returns a regular decagon with a radius of 5 units - i.e. the square-root of (3*3)+(4*4) - and initial vertex located at coordinate position [3,4] units.
Additional Notes: REG → REGULAR-POLYGON : Generate 2D Regular-Polygon
→ 'instantiates an N-sided regular 2D polygon centered at the origin (0,0)'
Classification:→ { instantiative, convex, cyclic };
Alias & Synonyms:→ { reg, reg_n, regular, reg_poly, regular_polygon };
Invocation Options:prefix G2 reg ( I sides )prefix G2 reg ( D radius, I sides )prefix G2 reg ( D vx, D vy, I sides )Input Arguments:•
D radius :
default = 0.5 : the radius of the origin centered regular polygon - a positive decimal number greater than zero.•
I sides :
default = 16 : the number of sides (or edges) in the regular polygon - a positive integer greater than over equal to 3.•
D vx :
the x-axis component of the first vertex coordinate position in the regular polygon.•
D vy :
the y-axis component of the first vertex coordinate position in the regular polygon.→ radius > 0
→ sides >= 3
→ |( vx, vy )| > 0
Vertex Count:→ |V| = sidesPractical Examples:return reg(); // returns the default zero-argument unit reg
Additional Notes: POLYGON : Generate 2D Cyclic-Polygon
→ 'instantiates a data-driven 2D polygon defined by a set of positional coordinate values'
Classification:→ { instantiative, cyclic };
Alias & Synonyms:→ { poly, poly_2D, polygon, polygon_2D };
Invocation Options:prefix G2 poly ( D[] coordinates )prefix G2 poly ( G2 source_shape )Input Arguments:•
D[] coordinates :
the vertex coordinate position data that defines the polygon - an array containing pairs of (x,y) decimal values.•
G2 source_shape :
the source shape whose vertex data is to be used to derive the vertex coordinate position data of the newly instantiated polygon.→ |coordinates| >= 6
→ ( |coordinates| % 2 ) == 0
Vertex Count:→ |V| = |coordinates| / 2Practical Examples:return poly(); // returns the default zero-argument unit poly
Additional Notes: B-POLYGON : Generate 2D Beveled-Cyclic-Polygon
→ 'instantiates a beveled-corner data-driven 2D polygon defined by a bevel distance and a set of positional coordinate values'
Classification:→ { instantiative, cyclic };
Alias & Synonyms:→ { b_poly, b_poly_2D, b_polygon, b_polygon_2D, bevel_poly, bevel_poly_2D, bevel_polygon, bevel_polygon_2D, beveled_poly, beveled_poly_2D, beveled_polygon, beveled_polygon_2D, ... (+12) };
Invocation Options:prefix G2 bpoly ( D bevel_distance, D[] coordinates )prefix G2 bpoly ( D bevel_distance, G2 source_shape )Input Arguments:•
D bevel_distance :
default = 0.125 : the bevel/chamfer distance/radius applied to compatible corners of the bpolygon - a positive decimal greater than zero and less than half of the minimum edge-length of the coordinate data.•
D[] coordinates :
the vertex coordinate position data that defines the base polygon used to construct the bpolygon - an array containing pairs of (x,y) decimal values.•
G2 source_shape :
the source shape whose vertex data is to be used to derive the vertex coordinate position data of the base polygon used to construct the newly instantiated bpolygon.→ bevel > 0
→ |coordinates| >= 6
→ ( |coordinates| % 2 ) == 0
Vertex Count:→ |V| = ( |coordinates| / 2 ) * 2Practical Examples:return bpoly(); // returns the default zero-argument unit bpoly
Alias Formation Rules:Additional Notes: R-POLYGON : Generate 2D Rounded-Cyclic-Polygon
→ 'instantiates a rounded-corner data-driven 2D polygon defined by a round radius, a number of round steps and a set of positional coordinate values'
Classification:→ { instantiative, cyclic };
Alias & Synonyms:→ { r_poly, r_poly_2D, r_polygon, r_polygon_2D, rnd_poly, rnd_poly_2D, rnd_polygon, rnd_polygon_2D, round_poly, round_poly_2D, round_polygon, round_polygon_2D, ... (+4) };
Invocation Options:prefix G2 rpoly ( D radius, I steps, D[] coordinates )prefix G2 rpoly ( D radius, I steps, G2 source_shape )Input Arguments:•
D radius :
default = 0.125 : the rounding radius applied to compatible corners of the rpolygon - a positive decimal greater than zero and less than half of the minimum edge-length of the coordinate data.•
I steps :
default = 8 : the number of rounding steps applied to compatible corners of the rpolygon - a positive integer greater than or equal to 1.•
D[] coordinates :
the vertex coordinate position data that defines the base polygon used to construct the rpolygon - an array containing pairs of (x,y) decimal values.•
G2 source_shape :
the source shape whose vertex data is to be used to derive the vertex coordinate position data of the base polygon used to construct the newly instantiated rpolygon.→ radius > 0
→ steps >= 1
→ |coordinates| >= 6
→ ( |coordinates| % 2 ) == 0
Vertex Count:→ |V| = ( |coordinates| / 2 ) * ( steps + 1 )Practical Examples:return rpoly(); // returns the default zero-argument unit rpoly
Alias Formation Rules:Additional Notes: CHARACTER-2D :
Generate 2D Character-Symbol→ 'instantiates a 2D symbolic (alpha-numeric) character polygonal shape' B-CHARACTER-2D :
Generate 2D Beveled-Character-Symbol→ 'instantiates a beveled-corner 2D symbolic (alpha-numeric) character polygonal shape' R-CHARACTER-2D :
Generate 2D Rounded-Character-Symbol→ 'instantiates a rounded-corner 2D symbolic (alpha-numeric) character polygonal shape' TEXT-2D :
Generate 2D Character-Sequence→ 'instantiates a 2D symbolic (alpha-numeric) character sequence compound polygonal shape' B-TEXT-2D :
Generate 2D Beveled-Character-Sequence→ 'instantiates a beveled-corner 2D symbolic (alpha-numeric) character sequence compound polygonal shape' R-TEXT-2D :
Generate 2D Rounded-Character-Sequence→ 'instantiates a rounded-corner 2D symbolic (alpha-numeric) character sequence compound polygonal shape' LINE : Generate 2D Line
→ 'instantiates a 2D line-segment defined by a start and end position'
Classification:→ { instantiative, open };
Alias & Synonyms:→ { line, line_2D };
Invocation Options:prefix G2 line ( D x1, D y1, D x2, D y2 )Input Arguments:•
D x1 :
default = -0.5 : the x-axis component of the first vertex coordinate position of the line - its start/initial x-value.•
D y1 :
default = -0.5 : the y-axis component of the first vertex coordinate position of the line - its starting/initial y-value.•
D x2 :
default = 0.5 : the x-axis component of the second vertex coordinate position of the line - its end/finish x-value.•
D y2 :
default = 0.5 : the y-axis component of the second vertex coordinate position of the line - its end/finish y-value.→ ( x1, y1 ) != ( x2, y2 )
→ |( x2, y2 ) - ( x1, y1 )| > 0
Vertex Count:→ |V| = 2Practical Examples:return line(); // returns the default zero-argument unit line
Additional Notes: O-ARC : Generate 2D Open-Arc
→ 'instantiates a 2D open circular arc polyline path'
Classification:→ { instantiative, open };
Alias & Synonyms:→ { o_arc, open_arc };
Invocation Options:prefix G2 oarc ( I segments, D start_angle, D end_angle )prefix G2 oarc ( D radius, I segments, D start_angle, D end_angle )prefix G2 oarc ( D ox, D oy, D radius, I segments, D start_angle, D end_angle )Input Arguments:•
D ox :
default = 0 : the origin x-axis position of the oarc - its center or pivot - a decimal number.•
D oy :
default = 0 : the origin y-axis position of the oarc - its center or pivot a decimal number.•
D radius :
default = 0.5 : the radius of the oarc - a positive non-zero deecimal number.•
I segments :
default = 24 : the number of circular discretisation steps used to construct the oarc - a positive integer greater than or equal to 1.•
D start_angle :
default = 0 : the starting angle for the oarc's sweep specified in degrees.•
D end_angle :
default = 270 : the ending angle for the oarc's sweep specified in degrees.→ radius > 0
→ segments >= 1
→ start_angle != end_angle
→ |( end_angle - start_angle )| < 360
Vertex Count:→ |V| = ( segments + 1 )Practical Examples:return oarc(); // returns the default zero-argument unit oarc
Additional Notes: O-ARCH : Generate 2D Open-Archway
→ 'instantiates a 2D open circular archway polyline path'
Classification:→ { instantiative, open };
Alias & Synonyms:→ { o_arch, o_archway, open_arch, open_archway };
Invocation Options:prefix G2 oarch ( D radius, D length )prefix G2 oarch ( D radius, D length, I steps )prefix G2 oarch ( D radius, D y, D length, I steps )Input Arguments:•
D radius :
default = 0.5 : the radius of the circular portion of the oarch - a non-zero positive decimal.•
D y :
default = -0.5 : the lowest y-axis position of the oarch - or its ground position.•
D length :
default = 0.5 : the length of the upright portion of the oarch - i.e. the height of its verticals - a positive non-zero decimal.•
I steps :
default = 32 : the number of semi-circular steps used to construct the oarch - a positive integer greater than or equal to 1.→ [ radius, length ] > 0
→ steps >= 1
Vertex Count:→ |V| = ( segments + 1 + 2 )Practical Examples:return oarch(); // returns the default zero-argument unit oarch
Additional Notes: PATH : Generate 2D Open-Polyline
→ 'instantiates a data-driven 2D polyline path defined by a set of positional coordinate values'
Classification:→ { instantiative, open };
Alias & Synonyms:→ { path, polyline, polyline_path };
Invocation Options:prefix G2 path ( D[] coordinates )prefix G2 path ( G2 source_shape )Input Arguments:•
D[] coordinates :
the vertex coordinate position data that defines the path - an array containing pairs of (x,y) decimal values.•
G2 source_shape :
the source shape whose vertex data is to be used to derive the vertex coordinate position data of the newly instantiated path.→ |coordinates| >= 4
→ ( |coordinates| % 2 ) == 0
Vertex Count:→ |V| = |coordinates| / 2Practical Examples:return path(); // returns the default zero-argument unit path
Additional Notes: B-PATH : Generate 2D Beveled-Open-Polyline
→ 'instantiates a beveled-corner data-driven 2D polyline path defined by a bevel distance and a set of positional coordinate values'
Classification:→ { instantiative, open };
Alias & Synonyms:→ { b_path, b_polyline, b_polyline_path, bevel_path, bevel_polyline, bevel_polyline_path, beveled_path, beveled_polyline, beveled_polyline_path, bevelled_path, bevelled_polyline, bevelled_polyline_path, ... (+6) };
Invocation Options:prefix G2 bpath ( D bevel_distance, D[] coordinates )prefix G2 bpath ( D bevel_distance, G2 source_shape )Input Arguments:•
D bevel_distance :
default = 0.05 : the bevel/chamfer distance/radius applied to compatible corners of the bpath - a positive decimal greater than zero and less than half of the minimum edge-length of the coordinate data.•
D[] coordinates :
the vertex coordinate position data that defines the base path used to construct the bpath - an array containing pairs of (x,y) decimal values.•
G2 source_shape :
the source shape whose vertex data is to be used to derive the vertex coordinate position data of the base path used to construct the newly instantiated bpath.→ bevel_distance > 0
→ |coordinates| >= 6
→ ( |coordinates| % 2 ) == 0
Vertex Count:→ |V| = ( |coordinates| / 2 ) * 2 - 2Practical Examples:return bpath(); // returns the default zero-argument unit bpath
Alias Formation Rules:Additional Notes: R-PATH : Generate 2D Rounded-Open-Polyline
→ 'instantiates a rounded-corner data-driven 2D polyline path defined by a round radius, a number of round steps and a set of positional coordinate values'
Classification:→ { instantiative, open };
Alias & Synonyms:→ { r_path, r_polyline, r_polyline_path, rnd_path, rnd_polyline, rnd_polyline_path, round_path, round_polyline, round_polyline_path, rounded_path, rounded_polyline, rounded_polyline_path };
Invocation Options:prefix G2 rpath ( D radius, I steps, D[] coordinates )prefix G2 rpath ( D radius, I steps, G2 source_shape )Input Arguments:•
D radius :
default = 0.05 : the rounding radius applied to compatible corners of the rpath - a positive decimal greater than zero and less than half of the minimum edge-length of the coordinate data.•
I steps :
default = 8 : the number of rounding steps applied to compatible corners of the rpath - a positive integer greater than or equal to 1.•
D[] coordinates :
the vertex coordinate position data that defines the base path used to construct the rpath - an array containing pairs of (x,y) decimal values.•
G2 source_shape :
the source shape whose vertex data is to be used to derive the vertex coordinate position data of the base polygon used to construct the newly instantiated rpath.→ radius > 0
→ steps >= 1
→ |coordinates| >= 6
→ ( |coordinates| % 2 ) == 0
Vertex Count:→ |V| = ( |coordinates| / 2 ) * ( steps + 1 ) - ( steps * 2 )Practical Examples:return rpath(); // returns the default zero-argument unit rpath
Additional Notes: Polyhedral Solids
Figure 5.2: hierarchical map of the set of functions in qmsh that create solid (volumetric) polyhedra.
CUBE : Generate 3D Platonic-Cuboid
→ 'instantiates a 3D axis-aligned cuboidal solid'
Classification:→ { instantiative, platonic, convex, orthogonal };
Alias & Synonyms:→ { cube, box_3D, cuboid };
Invocation Options:prefix G3 cube ( D size )prefix G3 cube ( D width, D height, D depth )prefix G3 cube ( D x, D y, D z, D width, D height, D depth )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the cube - a non-zero positive decimal number.•
D x :
default = -0.5 * width : the axis-aligned bounding-box minimum x-coordinate value of the cube - a decimal number.•
D y :
default = -0.5 * height : the axis-aligned bounding-box minimum y-coordinate value of the cube - a decimal number.•
D z :
default = -0.5 * depth : the axis-aligned bounding-box minimum z-coordinate value of the cube - a decimal number.•
D width :
default = 1 : the x-axis extent of the cube - a non-zero positive decimal number - the maximum x-coordinate value is equal to (x + width).•
D height :
default = 1 : the y-axis extent of the cube - a non-zero positive decimal number - the maximum y-coordinate value is equal to (y + height).•
D depth :
default = 1 : the z-axis extent of the cube - a non-zero positive decimal number - the maximum z-coordinate value is equal to (z + depth).→ [ size, width, height, depth ] > 0
Topology Types:→ [ quadrilaterals ]Vertex Count:→ |V| = 24Polygon Count:→ |P| = 6Practical Examples:return cube(); // returns the default zero-argument unit cube
return cube(6); // returns a uniform cube with width, height and depth equal to 6 units
return cuboid(1,2,3); // returns a non-uniformly scaled cube centered about the origin - with width, height and depth equal to [1,2,3] units
return box3D(0,-5,2,8,10,4); // returns a non-uniformly scaled, offset cube with minimum aabb position equal to [0,-5,2] and a width, height and depth equal to [8,10,4] units
Additional Notes: TETRAHEDRON : Generate 3D Platonic-Tetrahedron
→ 'instantiates a 3D tetrahedral solid centered at the origin (0,0,0)'
Classification:→ { instantiative, platonic, convex };
Alias & Synonyms:→ { tetrahedron };
Invocation Options:prefix G3 tetrahedron ( D size )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the tetrahedron - a non-zero positive decimal number.→ size > 0
Topology Types:→ [ triangles ]Vertex Count:→ |V| = 12Polygon Count:→ |P| = 4Practical Examples:return tetrahedron(); // returns the default zero-argument unit tetrahedron
return tetrahedron(3.21); // returns a tetrahedron with a maximum AABB extent of 3.21
Additional Notes: OCTAHEDRON : Generate 3D Platonic-Octahedron
→ 'instantiates a 3D octahedral solid centered at the origin (0,0,0)'
Classification:→ { instantiative, platonic, convex };
Alias & Synonyms:→ { octahedron };
Invocation Options:prefix G3 octahedron ( D size )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the octahedron - a non-zero positive decimal number.→ size > 0
Topology Types:→ [ triangles ]Vertex Count:→ |V| = 24Polygon Count:→ |P| = 8Practical Examples:return octahedron(); // returns the default zero-argument unit octahedron
return octahedron(3.21); // returns an octahedron with a maximum AABB extent of 3.21
Additional Notes: DODECAHEDRON : Generate 3D Platonic-Docedahedron
→ 'instantiates a 3D dodecahedral solid centered at the origin (0,0,0)'
Classification:→ { instantiative, platonic, convex };
Alias & Synonyms:→ { dodecahedron };
Invocation Options:prefix G3 dodecahedron ( D size )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the dodecahedron - a non-zero positive decimal number.→ size > 0
Topology Types:→ [ pentagons ]Vertex Count:→ |V| = 60Polygon Count:→ |P| = 12Practical Examples:return dodecahedron(); // returns the default zero-argument unit dodecahedron
return dodecahedron(3.21); // returns a dodecahedron with a maximum AABB extent of 3.21
Additional Notes: ICOSAHEDRON : Generate 3D Platonic-Icosahedron
→ 'instantiates a 3D icosahedral solid centered at the origin (0,0,0)'
Classification:→ { instantiative, platonic, convex };
Alias & Synonyms:→ { icosahedron };
Invocation Options:prefix G3 icosahedron ( D size )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the icosahedron - a non-zero positive decimal number.→ size > 0
Topology Types:→ [ triangles ]Vertex Count:→ |V| = 60Polygon Count:→ |P| = 20Practical Examples:return icosahedron(); // returns the default zero-argument unit icosahedron
return icosahedron(3.21); // returns an icosahedron with a maximum AABB extent of 3.21
Additional Notes: M-CUBE : Generate 3D Manifold-Platonic-Cuboid
→ 'instantiates an axis-aligned 3D manifold cuboidal solid'
Classification:→ { instantiative, platonic, convex, orthogonal };
Alias & Synonyms:→ { m_cube, m_box_3D, m_cuboid, manifold_cube, manifold_box_3D, manifold_cuboid };
Invocation Options:prefix G3 mcube ( D size )prefix G3 mcube ( D width, D height, D depth )prefix G3 mcube ( D x, D y, D z, D width, D height, D depth )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the mcube - a non-zero positive decimal number.•
D x :
default = -0.5 * width : the axis-aligned bounding-box minimum x-coordinate value of the mcube - a decimal number.•
D y :
default = -0.5 * height : the axis-aligned bounding-box minimum y-coordinate value of the mcube - a decimal number.•
D z :
default = -0.5 * depth : the axis-aligned bounding-box minimum z-coordinate value of the mcube - a decimal number.•
D width :
default = 1 : the x-axis extent of the mcube - a non-zero positive decimal number - the maximum x-coordinate value is equal to (x + width).•
D height :
default = 1 : the y-axis extent of the mcube - a non-zero positive decimal number - the maximum y-coordinate value is equal to (y + height).•
D depth :
default = 1 : the z-axis extent of the mcube - a non-zero positive decimal number - the maximum z-coordinate value is equal to (z + depth).→ [ size, width, height, depth ] > 0
Topology Types:→ [ quadrilaterals ]Vertex Count:→ |V| = 8Polygon Count:→ |P| = 6Practical Examples:return mcube(); // returns the default zero-argument unit mcube
return mcube(6); // returns a uniform mcube with width, height and depth equal to 6 units
return cuboid(1,2,3); // returns a non-uniformly scaled mcube centered about the origin - with width, height and depth equal to [1,2,3] units
return mbox3D(0,-5,2,8,10,4); // returns a non-uniformly scaled, offset mcube with minimum aabb position equal to [0,-5,2] and a width, height and depth equal to [8,10,4] units
Additional Notes: M-TETRAHEDRON : Generate 3D Manifold-Platonic-Tetrahedron
→ 'instantiates a manifold 3D tetrahedral solid centered at the origin (0,0,0)'
Classification:→ { instantiative, platonic, convex };
Alias & Synonyms:→ { m_tetrahedron, manifold_tetrahedron };
Invocation Options:prefix G3 mtetrahedron ( D size )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the mtetrahedron - a non-zero positive decimal number.→ size > 0
Topology Types:→ [ triangles ]Vertex Count:→ |V| = 4Polygon Count:→ |P| = 4Practical Examples:return mtetrahedron(); // returns the default zero-argument unit mtetrahedron
return mtetrahedron(3.21); // returns a mtetrahedron with a maximum AABB extent of 3.21
Additional Notes: M-OCTAHEDRON : Generate 3D Manifold-Platonic-Octahedron
→ 'instantiates a manifold 3D octahedral solid centered at the origin (0,0,0)'
Classification:→ { instantiative, platonic, convex };
Alias & Synonyms:→ { m_octahedron, manifold_octahedron };
Invocation Options:prefix G3 moctahedron ( D size )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the moctahedron - a non-zero positive decimal number.→ size > 0
Topology Types:→ [ triangles ]Vertex Count:→ |V| = 6Polygon Count:→ |P| = 8Practical Examples:return moctahedron(); // returns the default zero-argument unit moctahedron
return moctahedron(3.21); // returns an moctahedron with a maximum AABB extent of 3.21
Additional Notes: M-DODECAHEDRON : Generate 3D Manifold-Platonic-Dodecahedron
→ 'instantiates a manifold 3D dodecahedral solid centered at the origin (0,0,0)'
Classification:→ { instantiative, platonic, convex };
Alias & Synonyms:→ { m_dodecahedron, manifold_dodecahedron };
Invocation Options:prefix G3 mdodecahedron ( D size )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the mdodecahedron - a non-zero positive decimal number.→ size > 0
Topology Types:→ [ pentagons ]Vertex Count:→ |V| = 20Polygon Count:→ |P| = 12Practical Examples:return mdodecahedron(); // returns the default zero-argument unit mdodecahedron
return mdodecahedron(3.21); // returns a mdodecahedron with a maximum AABB extent of 3.21
Additional Notes: M-ICOSAHEDRON : Generate 3D Manifold-Platonic-Icosahedron
→ 'instantiates a manifold 3D icosahedral solid centered at the origin (0,0,0)'
Classification:→ { instantiative, platonic, convex };
Alias & Synonyms:→ { m_icosahedron, manifold_icosahedron };
Invocation Options:prefix G3 micosahedron ( D size )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the micosahedron - a non-zero positive decimal number.→ size > 0
Topology Types:→ [ triangles ]Vertex Count:→ |V| = 12Polygon Count:→ |P| = 20Practical Examples:return micosahedron(); // returns the default zero-argument unit micosahedron
return micosahedron(3.21); // returns an micosahedron with a maximum AABB extent of 3.21
Additional Notes: Axis-of-Revolution Solids
CONE : Generate 3D Cone
→ 'instantiates a 3D conic solid centered at the origin (0,0,0)'
Classification:→ { instantiative, developable, convex };
Alias & Synonyms:→ { cone };
Invocation Options:prefix G3 cone ( I segments )prefix G3 cone ( D radius, D length )prefix G3 cone ( D radius, D length, I segments )Input Arguments:•
D radius :
default = 0.5 : the radius of the cone (diameter = radius * 2) - a non-zero positive decimal number.•
D length :
default = 1.0 : the length of the cone (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretisation resolution or the number of circular steps) - a positive whole number greater than or equal to 3.→ [ radius, length ] > 0
→ segments >= 3
Topology Types:→ [ triangles, N-gons: where N = segments ]Vertex Count:→ |V| = ( segments * 2 + 2 )Polygon Count:→ |P| = ( segments + 1 )Practical Examples:return cone(); // returns the default zero-argument unit cone
return cone(16); // returns a unit cone with the default radius and height (0.5 and 1.0 units) and 16 circular segments
return cone(2,5.5); // returns a cone with a base diameter of 4 units, a height of 5.5 units and the default 32 circular segments
return cone(1,5,64); // returns a cone with a base diameter of 2 units, a height of 5 units and 64 segments
Additional Notes:The cone function's overloads are equivalent to the cylinder function's overloads.
CYLINDER : Generate 3D Cylinder
→ 'instantiates a 3D cylindrical solid centered at the origin (0,0,0)'
Classification:→ { instantiative, developable, convex };
Alias & Synonyms:→ { cylinder };
Invocation Options:prefix G3 cylinder ( I segments )prefix G3 cylinder ( D radius, D length )prefix G3 cylinder ( D radius, D length, I segments )Input Arguments:•
D radius :
default = 0.5 : the radius of the cylinder (diameter = radius * 2) - a non-zero positive decimal number.•
D length :
default = 1.0 : the length of the cylinder (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretisation resolution or the number of circular steps) - a positive whole number greater than or equal to 3.→ [ radius, length ] > 0
→ segments >= 3
Topology Types:→ [ quadrilaterals, N-gons: where N = segments ]Vertex Count:→ |V| = ( segments * 4 + 2 )Polygon Count:→ |P| = ( segments + 2 )Practical Examples:return cylinder(); // returns the default zero-argument unit cylinder
return cylinder(16); // returns a unit cylinder with the default radius and height (0.5 and 1.0 units) and 16 circular segments
return cylinder(2,5.5); // returns a cylinder with a base diameter of 4 units, a height of 5.5 units and the default 32 circular segments
return cylinder(1,5,64); // returns a cylinder with a diameter of 2 units, a height of 5 units and 64 segments
Additional Notes:The cylinder function's overloads are equivalent to the cone function's overloads.
CYLICONE : Generate 3D Cyclicone
→ 'instantiates a 3D parametric conic-cylindrical solid centered at the origin (0,0,0)'
Classification:→ { instantiative, developable, convex };
Alias & Synonyms:→ { cylicone };
Invocation Options:prefix G3 cylicone ( D lower_radius, D upper_radius )prefix G3 cylicone ( D lower_radius, D upper_radius, I segments )prefix G3 cylicone ( D lower_radius, D upper_radius, D length, I segments )Input Arguments:•
D lower_radius :
default = 0.5 : the radius at the base of the cylicone - a non-zero positive decimal number.•
D upper_radius :
default = 0.25 : the radius at the top of the cylicone - a non-zero positive decimal number.•
D length :
default = 1.0 : the length of the cylicone (i.e. its height along the y-axis or it vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretisation resolution or the number of circular steps) - a positive whole number greater than or equal to 3.→ radius > 0
→ [ lower_radius, upper_radius ] >= 0
→ segments >= 3
Topology Types:→ [ triangles, quadrilaterals, N-gons: where N = segments ]Vertex Count:→ |V| = ( lower_radius == 0 || upper_radius == 0 ) ? ( segments * 2 + 2 ) : ( segments * 4 + 2 )Polygon Count:→ |P| = ( lower_radius == 0 || upper_radius == 0 ) ? ( segments + 1 ) : ( segments + 2 )Practical Examples:return cylicone(); // returns the default zero-argument unit cylicone
return cylicone(1,2);
// returns a cylicone with a lower-radius of 1 unit, an upper-radius of 2 units, and the default length (1) and segments (32)
return cylicone(0.5,1,16);
// returns a cylicone with a lower-radius of 0.5 units, an upper-radius of 1 unit, the default length (1 unit) and 16 circular segments
return cylicone(1,0.5,4,64);
// returns a cylicone with a lower-radius of 1, an upper-radius of 0.5, a length of 4 and 64 segments
Additional Notes: SPHERE : Generate 3D Sphere
→ 'instantiates a 3D polar-sphere solid centered at the origin (0,0,0)'
Classification:→ { instantiative, convex };
Alias & Synonyms:→ { sphere };
Invocation Options:prefix G3 sphere ( D diameter )prefix G3 sphere ( I slices, I stacks )prefix G3 sphere ( D diameter, I slices, I stacks )Input Arguments:•
D diameter :
default = 1.0 : the diameter of the sphere - a non-zero positive decimal number.•
I slices :
default = 32 : the number of longitudinal segments (i.e. the discretisation resolution or the number of circular steps about the Y-axis) - a positive whole number greater than or equal to 3.•
I stacks :
default = 16 : the number of latitudinal segments (i.e. the discretisation resolution or the number of half-circle steps from the sphere's north pole to its south pole) - a positive whole number greater than or equal to 2.→ diameter > 0
→ slices >= 3
→ stacks >= 2
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( slices * ( stacks - 1 ) + 2 )Polygon Count:→ |P| = ( slices * stacks )Practical Examples:return sphere(); // returns the default zero-argument unit sphere
return sphere(2.4);
// returns a sphere with a diameter of 2.4 units and the default slices (32) and stacks (16)
return sphere(16,8);
// returns a sphere with the default diameter (1 unit) and respectively 16 and 8 slices and stacks
return sphere(4,64,32);
// returns a sphere with diameter of 4 units, 64 circular slices and 32 semi-circular stacks
Additional Notes: CAPSULE : Generate 3D Capsule
→ 'instantiates a 3D polar-capsule solid centered at the origin (0,0,0)'
Classification:→ { instantiative, convex };
Alias & Synonyms:→ { capsule, cap_3D, capsule_3D };
Invocation Options:prefix G3 capsule ( D radius, D length )prefix G3 capsule ( D radius, D length, I slices, I stacks )Input Arguments:•
D radius :
default = 0.25 : the radius of the capsule's hemispheres - a non-zero positive decimal number.•
D length :
default = 0.5 : the length of the capsule's straight-edge section (i.e. its cylindrical portion's height along the Y-axis between its north and south hemispheres) - a non-zero positive decimal number.•
I slices :
default = 32 : the number of longitudinal segments (i.e. the discretisation resolution or the number of circular steps about the Y-axis) - a positive whole number greater than or equal to 3.•
I stacks :
default = 16 : the number of latitudinal segments (i.e. the discretisation resolution or the number of quarter-circle steps from each of the capsule's hemisphere's poles, to their equators) - a positive whole number greater than or equal to 1.→ [ radius, length ] > 0
→ slices >= 3
→ stacks >= 1
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( slices * stacks * 2 + 2 )Polygon Count:→ |P| = ( slices + slices * stacks * 2 )Practical Examples:return capsule(); // returns the default zero-argument unit capsule
return capsule(1,10);
// returns a capsule with a radius of 1 unit, a length of 10-units and the default 32 and 16 longitudinal slices and latitudinal stacks
return capsule(5,20,4,8);
// returns a capsule with a radius of 5 units, a cylindrical-length of 20 units, 4 longitudinal steps and 8 latitudinal steps for each hemisphere
Additional Notes: ELLIPSOID : Generate 3D Ellipsoid
→ 'instantiates a 3D polar-ellipsoid solid (a non-uniformly scaled sphere) centered at the origin (0,0,0)'
Classification:→ { instantiative, convex };
Alias & Synonyms:→ { ellipsoid };
Invocation Options:prefix G3 ellipsoid ( D size_x, D size_y, D size_z )prefix G3 ellipsoid ( D size_x, D size_y, D size_z, I slices, I stacks )Input Arguments:•
D size_x :
default = 0.5 : the width of the ellipsoid (i.e. its extent along the x-axis) - a non-zero positive decimal number.•
D size_y :
default = 1 : the height of the ellipsoid (i.e. its extent along the y-axis) - a non-zero positive decimal number.•
D size_z :
default = 0.25 : the depth of the ellipsoid (i.e. its extent along the z-axis) - a non-zero positive decimal number.•
I slices :
default = 32 : the number of longitudinal segments in the base sphere used to construct the ellipsoid (i.e. the discretisation resolution or the number of circular steps about the Y-axis) - a positive whole number greater than or equal to 3.•
I stacks :
default = 16 : the number of latitudinal segments in the base sphere used to construct the ellipsoid (i.e. the discretisation resolution or the number of half-circle steps from the base sphere's north pole to its south pole) - a positive whole number greater than or equal to 2.→ [ size_x, size_y, size_z ] > 0
→ slices >= 3
→ stacks >= 2
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( slices * ( stacks - 2 ) + 2 )Polygon Count:→ |P| = ( slices * stacks )Practical Examples:return ellipsoid(); // returns the default zero-argument unit ellipsoid
return ellipsoid(1,2,3);
// returns an ellipsoid with a width, height and depth (of respectively) 1, 2, and 3 units and the default slices (32) and stacks (16)
return ellipsoid(2,1,2,64,4);
// returns an ellipsoid with a width, height and depth (of respectively) 2, 1 and 2 units, and with 64 longitudinal steps and 4 latitudinal steps
Additional Notes: TORUS : Generate 3D Torus
→ 'instantiates a 3D toroidal solid defined by a major and a minor circle and centered at the origin (0,0,0)'
Classification:→ { instantiative, complex };
Alias & Synonyms:→ { torus };
Invocation Options:prefix G3 torus ( D major_radius, D minor_radius )prefix G3 torus ( D major_radius, D minor_radius, I major_steps, I minor_steps )Input Arguments:•
D major_radius :
default = 0.35 : the radius of the major circle used to construct the torus - a non-zero positive decimal number.•
D minor_radius :
default = 0.15 : the radius of the minor circle used to construct the torus - a non-zero positive decimal number.•
I major_steps :
default = 32 : the number of segments in the major circle - a positive whole number greater than or equal to 3 - such that higher values equate to a more accurate approximation of a circle.•
I minor_steps :
default = 16 : the number of segments in the minor circle - a positive whole number greater than or equal to 3 - such that higher values equate to a more accurate approximation of a circle.→ [ major_radius, minor_radius ] > 0
→ [ major_steps, minor_steps ] >= 3
→ minor_radius < ( major_radius * 0.5 )
Topology Types:→ [ quadrilaterals ]Vertex Count:→ |V| = ( major_steps * minor_steps )Polygon Count:→ |P| = ( major_steps * minor_steps )Practical Examples:return torus(); // returns the default zero-argument unit torus
return torus(8,1);
// returns a torus with a major radius of 8 units, a minor radius of 1 unit and the default major and minor steps (32 and 16)
return torus(5,0.5,64,4);
// returns a torus with a major radius of 5 units, a minor radius of 0.5 units, 64 major steps and 4 minor steps
Additional Notes: PYRAMID : Generate 3D Pyramid
→ 'instantiates a 3D fixed-form pyramid solid centered at the origin (0,0,0)'
Classification:→ { instantiative, convex };
Alias & Synonyms:→ { pyramid };
Invocation Options:prefix G3 pyramid ( D size )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the pyramid - a non-zero positive decimal number.→ size > 0
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = 16Polygon Count:→ |P| = 5Practical Examples:return pyramid(); // returns the default zero-argument unit pyramid
return pyramid(3.21); // returns a pyramid with a maximum AABB extent of 3.21
Additional Notes: GABLE : Generate 3D Gable
→ 'instantiates a 3D fixed-form gable solid centered at the origin (0,0,0)'
Classification:→ { instantiative, convex };
Alias & Synonyms:→ { gable };
Invocation Options:prefix G3 gable ( D size )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the gable - a non-zero positive decimal number.→ size > 0
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = 18Polygon Count:→ |P| = 5Practical Examples:return gable(); // returns the default zero-argument unit gable
return gable(3.21); // returns a gable with a maximum AABB extent of 3.21
Additional Notes: DIAMOND : Generate 3D Diamond
→ 'instantiates a 3D fixed-form diamond solid centered at the origin (0,0,0)'
Classification:→ { instantiative, convex };
Alias & Synonyms:→ { diamond };
Invocation Options:prefix G3 diamond ( D size )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the diamond - a non-zero positive decimal number.→ size > 0
Topology Types:→ [ triangles ]Vertex Count:→ |V| = 24Polygon Count:→ |P| = 8Practical Examples:return diamond(); // returns the default zero-argument unit diamond
return diamond(3.21); // returns a diamond with a maximum AABB extent of 3.21
Additional Notes: WEDGE : Generate 3D Wedge
→ 'instantiates a 3D fixed-form wedge solid centered at the origin (0,0,0)'
Classification:→ { instantiative, convex };
Alias & Synonyms:→ { wedge };
Invocation Options:prefix G3 wedge ( D size )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the wedge - a non-zero positive decimal number.→ size > 0
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = 18Polygon Count:→ |P| = 5Practical Examples:return wedge(); // returns the default zero-argument unit wedge
return wedge(3.21); // returns a wedge with a maximum AABB extent of 3.21
Additional Notes: BRACKET : Generate 3D Bracket
→ 'instantiates a 3D fixed-form right-angled bracket solid centered at the origin (0,0,0)'
Classification:→ { instantiative, concave, orthogonal };
Alias & Synonyms:→ { bracket };
Invocation Options:prefix G3 bracket ( D size )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the bracket - a non-zero positive decimal number.→ size > 0
Topology Types:→ [ quadrilaterals ]Vertex Count:→ |V| = 44Polygon Count:→ |P| = 14Practical Examples:return bracket(); // returns the default zero-argument unit bracket
return bracket(3.21); // returns a bracket with a maximum AABB extent of 3.21
Additional Notes: TAPER-TOP-BOX : Generate 3D Taper-Top-Box
→ 'instantiates a parametric 3D taper-top parallax building-block solid'
Classification:→ { instantiative };
Alias & Synonyms:→ { t_box, t_t_box, taper_box, taper_top_box, tapered_box, tapered_top_box };
Invocation Options:prefix G3 tbox ( D size_x, D size_z, D ground_y, D mass_y, D roof_y, D scale_x, D scale_z, D offset_x, D offset_z )Input Arguments:•
D size_x :
default = 1 : the extent of the taper-box mass along the x-axis - equivalent to its width - a positive decimal number greater than zero.•
D size_z :
default = 1 : the extent of the taper-box mass along the z-axis - equivalent to its depth - a positive decimal number greater than zero.•
D ground_y :
default = -0.5 : the smallest (lowest) y-axis position of the taper-box mass - i.e. the ground position - a positive or negative decimal.•
D mass_y :
default = 0 : the middle (intermediary) y-axis position for the taper-box mass - a positive or negative decimal greater than the ground_y value.•
D roof_y :
default = 0.5 : the upper (highest) y-axis position for the taper-box mass - i.e. its roof peak position - a positive or negative decimal.•
D scale_x :
default = 1 : the tapering scale factor applied to the roof of the mass along the x-axis - expressed in unit normalised form - in the range [0:1] inclusive.•
D scale_z :
default = 0 : the tapering scale factor applied to the roof of the mass along the z-axis - expressed in unit normalised form - in the range [0:1] inclusive.•
D offset_x :
default = 0 : the shearing offset (translational shift) factor applied to the roof of the mass along the x-axis - expressed in unit normalised form - in the range [-0.5:0.5] inclusive.•
D offset_z :
default = 0 : the shearing offset (translational shift) factor applied to the roof of the mass along the z-axis - epxressed in unit normalised form - in the range [-0.5:0.5] inclusive.→ [ size_x, size_z, scale_x, scale_z ] > 0
→ [ mass_y, roof_y ] > ground_y
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = 40Polygon Count:→ |P| = 10 - ( ( scale_x * scale_z ) == 0 ? 1 : 0 )Practical Examples:return tbox(); // returns the default zero-argument unit tbox
Additional Notes: ROUND-TOP-BOX : Generate 3D Rounded-Taper-Top-Box
→ 'instantiates a parametric 3D rounded-taper-top parallax building-block solid'
Classification:→ { instantiative };
Alias & Synonyms:→ { r_t_box, r_t_t_box, round_taper_box, round_top_box, round_taper_top_box };
Invocation Options:prefix G3 rtbox ( D size_x, D size_z, D ground_y, D mass_y, D roof_y, D scale_x, D scale_z, D offset_x, D offset_z, I round_steps )Input Arguments:•
D size_x :
default = 1 : the extent of the round-taper-box mass along the x-axis - equivalent to its width - a positive decimal number greater than zero.•
D size_z :
default = 1 : the extent of the round-taper-box mass along the z-axis - equivalent to its depth - positive decimal number greater than zero.•
D ground_y :
default = -0.5 : the smallest (lowest) y-axis position of the round-taper-box mass - i.e. the ground position - a positive or negative decimal.•
D mass_y :
default = 0 : the middle (intermediary) y-axis position for the round-taper-box mass - a positive or negative decimal greater than the ground_y value.•
D roof_y :
default = 0.5 : the upper (highest) y-axis position for the taper-box mass - i.e. its roof peak position - a positive or negative decimal.•
D scale_x :
default = 1 : the tapering scale factor applied to the roof of the mass along the x-axis - expressed in unit normalised form - in the range [0:1] inclusive.•
D scale_z :
default = 0 : the tapering scale factor applied to the roof of the mass along the z-axis - expressed in unit normalised form - in the range [0:1] inclusive.•
D offset_x :
default = 0 : the shearing offset (translational shift) factor applied to the roof of the mass along the x-axis - expressed in unit normalised form - in the range [-0.5:0.5] inclusive.•
D offset_z :
default = 0 : the shearing offset (translational shift) factor applied to the roof of the mass along the z-axis - expressed in unit normalised form - in the range [-0.5:0.5] inclusive.•
I round_steps :
default = 16 : the number of circular discretisation steps to apply to the mass - a positive integer greater than or equal to 1.→ [ size_x, size_z, scale_x, scale_z ] > 0
→ [ mass_y, roof_y ] > ground_y
→ round_steps >= 1
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = 24 + ( ( round_steps + 1 ) * 2 * 4 )Polygon Count:→ |P| = 6 + ( round_steps * 4 ) - ( ( scale_x * scale_z ) == 0 ? 1 : 0 )Practical Examples:return rtbox(); // returns the default zero-argument unit rtbox
Additional Notes: BEZIER-TOP-BOX : Generate 3D Bezier-Taper-Top-Box
→ 'instantiates a parametric 3D bezier-taper-top parallax building-block solid'
Classification:→ { instantiative };
Alias & Synonyms:→ { b_t_box, b_t_t_box, bezier_taper_box, bezier_top_box, bezier_taper_top_box };
Invocation Options:prefix G3 btbox ( D size_x, D size_z, D ground_y, D mass_y, D roof_y, D scale_x, D scale_z, D offset_x, D offset_z, I bezier_steps )Input Arguments:•
D size_x :
default = 1 : the extent of the bezier-taper-box mass along the x-axis - equivalent to its width - a positive decimal number greater than zero.•
D size_z :
default = 1 : the extent of the bezier-taper-box mass along the z-axis - equivalent to its depth - a positive decimal number greater than zero.•
D ground_y :
default = -0.5 : the smallest (lowest) y-axis position of the bezier-taper-box mass - i.e. the ground position - a positive or negative decimal.•
D mass_y :
default = 0 : the middle (intermediary) y-axis position for the bezier-taper-box mass - a positive or negative decimal greater than the ground_y value.•
D roof_y :
default = 0.5 : the upper (highest) y-axis position for the bezier-taper-box mass - i.e. its roof peak position - a positive or negative decimal.•
D scale_x :
default = 1 : the tapering scale factor applied to the roof of the mass along the x-axis - expressed in unit normalised form - in the range [0:1] inclusive.•
D scale_z :
default = 0 : the tapering scale factor applied to the roof of the mass along the z-axis - expressed in unit normalised form - in the range [0:1] inclusive.•
D offset_x :
default = 0 : the shearing offset (translational shift) factor applied to the roof of the mass along the x-axis - expressed in unit normalised form - in the range [-0.5:0.5] inclusive.•
D offset_z :
default = 0 : the shearing offset (translational shift) factor applied to the roof of the mass along the z-axis - expressed in unit normalised form - in the range [-0.5:0.5] inclusive.•
I bezier_steps :
default = 16 : the number of bezier discretisation steps to apply to the mass - a positive integer greater than or equal to 1.→ [ size_x, size_z, scale_x, scale_z ] > 0
→ [ mass_y, roof_y ] > ground_y
→ bezier_steps >= 1
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = 24 + ( ( bezier_steps + 1 ) * 2 * 4 )Polygon Count:→ |P| = 6 + ( bezier_steps * 4 ) - ( ( scale_x * scale_z ) == 0 ? 1 : 0 )Practical Examples:return btbox(); // returns the default zero-argument unit btbox
Additional Notes: P-CONE : Generate 3D Polar-Cone
→ 'instantiates a 3D polar conic solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { p_cone, polar_cone, pole_cone, polar_point_cone };
Invocation Options:prefix G3 pcone ( I segments )prefix G3 pcone ( D radius, D length )prefix G3 pcone ( D radius, D length, I segments )Input Arguments:•
D radius :
default = 0.5 : the radius of the pcone (diameter = radius * 2) - a non-zero positive decimal number.•
D length :
default = 1.0 : the length of the pcone (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretisation resolution or the number of circular steps) - a positive whole number greater than or equal to 3.→ [ radius, length ] > 0
→ segments >= 3
Topology Types:→ [ triangles ]Vertex Count:→ |V| = ( segments * 2 + 2 )Polygon Count:→ |P| = ( segments * 2 )Practical Examples:return pcone(); // returns the default zero-argument unit pcone
return pcone(16); // returns a unit pcone with the default radius and height (0.5 and 1.0 units) and 16 circular segments
return pcone(2,5.5); // returns a pcone with a base diameter of 4 units, a height of 5.5 units and the default 32 circular segments
return pcone(1,5,64); // returns a pcone with a base diameter of 2 units, a height of 5 units and 64 segments
Additional Notes: P-CYLINDER : Generate 3D Polar-Cylinder
→ 'instantiates a 3D polar cylindrical solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { p_cylinder, polar_cylinder, pole_cylinder, polar_point_cylinder };
Invocation Options:prefix G3 pcylinder ( I segments )prefix G3 pcylinder ( D radius, D length )prefix G3 pcylinder ( D radius, D length, I segments )Input Arguments:•
D radius :
default = 0.5 : the radius of the pcylinder (diameter = radius * 2) - a non-zero positive decimal number.•
D length :
default = 1.0 : the length of the pcylinder (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretisation resolution or the number of circular steps) - a positive whole number greater than or equal to 3.→ [ radius, length ] > 0
→ segments >= 3
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( segments * 4 + 2 )Polygon Count:→ |P| = ( segments * 3 )Practical Examples:return pcylinder(); // returns the default zero-argument unit pcylinder
return pcylinder(16); // returns a unit pcylinder with the default radius and height (0.5 and 1.0 units) and 16 circular segments
return pcylinder(2,5.5); // returns a pcylinder with a base diameter of 4 units, a height of 5.5 units and the default 32 circular segments
return pcylinder(1,5,64); // returns a pcylinder with a diameter of 2 units, a height of 5 units and 64 segments
Additional Notes: P-CYLICONE : Generate 3D Polar-Cylicone
→ 'instantiates a 3D polar parametric conic-cylindrical solid centered at the origin (0,0,0) '
Classification:→ { instantiative };
Alias & Synonyms:→ { p_cylicone, polar_cylicone, pole_cylicone, polar_point_cylicone };
Invocation Options:prefix G3 pcylicone ( D lower_radius, D upper_radius )prefix G3 pcylicone ( D lower_radius, D upper_radius, I segments )prefix G3 pcylicone ( D lower_radius, D upper_radius, D length, I segments )Input Arguments:•
D lower_radius :
default = 0.5 : the radius at the base of the pcylicone - a non-zero positive decimal number.•
D upper_radius :
default = 0.25 : the radius at the top of the pcylicone - a non-zero positive decimal number.•
D length :
default = 1.0 : the length of the pcylicone (i.e. its height along the y-axis or it vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretisation resolution or the number of circular steps) - a positive whole number greater than or equal to 3.→ [ radius, length ] > 0
→ [ lower_radius, upper_radius ] >= 0
→ segments >= 3
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( lower_radius == 0 || upper_radius == 0 ) ? ( segments * 2 + 2 ) : ( segments * 4 + 2 )Polygon Count:→ |P| = ( lower_radius == 0 || upper_radius == 0 ) ? ( segments * 2 ) : ( segments * 3 )Practical Examples:return pcylicone(); // returns the default zero-argument unit pcylicone
return pcylicone(1,2);
// returns a pcylicone with a lower-radius of 1 unit, an upper-radius of 2 units, and the default length (1) and segments (32)
return pcylicone(0.5,1,16);
// returns a pcylicone with a lower-radius of 0.5 units, an upper-radius of 1 unit, the default length (1 unit) and 16 circular segments
return pcylicone(1,0.5,4,64);
// returns a pcylicone with a lower-radius of 1, an upper-radius of 0.5, a length of 4 and 64 segments
Additional Notes: C-SPHERE : Generate 3D Capped-Sphere
→ 'instantiates a 3D flat-topped (capped) spherical solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { c_sphere, cap_sphere, capped_sphere };
Invocation Options:prefix G3 csphere ( D diameter )prefix G3 csphere ( I slices, I stacks )prefix G3 csphere ( D diameter, I slices, I stacks )Input Arguments:•
D diameter :
default = 1.0 : the diameter of the csphere - a non-zero positive decimal number.•
I slices :
default = 32 : the number of longitudinal segments (i.e. the discretisation resolution or the number of circular steps about the Y-axis) - a positive whole number greater than or equal to 3.•
I stacks :
default = 16 : the number of latitudinal segments (i.e. the discretisation resolution or the number of half-circle steps from the csphere's north pole to its south pole) - a positive whole number greater than or equal to 3.→ diameter > 0
→ slices >= 3
→ stacks >= 3
Topology Types:→ [ quadrilaterals, N-gons: where N = slices ]Vertex Count:→ |V| = ( slices * ( stacks - 1 ) + 2 )Polygon Count:→ |P| = ( slices * ( stacks - 2 ) + 2 )Practical Examples:return csphere(); // returns the default zero-argument unit csphere
return csphere(2.4);
// returns a csphere with a diameter of 2.4 units and the default slices (32) and stacks (16)
return csphere(16,8);
// returns a csphere with the default diameter (1 unit) and respectively 16 and 8 slices and stacks
return csphere(4,64,32);
// returns a csphere with diameter of 4 units, 64 circular slices and 32 semi-circular stacks
Additional Notes: C-CAPSULE : Generate 3D Capped-Capsule
→ 'instantiates a 3D flat-topped (capped) capsule solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { c_capsule, c_cap_3D, c_capsule_3D, cap_capsule, cap_cap_3D, cap_capsule_3D, capped_capsule, capped_cap_3D, capped_capsule_3D };
Invocation Options:prefix G3 ccapsule ( D radius, D length )prefix G3 ccapsule ( D radius, D length, I slices, I stacks )Input Arguments:•
D radius :
default = 0.25 : the radius of the ccapsule's hemispheres - a non-zero positive decimal number.•
D length :
default = 0.5 : the length of the ccapsule's straight-edge section (i.e. its cylindrical portion's height along the Y-axis between its north and south hemispheres) - a non-zero positive decimal number.•
I slices :
default = 32 : the number of longitudinal segments (i.e. the discretisation resolution or the number of circular steps about the Y-axis) - a positive whole number greater than or equal to 3.•
I stacks :
default = 16 : the number of latitudinal segments (i.e. the discretisation resolution or the number of quarter-circle steps from each of the ccapsule's hemisphere's poles, to their equators) - a positive whole number greater than or equal to 2.→ [ radius, length ] > 0
→ slices >= 3
→ stacks >= 2
Topology Types:→ [ quadrilaterals, N-gons: where N = slices ]Vertex Count:→ |V| = ( slices * stacks * 2 + 2 )Polygon Count:→ |P| = ( slices + 2 + slices * ( stacks - 1 ) * 2 )Practical Examples:return ccapsule(); // returns the default zero-argument unit ccapsule
return ccapsule(1,10);
// returns a ccapsule with a radius of 1 unit, a length of 10-units and the default 32 and 16 longitudinal slices and latitudinal stacks
return ccapsule(5,20,4,8);
// returns a ccapsule with a radius of 5 units, a cylindrical-length of 20 units, 4 longitudinal steps and 8 latitudinal steps for each hemisphere
Additional Notes: C-ELLIPSOID : Generate 3D Capped-Ellipsoid
→ 'instantiates a 3D flat-topped (capped) ellipsoidal solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { c_ellipsoid, cap_ellipsoid, capped_ellipsoid };
Invocation Options:prefix G3 cellipsoid ( D size_x, D size_y, D size_z )prefix G3 cellipsoid ( D size_x, D size_y, D size_z, I slices, I stacks )Input Arguments:•
D size_x :
default = 0.5 : the width of the cellipsoid (i.e. its extent along the x-axis) - a non-zero positive decimal number.•
D size_y :
default = 1 : the height of the cellipsoid (i.e. its extent along the y-axis) - a non-zero positive decimal number.•
D size_z :
default = 0.25 : the depth of the cellipsoid (i.e. its extent along the z-axis) - a non-zero positive decimal number.•
I slices :
default = 32 : the number of longitudinal segments in the base sphere used to construct the cellipsoid (i.e. the discretisation resolution or the number of circular steps about the Y-axis) - a positive whole number greater than or equal to 3.•
I stacks :
default = 16 : the number of latitudinal segments in the base sphere used to construct the cellipsoid (i.e. the discretisation resolution or the number of half-circle steps from the base sphere's north pole to its south pole) - a positive whole number greater than or equal to 3.→ [ size_x, size_y, size_z ] > 0
→ slices >= 3
→ stacks >= 3
Topology Types:→ [ quadrilaterals, N-gons: where N = slices ]Vertex Count:→ |V| = ( slices * ( stacks - 2 ) + 2 )Polygon Count:→ |P| = ( slices * ( stacks - 2 ) + 2 )Practical Examples:return cellipsoid(); // returns the default zero-argument unit cellipsoid
return cellipsoid(1,2,3);
// returns a cellipsoid with a width, height and depth (of respectively) 1, 2, and 3 units and the default slices (32) and stacks (16)
return cellipsoid(2,1,2,64,4);
// returns a cellipsoid with a width, height and depth (of respectively) 2, 1 and 2 units, and with 64 longitudinal steps and 4 latitudinal steps
Additional Notes: B-CUBE : Generate 3D Beveled-Cuboid
→ 'instantiates a 3D beveled (chamfered-edge) cuboidal solid'
Classification:→ { instantiative };
Alias & Synonyms:→ { b_cube, b_box_3D, b_cuboid, bevel_cube, bevel_box_3D, bevel_cuboid, beveled_cube, beveled_box_3D, beveled_cuboid, bevelled_cube, bevelled_box_3D, bevelled_cuboid, ... (+6) };
Invocation Options:prefix G3 bcube ( D bevel_distance )prefix G3 bcube ( D size, D bevel_distance )prefix G3 bcube ( D width, D height, D depth, D bevel_distance )prefix G3 bcube ( D x, D y, D z, D width, D height, D depth, D bevel_distance )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the bcube - a non-zero positive decimal number.•
D x :
default = -0.5 * width : the axis-aligned bounding-box minimum x-coordinate value of the bcube - a decimal number.•
D y :
default = -0.5 * height : the axis-aligned bounding-box minimum y-coordinate value of the bcube - a decimal number.•
D z :
default = -0.5 * depth : the axis-aligned bounding-box minimum z-coordinate value of the bcube - a decimal number.•
D width :
default = 1 : the x-axis extent of the bcube - a non-zero positive decimal number - the maximum x-coordinate value is equal to (x + width).•
D height :
default = 1 : the y-axis extent of the bcube - a non-zero positive decimal number - the maximum y-coordinate value is equal to (y + height).•
D depth :
default = 1 : the z-axis extent of the bcube - a non-zero positive decimal number - the maximum z-coordinate value is equal to (z + depth).•
D bevel_distance :
default = 0.125 : the projective-inset distance (i.e the perpandicular chamfer or bevel length) applied to the bcube - a non-zero positive decimal number - which must be less than half of the minimum of the bcubes's width, height, depth or uniform size factor.→ [ size, width, height, depth, bevel_distance ] > 0
→ [ size, width, height, depth ] > ( bevel_distance * 2 )
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = 96Polygon Count:→ |P| = 26Practical Examples:return bcube(); // returns the default zero-argument unit bcube
Alias Formation Rules:Additional Notes: B-CONE : Generate 3D Beveled-Cone
→ 'instantiates a 3D beveled (chamfered-edge) conic solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { b_cone, bevel_cone, beveled_cone, bevelled_cone, chamfer_cone, chamfered_cone };
Invocation Options:prefix G3 bcone ( D bevel_distance )prefix G3 bcone ( I segments, D bevel_distance )prefix G3 bcone ( D radius, D length, D bevel_distance )prefix G3 bcone ( D radius, D length, I segments, D bevel_distance )Input Arguments:•
D radius :
default = 0.5 : the radius of the bcone (diameter = radius * 2) - a non-zero positive decimal number.•
D length :
default = 1 : the length of the bcone (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretistion resolution or the number of circular steps) - a positive whole number greater than or equal to 3.•
D bevel_distance :
default = 0.125 : the projective-inset distance (i.e the perpandicular chamfer or bevel length) applied to the bcone - a non-zero positive decimal number - which must be less than the bcone's radius and less than the bcones's length.→ [ radius, length, bevel_distance ] > 0
→ segments >= 3
→ [ radius, length ] > bevel_distance
Topology Types:→ [ triangles, quadrilaterals, N-gons: where N = segments ]Vertex Count:→ |V| = ( segments * 4 + 2 )Polygon Count:→ |P| = ( segments * 2 + 1 )Practical Examples:return bcone(); // returns the default zero-argument unit bcone
Additional Notes: B-CYLINDER : Generate 3D Beveled-Cylinder
→ 'instantiates a 3D beveled (chamfered-edge) cylindrical solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { b_cylinder, bevel_cylinder, beveled_cylinder, bevelled_cylinder, chamfer_cylinder, chamfered_cylinder };
Invocation Options:prefix G3 bcylinder ( D bevel_distance )prefix G3 bcylinder ( I segments, D bevel_distance )prefix G3 bcylinder ( D radius, D length, D bevel_distance )prefix G3 bcylinder ( D radius, D length, I segments, D bevel_distance )Input Arguments:•
D radius :
default = 0.5 : the radius of the bcylinder (diameter = radius * 2) - a non-zero positive decimal number.•
D length :
default = 1 : the length of the bcylinder (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretistion resolution or the number of circular steps) - a positive whole number greater than or equal to 3.•
D bevel_distance :
default = 0.125 : the projective-inset distance (i.e the perpandicular chamfer or bevel length) applied to the bcylinder - a non-zero positive decimal number - which must be less than the bcylinder's radius and less than half of the bcylinder's length.→ [ radius, length, bevel_distance ] > 0
→ segments >= 3
→ radius > bevel_distance
→ length > ( bevel_distance * 2 )
Topology Types:→ [ quadrilaterals, N-gons: where N = segments ]Vertex Count:→ |V| = ( segments * 8 + 2 )Polygon Count:→ |P| = ( segments * 3 + 2 )Practical Examples:return bcylinder(); // returns the default zero-argument unit bcylinder
Additional Notes: B-CYLICONE : Generate 3D Beveled-Cylicone
→ 'instantiates a 3D beveled (chamfered-edge) conic-cylindrical solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { b_cylicone, bevel_cylicone, beveled_cylicone, bevelled_cylicone, chamfer_cylicone, chamfered_cylicone };
Invocation Options:prefix G3 bcylicone ( D bevel_distance )prefix G3 bcylicone ( D lower_radius, D upper_radius, D bevel_distance )prefix G3 bcylicone ( D lower_radius, D upper_radius, I segments, D bevel_distance )prefix G3 bcylicone ( D lower_radius, D upper_radius, D length, I segments, D bevel_distance )Input Arguments:•
D lower_radius :
default = 0.5 : the radius at the base of the bcylicone - a non-zero positive decimal number.•
D upper_radius :
default = 0.25 : the radius at the top of the bcylicone - a non-zero positive decimal number.•
D length :
default = 1 : the length of the bcylicone (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretistion resolution or the number of circular steps) - a positive whole number greater than or equal to 3.•
D bevel_distance :
default = 0.125 : the projective-inset distance (i.e the perpandicular chamfer or bevel length) applied to the bcylicone (both its lower and upper circular edges) - a non-zero positive decimal number - which must be less than the bcylicone's lower and upper radii and less than half of the bcylicone's length.→ [ length, bevel_distance ] > 0
→ segments >= 3
→ [ lower_radius, upper_radius ] > bevel_distance
→ length > ( bevel_distance * 2 )
Topology Types:→ [ quadrilaterals, N-gons: where N = segments ]Vertex Count:→ |V| = ( segments * 8 + 2 )Polygon Count:→ |P| = ( segments * 3 + 2 )Practical Examples:return bcylicone(); // returns the default zero-argument unit bcylicone
Additional Notes: B-PYRAMID : Generate 3D Beveled-Pyramid
→ 'instantiates a 3D beveled (chamfered-edge) fixed-form pyramid solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { b_pyramid, bevel_pyramid, beveled_pyramid, bevelled_pyramid, chamfer_pyramid, chamfered_pyramid };
Invocation Options:prefix G3 bpyramid ( D bevel_distance )prefix G3 bpyramid ( D size, D bevel_distance )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the bpyramid - a non-zero positive decimal number.•
D bevel_distance :
default = 0.125 * size : the projective-inset distance (i.e. the perpandicular chamfer or bevel length) applied to the bpyramid - a non-zero positive decimal number - which must be less than half of the uniform scale factor size of the bpyramid.→ [ size, bevel_distance ] > 0
→ size > ( bevel_distance * 2 )
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = 32Polygon Count:→ |P| = 9Practical Examples:return bpyramid(); // returns the default zero-argument unit bpyramid
return bpyramid(0.05);
// returns a bpyramid with a bevel distance of 0.05 units and the default scale factor size of 1 unit
return bpyramid(8,1);
// returns a bpyramid with a uniform size of 8 units and a bevel distance of 1 unit
Additional Notes: B-GABLE : Generate 3D Beveled-Gable
→ 'instantiates a 3D beveled (chamfered-edge) fixed-form gable solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { b_gable, bevel_gable, beveled_gable, bevelled_gable, chamfer_gable, chamfered_gable };
Invocation Options:prefix G3 bgable ( D bevel_distance )prefix G3 bgable ( D size, D bevel_distance )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the bgable - a non-zero positive decimal number.•
D bevel_distance :
default = 0.125 * size : the projective-inset distance (i.e. the perpandicular chamfer or bevel length) applied to the bgable - a non-zero positive decimal number - which must be less than (TODO) of the uniform scale factor size of the bgable.→ [ size, bevel_distance ] > 0
→ size > ( bevel_distance * TODO )
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = 72Polygon Count:→ |P| = 20Practical Examples:return bgable(); // returns the default zero-argument unit bgable
return bgable(0.05);
// returns a bgable with a bevel distance of 0.05 units and the default scale factor size of 1 unit
return bgable(8,1);
// returns a bgable with a uniform size of 8 units and a bevel distance of 1 unit
Additional Notes: B-WEDGE : Generate 3D Beveled-Wedge
→ 'instantiates a 3D beveled (chamfered-edge) fixed-form wedge solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { b_wedge, bevel_wedge, beveled_wedge, bevelled_wedge, chamfer_wedge, chamfered_wedge };
Invocation Options:prefix G3 bwedge ( D bevel_distance )prefix G3 bwedge ( D size, D bevel_distance )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the bwedge - a non-zero positive decimal number.•
D bevel_distance :
default = 0.125 * size : the projective-inset distance (i.e. the perpandicular chamfer or bevel length) applied to the bwedge - a non-zero positive decimal number - which must be less than (TODO) of the uniform scale factor size of the bwedge.→ [ size, bevel_distance ] > 0
→ size > ( bevel_distance * TODO )
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = 72Polygon Count:→ |P| = 20Practical Examples:return bwedge(); // returns the default zero-argument unit bwedge
return bwedge(0.05);
// returns a bwedge with a bevel distance of 0.05 units and the default scale factor size of 1 unit
return bwedge(8,1);
// returns a bwedge with a uniform size of 8 units and a bevel distance of 1 unit
Additional Notes: B-DIAMOND : Generate 3D Beveled-Diamond
→ 'instantiates a 3D beveled (chamfered-edge) fixed-form diamond solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { b_diamond, bevel_diamond, beveled_diamond, bevelled_diamond, chamfer_diamond, chamfered_diamond };
Invocation Options:prefix G3 bdiamond ( D bevel_distance )prefix G3 bdiamond ( D size, D bevel_distance )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the bdiamond - a non-zero positive decimal number.•
D bevel_distance :
default = 0.125 * size : the projective-inset distance (i.e. the perpandicular chamfer or bevel length) applied to the bdiamond - a non-zero positive decimal number - which must be less than (TODO) of the uniform scale factor size of the bdiamond.→ [ size, bevel_distance ] > 0
→ size > ( bevel_distance * TODO )
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = 40Polygon Count:→ |P| = 12Practical Examples:return bdiamond(); // returns the default zero-argument unit bdiamond
return bdiamond(0.05);
// returns a bdiamond with a bevel distance of 0.05 units and the default scale factor size of 1 unit
return bdiamond(8,1);
// returns a bdiamond with a uniform size of 8 units and a bevel distance of 1 unit
Additional Notes: B-BRACKET : Generate 3D Beveled-Bracket
→ 'instantiates a 3D beveled (chamfered-edge) fixed-form right-angled bracket solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { b_bracket, bevel_bracket, beveled_bracket, bevelled_bracket, chamfer_bracket, chamfered_bracket };
Invocation Options:prefix G3 bbracket ( D bevel_distance )prefix G3 bbracket ( D size, D bevel_distance )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the bbracket - a non-zero positive decimal number.•
D bevel_distance :
default = 0.125 * size : the projective-inset distance (i.e. the perpandicular chamfer or bevel length) applied to the bbracket - a non-zero positive decimal number - which must be less than a quarter of the uniform scale factor size of the bbracket.→ [ size, bevel_distance ] > 0
→ size > ( bevel_distance * 4 )
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = 144Polygon Count:→ |P| = 44Practical Examples:return bbracket(); // returns the default zero-argument unit bbracket
return bbracket(0.05);
// returns a bbracket with a bevel distance of 0.05 units and the default scale factor size of 1 unit
return bbracket(8,1);
// returns a bbracket with a uniform size of 8 units and a bevel distance of 1 unit
Additional Notes: R-CUBE : Generate 3D Rounded-Cuboid
→ 'instantiates a 3D rounded (smooth-edged) cuboidal solid'
Classification:→ { instantiative };
Alias & Synonyms:→ { r_cube, r_box_3D, r_cuboid, rnd_cube, rnd_box_3D, rnd_cuboid, round_cube, round_box_3D, round_cuboid, rounded_cube, rounded_box_3D, rounded_cuboid };
Invocation Options:prefix G3 rcube ( D size )prefix G3 rcube ( D round_radius, I round_steps )prefix G3 rcube ( D size, D round_radius, I round_steps )prefix G3 rcube ( D width, D height, D depth, D round_radius, I round_steps )prefix G3 rcube ( D x, D y, D z, D width, D height, D depth, D round_radius, I round_steps )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the rcube - a non-zero positive decimal number.•
D x :
default = -0.5 * width : the axis-aligned bounding-box minimum x-coordinate value of the rcube - a decimal number.•
D y :
default = -0.5 * height : the axis-aligned bounding-box minimum y-coordinate value of the rcube - a decimal number.•
D z :
default = -0.5 * depth : the axis-aligned bounding-box minimum z-coordinate value of the rcube - a decimal number.•
D width :
default = 1 : the x-axis extent of the rcube - a non-zero positive decimal number - the maximum x-coordinate value is equal to (x + width).•
D height :
default = 1 : the y-axis extent of the rcube - a non-zero positive decimal number - the maximum y-coordinate value is equal to (y + height).•
D depth :
default = 1 : the z-axis extent of the rcube - a non-zero positive decimal number - the maximum z-coordinate value is equal to (z + depth).•
D round_radius :
default = 0.125 : the radius applied to round the corners and edges of the rcube - a non-zero positive decimal number which must be less than half of the minimum of the rcube's width, height, depth or uniform size factor.•
I round_steps :
default = 8 : the number of steps used to round the corners and edges of the rcube - a positive whole number greater than or equal to 1.→ [ size, width, height, depth, round_radius ] > 0
→ round_steps >= 1
→ [ size, width, height, depth ] > ( round_radius * 2 )
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( ( ( round_steps + 1 ) * round_steps ) + 1 ) * 8Polygon Count:→ |P| = ( ( round_steps * round_steps ) * 8 ) + 6 + ( round_steps * 4 * 3 )Practical Examples:return rcube(); // returns the default zero-argument unit rcube
Additional Notes: R-CONE : Generate 3D Rounded-Cone
→ 'instantiates a 3D rounded (smooth-edged) conic solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { r_cone, rnd_cone, round_cone, rounded_cone };
Invocation Options:prefix G3 rcone ( I segments )prefix G3 rcone ( D round_radius, I round_steps )prefix G3 rcone ( I segments, D round_radius, I round_steps )prefix G3 rcone ( D radius, D length, D round_radius, I round_steps )prefix G3 rcone ( D radius, D length, I segments, D round_radius, I round_steps )Input Arguments:•
D radius :
default = 0.5 : the radius of the rcone (diameter = radius * 2) - a non-zero positive decimal number.•
D length :
default = 1 : the length of the rcone (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretistion resolution or the number of circular steps) - a positive whole number greater than or equal to 3.•
D round_radius :
default = 0.125 : the radius applied to round the circular edge of the rcone - a non-zero positive decimal number which must be less than the radius of the the rcone and less than the length of the rcone.•
I round_steps :
default = 8 : the number of steps used to round the circular edge of the rcone (i.e. the discretisation resolution) - a positive whole number greater than or equal to 1.→ [ radius, length, round_radius ] > 0
→ segments >= 3
→ [ radius, length ] > round_radius
→ round_steps >= 1
Topology Types:→ [ triangles, quadrilaterals, N-gons: where N = segments ]Vertex Count:→ |V| = ( ( round_steps + 1 ) * segments ) + 2Polygon Count:→ |P| = ( ( round_steps + 1 ) * segments ) + 1Practical Examples:return rcone(); // returns the default zero-argument unit rcone
Additional Notes: R-CYLINDER : Generate 3D Rounded-Cylinder
→ 'instantiates a 3D rounded (smooth-edged) cylindrical solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { r_cylinder, rnd_cylinder, round_cylinder, rounded_cylinder };
Invocation Options:prefix G3 rcylinder ( I segments )prefix G3 rcylinder ( D round_radius, I round_steps )prefix G3 rcylinder ( I segments, D round_radius, I round_steps )prefix G3 rcylinder ( D radius, D length, D round_radius, I round_steps )prefix G3 rcylinder ( D radius, D length, I segments, D round_radius, I round_steps )Input Arguments:•
D radius :
default = 0.5 : the radius of the rcylinder (diameter = radius * 2) - a non-zero positive decimal number.•
D length :
default = 1 : the length of the rcylinder (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretistion resolution or the number of circular steps) - a positive whole number greater than or equal to 3.•
D round_radius :
default = 0.125 : the radius applied to round the circular edges of the rcylinder - a non-zero positive decimal number which must be less than the radius of the rcylinder and less than half the length of the rcylinder.•
I round_steps :
default = 8 : the number of steps used to round the circular edges of the rcylinder (i.e. the discretisation resolution) - a positive whole number greater than or equal to 1.→ [ radius, length, round_radius ] > 0
→ segments >= 3
→ radius > round_radius
→ length > ( round_radius * 2 )
→ round_steps >= 1
Topology Types:→ [ quadrilaterals, N-gons: where N = segments ]Vertex Count:→ |V| = ( ( ( round_steps + 1 ) * 2 ) * segments ) + 2Polygon Count:→ |P| = ( round_steps * 2 + 1 ) * segments + 2Practical Examples:return rcylinder(); // returns the default zero-argument unit rcylinder
Additional Notes: R-CYLICONE : Generate 3D Rounded-Cylicone
→ 'instantiates a 3D rounded (smooth-edged) conic-cylindrical solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { r_cylicone, rnd_cylicone, round_cylicone, rounded_cylicone };
Invocation Options:prefix G3 rcylicone ( I segments )prefix G3 rcylicone ( D round_radius, I round_steps )prefix G3 rcylicone ( D lower_radius, D upper_radius, D round_radius, I round_steps )prefix G3 rcylicone ( D lower_radius, D upper_radius, I segments, D round_radius, I round_steps )prefix G3 rcylicone ( D lower_radius, D upper_radius, D length, I segments, D round_radius, I round_steps )Input Arguments:•
D lower_radius :
default = 0.5 : the radius at the base of the rcylicone - a non-zero positive decimal number.•
D upper_radius :
default = 0.25 : the radius at the top of the rcylicone - a non-zero positive decimal number.•
D length :
default = 1 : the length of the rcylicone (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretistion resolution or the number of circular steps) - a positive whole number greater than or equal to 3.•
D round_radius :
default = 0.125 : the radius applied to round the lower and upper circular edges of the rcylicone - a non-zero positive decimal number which must be less than both the lower and upper radii of the rcylicone and less than half the length of the rcylicone.•
I round_steps :
default = 8 : the number of steps used to round the lower and upper circular edges of the rcylicone (i.e. the discretisation resolution) - a positive whole number greater than or equal to 1.→ [ length, round_radius ] > 0
→ segments >= 3
→ [ lower_radius, upper_radius ] > round_radius
→ length > ( round_radius * 2 )
→ round_steps >= 1
Topology Types:→ [ triangles, quadrilaterals, N-gons: where N = segments ]Vertex Count:→ |V| = ( ( ( round_steps + 1 ) * 2 ) * segments ) + 2Polygon Count:→ |P| = ( round_steps * 2 + 1 ) * segments + 2Practical Examples:return rcylicone(); // returns the default zero-argument unit rcylicone
Additional Notes: R-PYRAMID : Generate 3D Rounded-Pyramid
→ 'instantiates a 3D rounded (smooth-edged) fixed-form pyramid solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { r_pyramid, rnd_pyramid, round_pyramid, rounded_pyramid };
Invocation Options:prefix G3 rpyramid ( D size )prefix G3 rpyramid ( D round_radius, I round_steps )prefix G3 rpyramid ( D size, D round_radius, I round_steps )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the rpyramid - a non-zero positive decimal number.•
D round_radius :
default = 0.125 * size : the radius applied to round the corners and edges of the rpyramid - a non-zero positive decimal number which must be less than half of the scale factor size of the rpyramid.•
I round_steps :
default = 8 : the number of steps used to round the corners and edges of the rpyramid (i.e. the discretisation resolution) - a positive whole number greater than or equal to 1.→ [ size, round_radius ] > 0
→ round_steps >= 1
→ size > ( round_radius * 2 )
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( ( round_steps + 1 + 2 ) * 2 - 2 ) * 4Polygon Count:→ |P| = ( ( round_steps + 1 ) * 4 ) + 1Practical Examples:return rpyramid(); // returns the default zero-argument unit rpyramid
return rpyramid(5.5);
// returns a rpyramid with a uniform scale factor size of 5.5 and the default round radius (0.125*size = 0.125*5.5 = 0.6875) and round steps (8)
return rpyramid(0.1,4);
// returns a rpyramid with a round radius of 0.1, 4 round steps and the default scale factor size of 1
return rpyramid(10,2,1);
// returns a rpyramid with a uniform scale factor size of 10, a round radius of 2 and a single round step for each edge - this has the effect of constructing the underlying geometry of a beveled variant whilst maintaining the interpolatability of attributes across the rpyramid
Additional Notes: R-GABLE : Generate 3D Rounded-Gable
→ 'instantiates a 3D rounded (smooth-edged) fixed-form gable solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { r_gable, rnd_gable, round_gable, rounded_gable };
Invocation Options:prefix G3 rgable ( D size )prefix G3 rgable ( D round_radius, I round_steps )prefix G3 rgable ( D size, D round_radius, I round_steps )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the rgable - a non-zero positive decimal number.•
D round_radius :
default = 0.125 * size : the radius applied to round the corners and edges of the rgable - a non-zero positive decimal number which must be less than (TODO) of the scale factor size of the rgable.•
I round_steps :
default = 8 : the number of steps used to round the corners and edges of the rgable (i.e. the discretisation resolution) - a positive whole number greater than or equal to 1.→ [ size, round_radius ] > 0
→ round_steps >= 1
→ size > ( round_radius * TODO )
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( 3 * ( round_steps + 1 ) * round_steps * 2 ) + ( 3 * 2 )Polygon Count:→ |P| = ( round_steps + 1 ) * 3 * ( round_steps - 1 ) * 2 + ( round_steps * 3 * 2 ) + ( 3 * 2 ) + ( ( round_steps + 1 ) * 3 ) + 2Practical Examples:return rgable(); // returns the default zero-argument unit rgable
return rgable(5.5);
// returns a rgable with a uniform scale factor size of 5.5 and the default round radius (0.125*size = 0.125*5.5 = 0.6875) and round steps (8)
return rgable(0.1,4);
// returns a rgable with a round radius of 0.1, 4 round steps and the default scale factor size of 1
return rgable(10,2,1);
// returns a rgable with a uniform scale factor size of 10, a round radius of 2 and a single round step for each edge - this has the effect of constructing the underlying geometry of a beveled variant whilst maintaining the interpolatability of attributes across the rgable
Additional Notes: R-WEDGE : Generate 3D Rounded-Wedge
→ 'instantiates a 3D rounded (smooth-edged) fixed-form wedge solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { r_wedge, rnd_wedge, round_wedge, rounded_wedge };
Invocation Options:prefix G3 rwedge ( D size )prefix G3 rwedge ( D round_radius, I round_steps )prefix G3 rwedge ( D size, D round_radius, I round_steps )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the rwedge - a non-zero positive decimal number.•
D round_radius :
default = 0.125 * size : the radius applied to round the corners and edges of the rwedge - a non-zero positive decimal number which must be less than (TODO) of the scale factor size of the rwedge.•
I round_steps :
default = 8 : the number of steps used to round the corners and edges of the rwedge (i.e. the discretisation resolution) - a positive whole number greater than or equal to 1.→ [ size, round_radius ] > 0
→ round_steps >= 1
→ size > ( round_radius * TODO )
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( 3 * ( round_steps + 1 ) * round_steps * 2 ) + ( 3 * 2 )Polygon Count:→ |P| = ( round_steps + 1 ) * 3 * ( round_steps - 1 ) * 2 + ( round_steps * 3 * 2 ) + ( 3 * 2 ) + ( ( round_steps + 1 ) * 3 ) + 2Practical Examples:return rwedge(); // returns the default zero-argument unit rwedge
return rwedge(5.5);
// returns a rwedge with a uniform scale factor size of 5.5 and the default round radius (0.125*size = 0.125*5.5 = 0.6875) and round steps (8)
return rwedge(0.1,4);
// returns a rwedge with a round radius of 0.1, 4 round steps and the default scale factor size of 1
return rwedge(10,2,1);
// returns a rwedge with a uniform scale factor size of 10, a round radius of 2 and a single round step for each edge - this has the effect of constructing the underlying geometry of a beveled variant whilst maintaining the interpolatability of attributes across the rwedge
Additional Notes: R-DIAMOND : Generate 3D Rounded-Diamond
→ 'instantiates a 3D rounded (smooth-edged) fixed-form diamond solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { r_diamond, rnd_diamond, round_diamond, rounded_diamond };
Invocation Options:prefix G3 rdiamond ( D size )prefix G3 rdiamond ( D round_radius, I round_steps )prefix G3 rdiamond ( D size, D round_radius, I round_steps )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the rdiamond - a non-zero positive decimal number.•
D round_radius :
default = 0.125 * size : the radius applied to round the corners and edges of the rdiamond - a non-zero positive decimal number which must be less than (TODO) of the scale factor size of the rdiamond.•
I round_steps :
default = 8 : the number of steps used to round the corners and edges of the rdiamond (i.e. the discretisation resolution) - a positive whole number greater than or equal to 1.→ [ size, round_radius ] > 0
→ round_steps >= 1
→ size > ( round_radius * TODO )
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( ( round_steps + 1 + 2 ) * 2 - 2 ) * 4Polygon Count:→ |P| = ( ( round_steps + 2 ) * 4 )Practical Examples:return rdiamond(); // returns the default zero-argument unit rdiamond
return rdiamond(5.5);
// returns a rdiamond with a uniform scale factor size of 5.5 and the default round radius (0.125*size = 0.125*5.5 = 0.6875) and round steps (8)
return rdiamond(0.1,4);
// returns a rdiamond with a round radius of 0.1, 4 round steps and the default scale factor size of 1
return rdiamond(10,2,1);
// returns a rdiamond with a uniform scale factor size of 10, a round radius of 2 and a single round step for each edge - this has the effect of constructing the underlying geometry of a beveled variant whilst maintaining the interpolatability of attributes across the rdiamond
Additional Notes: R-BRACKET : Generate 3D Rounded-Bracket
→ 'instantiates a 3D rounded (smooth-edged) fixed-form right-angled bracket solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { r_bracket, rnd_bracket, round_bracket, rounded_bracket };
Invocation Options:prefix G3 rbracket ( D size )prefix G3 rbracket ( D round_radius, I round_steps )prefix G3 rbracket ( D size, D round_radius, I round_steps )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the rbracket - a non-zero positive decimal number.•
D round_radius :
default = 0.125 * size : the radius applied to round the corners and edges of the rbracket - a non-zero positive decimal number which must be less than a quarter of the scale factor size of the rbracket.•
I round_steps :
default = 8 : the number of steps used to round the corners and edges of the rbracket (i.e. the discretisation resolution) - a positive whole number greater than or equal to 1.→ [ size, round_radius ] > 0
→ round_steps >= 1
→ size > ( round_radius * 4 )
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( 6 * ( round_steps + 1 ) * round_steps * 2 ) + ( 6 * 2 )Polygon Count:→ |P| = ( round_steps + 1 ) * 6 * ( round_steps - 1 ) * 2 + ( round_steps * 6 * 2 ) + ( 6 * 2 ) + ( ( round_steps + 1 ) * 6 ) + ( ( 6 - 2 ) * 2 )Practical Examples:return rbracket(); // returns the default zero-argument unit rbracket
return rbracket(5.5);
// returns a rbracket with a uniform scale factor size of 5.5 and the default round radius (0.125*size = 0.125*5.5 = 0.6875) and round steps (8)
return rbracket(0.1,4);
// returns a rbracket with a round radius of 0.1, 4 round steps and the default scale factor size of 1
return rbracket(10,2,1);
// returns a rbracket with a uniform scale factor size of 10, a round radius of 2 and a single round step for each edge - this has the effect of constructing the underlying geometry of a beveled variant whilst maintaining the interpolatability of attributes across the rbracket
Additional Notes: Sub-Divided-Variant Solids
S-CUBE : Generate 3D Sub-Divided-Cuboid
→ 'instantiates a 3D axis-aligned bi-linearly sub-divided cuboidal solid'
Classification:→ { instantiative };
Alias & Synonyms:→ { s_cube, s_box_3D, s_cuboid, sd_cube, sd_box_3D, sd_cuboid, subd_cube, subd_box_3D, subd_cuboid, sub_divide_cube, sub_divide_box_3D, sub_divide_cuboid, ... (+3) };
Invocation Options:prefix G3 scube ( I ncount )prefix G3 scube ( D size, I ncount )prefix G3 scube ( I xcount, I ycount, I zcount )prefix G3 scube ( D width, D height, D depth, I ncount )prefix G3 scube ( D width, D height, D depth, I xcount, I ycount, I zcount )prefix G3 scube ( D x, D y, D z, D width, D height, D depth, I xcount, I ycount, I zcount )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the scube - a non-zero positive decimal number.•
D x :
default = -0.5 * width : the axis-aligned bounding-box minimum x-coordinate value of the scube - a decimal number.•
D y :
default = -0.5 * height : the axis-aligned bounding-box minimum y-coordinate value of the scube - a decimal number.•
D z :
default = -0.5 * depth : the axis-aligned bounding-box minimum z-coordinate value of the scube - a decimal number.•
D width :
default = 1 : the x-axis extent of the scube - a non-zero positive decimal number - the maximum x-coordinate value is equal to (x + width).•
D height :
default = 1 : the y-axis extent of the scube - a non-zero positive decimal number - the maximum y-coordinate value is equal to (y + height).•
D depth :
default = 1 : the z-axis extent of the scube - a non-zero positive decimal number - the maximum z-coordinate value is equal to (z + depth).•
I ncount :
default = 4 : the uniform number of sub-division partitions applied to the scube along the x-axis, y-axis and z-axis.•
I xcount :
default = 4 : the number of sub-division partitions applied to the scube along the x-axis (i.e. along the scube's width) - a positive whole number greater than or equal to 1.•
I ycount :
default = 4 : the number of sub-division partitions applied to the scube along the y-axis (i.e. along the scube's height) - a positive whole number greater than or equal to 1.•
I zcount :
default = 4 : the number of sub-division partitions applied to the scube along the z-axis (i.e. along the scube's depth) - a positive whole number greater than or equal to 1.→ [ size, width, height, depth ] > 0
→ [ ncount, xcount, ycount, zcount ] >= 1
Topology Types:→ [ quadrilaterals ]Vertex Count:→ |V| = ( ( xcount + 1 ) * ( ycount + 1 ) * 2 ) + ( ( xcount + 1 ) * ( zcount + 1 ) * 2 ) + ( ( ycount + 1 ) + ( zcount + 1 ) * 2 )Polygon Count:→ |P| = ( xcount * ycount * 2 ) + ( xcount * zcount * 2 ) + ( ycount * zcount * 2 )Practical Examples:return scube(); // returns the default zero-argument unit scube
Alias Formation Rules:Additional Notes: S-CONE : Generate 3D Sub-Divided-Cone
→ 'instantiates a 3D bi-linearly sub-divided conic solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { s_cone, sd_cone, subd_cone, sub_divide_cone, sub_divided_cone };
Invocation Options:prefix G3 scone ( I segments )prefix G3 scone ( I xcount, I ycount )prefix G3 scone ( I segments, I xcount, I ycount )prefix G3 scone ( D radius, D length, I xcount, I ycount )prefix G3 scone ( D radius, D length, I segments, I xcount, I ycount )Input Arguments:•
D radius :
default = 0.5 : the radius of the scone (diameter = radius * 2) - a non-zero positive decimal number.•
D length :
default = 1 : the length of the scone (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretistion resolution or the number of circular steps) - a positive whole number greater than or equal to 3.•
I xcount :
default = 4 : the number of sub-division partitions applied to the scone along the x-axis (i.e. along the radius at its circular base) - a positive whole number greater than or equal to 1.•
I ycount :
default = 8 : the number of sub-division partitions applied to the scone along the y-axis (i.e. along its length or vertical height) - a positive whole number greater than or equal to 1.→ [ radius, length ] > 0
→ segments >= 3
→ [ xcount, ycount ] >= 1
Topology Types:→ [ triangles, quadrilaterals, N-gons: where N = segments ]Vertex Count:→ |V| = ( xcount * segments ) + ( ycount * segments ) + 2Polygon Count:→ |P| = ( ( ( xcount - 1 ) + ycount ) * segments ) + 1Practical Examples:return scone(); // returns the default zero-argument unit scone
Additional Notes: S-CYLINDER : Generate 3D Sub-Divided-Cylinder
→ 'instantiates a 3D bi-linearly sub-divided cylindrical solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { s_cylinder, sd_cylinder, subd_cylinder, sub_divide_cylinder, sub_divided_cylinder };
Invocation Options:prefix G3 scylinder ( I segments )prefix G3 scylinder ( I xcount, I ycount )prefix G3 scylinder ( I segments, I xcount, I ycount )prefix G3 scylinder ( D radius, D length, I xcount, I ycount )prefix G3 scylinder ( D radius, D length, I segments, I xcount, I ycount )Input Arguments:•
D radius :
default = 0.5 : the radius of the scylinder (diameter = radius * 2) - a non-zero positive decimal number.•
D length :
default = 1 : the length of the scylinder (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretistion resolution or the number of circular steps) - a positive whole number greater than or equal to 3.•
I xcount :
default = 4 : the number of sub-division partitions applied to the scylinder along the x-axis (i.e. along the radius at its circular base and top) - a positive whole number greater than or equal to 1.•
I ycount :
default = 8 : the number of sub-division partitions applied to the scylinder along the y-axis (i.e. along its length or vertical height) - a positive whole number greater than or equal to 1.→ [ radius, length ] > 0
→ segments >= 3
→ [ xcount, ycount ] >= 1
Topology Types:→ [ quadrilaterals, N-gons: where N = segments ]Vertex Count:→ |V| = ( xcount * segments * 2 ) + ( ( ycount + 1 ) * segments ) + 2Polygon Count:→ |P| = ( ( ( xcount - 1 ) * 2 + ycount ) * segments ) + 2Practical Examples:return scylinder(); // returns the default zero-argument unit scylinder
Additional Notes: S-CYLICONE : Generate 3D Sub-Divided-Cylicone
→ 'instantiates a 3D bi-linearly sub-divided conic-cylindrical solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { s_cylicone, sd_cylicone, subd_cylicone, sub_divide_cylicone, sub_divided_cylicone };
Invocation Options:prefix G3 scylicone ( I segments )prefix G3 scylicone ( D lower_radius, D upper_radius )prefix G3 scylicone ( I lower_xcount, I upper_xcount, I ycount )prefix G3 scylicone ( D lower_radius, D upper_radius, I lower_xcount, I upper_xcount, I ycount )prefix G3 scylicone ( D lower_radius, D upper_radius, D length, I segments, I lower_xcount, I upper_xcount, I ycount )Input Arguments:•
D lower_radius :
default = 0.5 : the radius at the base of the scylicone - a non-zero positive decimal number.•
D upper_radius :
default = 0.25 : the radius at the top of the scylicone - a non-zero positive decimal number.•
D length :
default = 1 : the length of the scylicone (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretistion resolution or the number of circular steps) - a positive whole number greater than or equal to 3.•
I lower_xcount :
default = 4 : the number of sub-division partitions applied to the scylicone along the x-axis at its lower circular edge - a positive whole number greater than or equal to 1.•
I upper_xcount :
default = 2 : the number of sub-division partitions applied to the scylicone along the x-axis at its upper circular edge - a positive whole number greater than or equal to 1.•
I ycount :
default = 8 : the number of sub-division partitions applied to the scylicone along the y-axis (i.e. along its length or vertical height) - a positive whole number greater than or equal to 1.→ [ radius, length ] > 0
→ [ lower_radius, upper_radius ] >= 0
→ segments >= 3
→ [ lower_xcount, upper_xcount, ycount ] >= 1
Topology Types:→ [ triangles, quadrilaterals, N-gons: where N = segments ]Vertex Count:→ |V| = ( lower_xcount * segments ) + ( upper_xcount * segments ) + ( ( ycount + 1 ) * segments ) + 2Polygon Count:→ |P| = ( ( lower_xcount + upper_xcount + ycount - 2 ) * segments ) + 2Practical Examples:return scylicone(); // returns the default zero-argument unit scylicone
Additional Notes: S-CAPSULE : Generate 3D Sub-Divided-Capsule
→ 'instantiates a 3D bi-linearly sub-divided capsule solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { s_capsule, s_cap_3D, s_capsule_3D, sd_capsule, sd_cap_3D, sd_capsule_3D, subd_capsule, subd_cap_3D, subd_capsule_3D, sub_divide_capsule, sub_divide_cap_3D, sub_divide_capsule_3D, ... (+3) };
Invocation Options:prefix G3 scapsule ( I sub_divide_count )prefix G3 scapsule ( D radius, D length, I sub_divide_count )prefix G3 scapsule ( D radius, D length, I segments, I steps, I sub_divide_count )Input Arguments:•
D radius :
default = 0.25 : the radius of the scapsule's hemispheres - a non-zero positive decimal number.•
D length :
default = 0.5 : the length of the scapsule's straight-edge section (i.e. its cylindrical portion's height along the y-axis between its north and south hemispheres) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal slices (i.e. the discretisation resolution or the number of circular steps about the y-axis) - a positive whole number greater than or equal to 3.•
I steps :
default = 16 : the number of latitudinal stacks (i.e. the discretisation resolution or the number of quarter-circle steps from each of the scapsule's hemisphere's poles, to their equators) - a positive whole number greater than or equal to 1.•
I sub_divide_count :
default = 8 : the number of sub-division partitions applied to the scapsule's straight-edge section along the y-axis - a positive whole number greater than or equal to 1.→ [ radius, length ] > 0
→ segments >= 3
→ [ steps, sub_divide_count ] >= 1
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( segments * steps * 2 ) + 2 + ( ( sub_divide_count - 1 ) * segments )Polygon Count:→ |P| = ( segments * ( steps - 1 ) * 2 ) + 2 + ( sub_divide_count * segments )Practical Examples:return scapsule(); // returns the default zero-argument unit scapsule
Alias Formation Rules:Additional Notes: O-CUBE : Generate 3D Octant-Cuboid
→ 'instantiates a 3D axis-aligned octant-split cuboidal solid'
Classification:→ { instantiative };
Alias & Synonyms:→ { o_cube, o_box_3D, o_cuboid, oct_cube, oct_box_3D, oct_cuboid, octa_cube, octa_box_3D, octa_cuboid, octo_cube, octo_box_3D, octo_cuboid, ... (+6) };
Invocation Options:prefix G3 ocube ( D size )prefix G3 ocube ( D width, D height, D depth )prefix G3 ocube ( D x, D y, D z, D width, D height, D depth )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the ocube - a non-zero positive decimal number.•
D x :
default = -0.5 * width : the axis-aligned bounding-box minimum x-coordinate value of the ocube - a decimal number.•
D y :
default = -0.5 * height : the axis-aligned bounding-box minimum y-coordinate value of the ocube - a decimal number.•
D z :
default = -0.5 * depth : the axis-aligned bounding-box minimum z-coordinate value of the ocube - a decimal number.•
D width :
default = 1 : the x-axis extent of the ocube - a non-zero positive decimal number - the maximum x-coordinate value is equal to (x + width).•
D height :
default = 1 : the y-axis extent of the ocube - a non-zero positive decimal number - the maximum y-coordinate value is equal to (y + height).•
D depth :
default = 1 : the z-axis extent of the ocube - a non-zero positive decimal number - the maximum z-coordinate value is equal to (z + depth).→ [ width, height, depth, size ] > 0
Topology Types:→ [ quadrilaterals ]Vertex Count:→ |V| = 54Polygon Count:→ |P| = 24Practical Examples:return ocube(); // returns the default zero-argument unit ocube
return ocube(6); // returns a uniform ocube with width, height and depth equal to 6 units
return cuboid(1,2,3); // returns a non-uniformly scaled ocube centered about the origin - with width, height and depth equal to [1,2,3] units
return obox3D(0,-5,2,8,10,4); // returns a non-uniformly scaled, offset ocube with minimum aabb position equal to [0,-5,2] and a width, height and depth equal to [8,10,4] units
Alias Formation Rules:Additional Notes: M-O-CUBE : Generate 3D Manifold-Octant-Cuboid
→ 'instantiates a 3D axis-aligned manifold octant-split cuboidal solid'
Classification:→ { instantiative };
Alias & Synonyms:→ { m_o_cube, m_o_box_3D, m_o_cuboid, m_oct_cube, m_oct_box_3D, m_oct_cuboid, m_octa_cube, m_octa_box_3D, m_octa_cuboid, m_octo_cube, m_octo_box_3D, m_octo_cuboid, ... (+24) };
Invocation Options:prefix G3 mocube ( D size )prefix G3 mocube ( D width, D height, D depth )prefix G3 mocube ( D x, D y, D z, D width, D height, D depth )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the mocube - a non-zero positive decimal number.•
D x :
default = -0.5 * width : the axis-aligned bounding-box minimum x-coordinate value of the mocube - a decimal number.•
D y :
default = -0.5 * height : the axis-aligned bounding-box minimum y-coordinate value of the mocube - a decimal number.•
D z :
default = -0.5 * depth : the axis-aligned bounding-box minimum z-coordinate value of the mocube - a decimal number.•
D width :
default = 1 : the x-axis extent of the mocube - a non-zero positive decimal number - the maximum x-coordinate value is equal to (x + width).•
D height :
default = 1 : the y-axis extent of the mocube - a non-zero positive decimal number - the maximum y-coordinate value is equal to (y + height).•
D depth :
default = 1 : the z-axis extent of the mocube - a non-zero positive decimal number - the maximum z-coordinate value is equal to (z + depth).→ [ width, height, depth, size ] > 0
Topology Types:→ [ quadrilaterals ]Vertex Count:→ |V| = 26Polygon Count:→ |P| = 24Practical Examples:return mocube(); // returns the default zero-argument unit mocube
return mocube(6); // returns a uniform mocube with width, height and depth equal to 6 units
return cuboid(1,2,3); // returns a non-uniformly scaled mocube centered about the origin - with width, height and depth equal to [1,2,3] units
return mobox3D(0,-5,2,8,10,4); // returns a non-uniformly scaled, offset mocube with minimum aabb position equal to [0,-5,2] and a width, height and depth equal to [8,10,4] units
Alias Formation Rules:Additional Notes: Hybrid-Combinatorial-Variant Solids
B-O-CUBE : Generate 3D Beveled-Octant-Cuboid
→ 'instantiates a 3D beveled (chamfered-edge) octant-split cuboidal solid'
Classification:→ { instantiative };
Alias & Synonyms:→ { b_o_cube, b_o_box_3D, b_o_cuboid, b_oct_cube, b_oct_box_3D, b_oct_cuboid, b_octa_cube, b_octa_box_3D, b_octa_cuboid, b_octo_cube, b_octo_box_3D, b_octo_cuboid, ... (+96) };
Invocation Options:prefix G3 bocube ( D bevel_distance )prefix G3 bocube ( D size, D bevel_distance )prefix G3 bocube ( D width, D height, D depth, D bevel_distance )prefix G3 bocube ( D x, D y, D z, D width, D height, D depth, D bevel_distance )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the bocube - a non-zero positive decimal number.•
D x :
default = -0.5 * width : the axis-aligned bounding-box minimum x-coordinate value of the bocube - a decimal number.•
D y :
default = -0.5 * height : the axis-aligned bounding-box minimum y-coordinate value of the bocube - a decimal number.•
D z :
default = -0.5 * depth : the axis-aligned bounding-box minimum z-coordinate value of the bocube - a decimal number.•
D width :
default = 1 : the x-axis extent of the bocube - a non-zero positive decimal number - the maximum x-coordinate value is equal to (x + width).•
D height :
default = 1 : the y-axis extent of the bocube - a non-zero positive decimal number - the maximum y-coordinate value is equal to (y + height).•
D depth :
default = 1 : the z-axis extent of the bocube - a non-zero positive decimal number - the maximum z-coordinate value is equal to (z + depth).•
D bevel_distance :
default = 0.125 : the projective-inset distance (i.e the perpandicular chamfer or bevel length) applied to the bocube - a non-zero positive decimal number - which must be less than half of the minimum of the bocubes's width, height, depth or uniform size factor.→ [ size, width, height, depth, bevel_distance ] > 0
→ [ size, width, height, depth ] > ( bevel_distance * 2 )
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = 150Polygon Count:→ |P| = 56Practical Examples:return bocube(); // returns the default zero-argument unit bocube
Alias Formation Rules:Additional Notes: R-O-CUBE : Generate 3D Rounded-Octant-Cuboid
→ 'instantiates a 3D rounded (smooth-edged) octant-split cuboidal solid'
Classification:→ { instantiative };
Alias & Synonyms:→ { r_o_cube, r_o_box_3D, r_o_cuboid, r_oct_cube, r_oct_box_3D, r_oct_cuboid, r_octa_cube, r_octa_box_3D, r_octa_cuboid, r_octo_cube, r_octo_box_3D, r_octo_cuboid, ... (+60) };
Invocation Options:prefix G3 rocube ( D size )prefix G3 rocube ( D round_radius, I round_steps )prefix G3 rocube ( D size, D round_radius, I round_steps )prefix G3 rocube ( D width, D height, D depth, D round_radius, I round_steps )prefix G3 rocube ( D x, D y, D z, D width, D height, D depth, D round_radius, I round_steps )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the rocube - a non-zero positive decimal number.•
D x :
default = -0.5 * width : the axis-aligned bounding-box minimum x-coordinate value of the rocube - a decimal number.•
D y :
default = -0.5 * height : the axis-aligned bounding-box minimum y-coordinate value of the rocube - a decimal number.•
D z :
default = -0.5 * depth : the axis-aligned bounding-box minimum z-coordinate value of the rocube - a decimal number.•
D width :
default = 1 : the x-axis extent of the rocube - a non-zero positive decimal number - the maximum x-coordinate value is equal to (x + width).•
D height :
default = 1 : the y-axis extent of the rocube - a non-zero positive decimal number - the maximum y-coordinate value is equal to (y + height).•
D depth :
default = 1 : the z-axis extent of the rocube - a non-zero positive decimal number - the maximum z-coordinate value is equal to (z + depth).•
D round_radius :
default = 0.125 : the radius applied to round the corners and edges of the rocube - a non-zero positive decimal number which must be less than half of the minimum of the rocube's width, height, depth or uniform size factor.•
I round_steps :
default = 8 : the number of steps used to round the corners and edges of the rocube - a positive whole number greater than or equal to 1.→ [ size, width, height, depth, round_radius ] > 0
→ round_steps >= 1
→ [ size, width, height, depth ] > ( round_radius * 2 )
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( 3 * 3 * 6 ) + ( ( round_steps + 1 ) * ( 3 + 3 + 3 ) * 4 ) + ( ( ( round_steps + 1 ) * round_steps + 1 ) * 8 )Polygon Count:→ |P| = ( 2 * 2 * 2 * 3 ) + ( round_steps * ( 2 + 2 + 2 ) * 4 ) + ( round_steps * round_steps * 8 )Practical Examples:return rocube(); // returns the default zero-argument unit rocube
Alias Formation Rules:Additional Notes: B-P-CONE : Generate 3D Beveled-Polar-Cone
→ 'instantiates a 3D beveled (chamfered-edge) polar conic solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { b_p_cone, b_polar_cone, b_pole_cone, b_polar_point_cone, bevel_p_cone, bevel_polar_cone, bevel_pole_cone, bevel_polar_point_cone, beveled_p_cone, beveled_polar_cone, beveled_pole_cone, beveled_polar_point_cone, ... (+12) };
Invocation Options:prefix G3 bpcone ( D bevel_distance )prefix G3 bpcone ( I segments, D bevel_distance )prefix G3 bpcone ( D radius, D length, D bevel_distance )prefix G3 bpcone ( D radius, D length, I segments, D bevel_distance )Input Arguments:•
D radius :
default = 0.5 : the radius of the bpcone (diameter = radius * 2) - a non-zero positive decimal number.•
D length :
default = 1 : the length of the bpcone (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretistion resolution or the number of circular steps) - a positive whole number greater than or equal to 3.•
D bevel_distance :
default = 0.125 : the projective-inset distance (i.e the perpandicular chamfer or bevel length) applied to the bpcone - a non-zero positive decimal number - which must be less than the bpcone's radius and less than the bpcones's length.→ [ radius, length, bevel_distance ] > 0
→ segments >= 3
→ [ radius, length ] > bevel_distance
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( segments * 4 + 2 )Polygon Count:→ |P| = ( segments * 3 )Practical Examples:return bpcone(); // returns the default zero-argument unit bpcone
Alias Formation Rules:Additional Notes: B-P-CYLINDER : Generate 3D Beveled-Polar-Cylinder
→ 'instantiates a 3D beveled (chamfered-edge) polar cylindrical solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { b_p_cylinder, b_polar_cylinder, b_pole_cylinder, b_polar_point_cylinder, bevel_p_cylinder, bevel_polar_cylinder, bevel_pole_cylinder, bevel_polar_point_cylinder, beveled_p_cylinder, beveled_polar_cylinder, beveled_pole_cylinder, beveled_polar_point_cylinder, ... (+12) };
Invocation Options:prefix G3 bpcylinder ( D bevel_distance )prefix G3 bpcylinder ( I segments, D bevel_distance )prefix G3 bpcylinder ( D radius, D length, D bevel_distance )prefix G3 bpcylinder ( D radius, D length, I segments, D bevel_distance )Input Arguments:•
D radius :
default = 0.5 : the radius of the bpcylinder (diameter = radius * 2) - a non-zero positive decimal number.•
D length :
default = 1 : the length of the bpcylinder (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretistion resolution or the number of circular steps) - a positive whole number greater than or equal to 3.•
D bevel_distance :
default = 0.125 : the projective-inset distance (i.e the perpandicular chamfer or bevel length) applied to the bpcylinder - a non-zero positive decimal number - which must be less than the bpcylinder's radius and less than half of the bpcylinder's length.→ [ radius, length, bevel_distance ] > 0
→ segments >= 3
→ radius > bevel_distance
→ length > ( bevel_distance * 2 )
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( segments * 8 + 2 )Polygon Count:→ |P| = ( segments * 5 )Practical Examples:return bpcylinder(); // returns the default zero-argument unit bpcylinder
Alias Formation Rules:Additional Notes: B-P-CYLICONE : Generate 3D Beveled-Polar-Cylicone
→ 'instantiates a 3D beveled (chamfered-edge) polar conic-cylindrical solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { b_p_cylicone, b_polar_cylicone, b_pole_cylicone, b_polar_point_cylicone, bevel_p_cylicone, bevel_polar_cylicone, bevel_pole_cylicone, bevel_polar_point_cylicone, beveled_p_cylicone, beveled_polar_cylicone, beveled_pole_cylicone, beveled_polar_point_cylicone, ... (+12) };
Invocation Options:prefix G3 bpcylicone ( D bevel_distance )prefix G3 bpcylicone ( D lower_radius, D upper_radius, D bevel_distance )prefix G3 bpcylicone ( D lower_radius, D upper_radius, I segments, D bevel_distance )prefix G3 bpcylicone ( D lower_radius, D upper_radius, D length, I segments, D bevel_distance )Input Arguments:•
D lower_radius :
default = 0.5 : the radius at the base of the bpcylicone - a non-zero positive decimal number.•
D upper_radius :
default = 0.25 : the radius at the top of the bpcylicone - a non-zero positive decimal number.•
D length :
default = 1 : the length of the bpcylicone (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretistion resolution or the number of circular steps) - a positive whole number greater than or equal to 3.•
D bevel_distance :
default = 0.125 : the projective-inset distance (i.e the perpandicular chamfer or bevel length) applied to the bpcylicone (both its lower and upper circular edges) - a non-zero positive decimal number - which must be less than the bpcylicone's lower and upper radii and less than half of the bpcylicone's length.→ [ length, bevel_distance ] > 0
→ segments >= 3
→ [ lower_radius, upper_radius ] > bevel_distance
→ length > ( bevel_distance * 2 )
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( segments * 8 + 2 )Polygon Count:→ |P| = ( segments * 5Practical Examples:return bpcylicone(); // returns the default zero-argument unit bpcylicone
Alias Formation Rules:Additional Notes: R-P-CONE : Generate 3D Rounded-Polar-Cone
→ 'instantiates a 3D rounded/smooth polar conic solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { r_p_cone, r_polar_cone, r_pole_cone, r_polar_point_cone, rnd_p_cone, rnd_polar_cone, rnd_pole_cone, rnd_polar_point_cone, round_p_cone, round_polar_cone, round_pole_cone, round_polar_point_cone, ... (+4) };
Invocation Options:prefix G3 rpcone ( I segments )prefix G3 rpcone ( D round_radius, I round_steps )prefix G3 rpcone ( I segments, D round_radius, I round_steps )prefix G3 rpcone ( D radius, D length, D round_radius, I round_steps )prefix G3 rpcone ( D radius, D length, I segments, D round_radius, I round_steps )Input Arguments:•
D radius :
default = 0.5 : the radius of the rpcone (diameter = radius * 2) - a non-zero positive decimal number.•
D length :
default = 1 : the length of the rpcone (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretistion resolution or the number of circular steps) - a positive whole number greater than or equal to 3.•
D round_radius :
default = 0.125 : the radius applied to round the circular edge of the rpcone - a non-zero positive decimal number which must be less than the radius of the the rpcone and less than the length of the rpcone.•
I round_steps :
default = 8 : the number of steps used to round the circular edge of the rpcone (i.e. the discretisation resolution) - a positive whole number greater than or equal to 1.→ [ radius, length, round_radius ] > 0
→ segments >= 3
→ [ radius, length ] > round_radius
→ round_steps >= 1
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( ( round_steps + 1 ) * segments ) + 2Polygon Count:→ |P| = ( ( round_steps + 2 ) * segments )Practical Examples:return rpcone(); // returns the default zero-argument unit rpcone
Alias Formation Rules:Additional Notes: R-P-CYLINDER : Generate 3D Rounded-Polar-Cylinder
→ 'instantiates a 3D rounded/smooth polar cylindrical solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { r_p_cylinder, r_polar_cylinder, r_pole_cylinder, r_polar_point_cylinder, rnd_p_cylinder, rnd_polar_cylinder, rnd_pole_cylinder, rnd_polar_point_cylinder, round_p_cylinder, round_polar_cylinder, round_pole_cylinder, round_polar_point_cylinder, ... (+4) };
Invocation Options:prefix G3 rpcylinder ( I segments )prefix G3 rpcylinder ( D round_radius, I round_steps )prefix G3 rpcylinder ( I segments, D round_radius, I round_steps )prefix G3 rpcylinder ( D radius, D length, D round_radius, I round_steps )prefix G3 rpcylinder ( D radius, D length, I segments, D round_radius, I round_steps )Input Arguments:•
D radius :
default = 0.5 : the radius of the rpcylinder (diameter = radius * 2) - a non-zero positive decimal number.•
D length :
default = 1 : the length of the rpcylinder (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretistion resolution or the number of circular steps) - a positive whole number greater than or equal to 3.•
D round_radius :
default = 0.125 : the radius applied to round the circular edges of the rpcylinder - a non-zero positive decimal number which must be less than the radius of the rpcylinder and less than half the length of the rpcylinder.•
I round_steps :
default = 8 : the number of steps used to round the circular edges of the rpcylinder (i.e. the discretisation resolution) - a positive whole number greater than or equal to 1.→ [ radius, length, round_radius ] > 0
→ segments >= 3
→ radius > round_radius
→ length > ( round_radius * 2 )
→ round_steps >= 1
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( ( ( round_steps + 1 ) * 2 ) * segments ) + 2Polygon Count:→ |P| = ( round_steps * 2 + 1 + 2 ) * segmentsPractical Examples:return rpcylinder(); // returns the default zero-argument unit rpcylinder
Alias Formation Rules:Additional Notes: R-P-CYLICONE : Generate 3D Rounded-Polar-Cylinder
→ 'instantiates a 3D rounded/smooth polar conic-cylindrical solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { r_p_cylicone, r_polar_cylicone, r_pole_cylicone, r_polar_point_cylicone, rnd_p_cylicone, rnd_polar_cylicone, rnd_pole_cylicone, rnd_polar_point_cylicone, round_p_cylicone, round_polar_cylicone, round_pole_cylicone, round_polar_point_cylicone, ... (+4) };
Invocation Options:prefix G3 rpcylicone ( I segments )prefix G3 rpcylicone ( D round_radius, I round_steps )prefix G3 rpcylicone ( D lower_radius, D upper_radius, D round_radius, I round_steps )prefix G3 rpcylicone ( D lower_radius, D upper_radius, I segments, D round_radius, I round_steps )prefix G3 rpcylicone ( D lower_radius, D upper_radius, D length, I segments, D round_radius, I round_steps )Input Arguments:•
D lower_radius :
default = 0.5 : the radius at the base of the rpcylicone - a non-zero positive decimal number.•
D upper_radius :
default = 0.25 : the radius at the top of the rpcylicone - a non-zero positive decimal number.•
D length :
default = 1 : the length of the rpcylicone (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretistion resolution or the number of circular steps) - a positive whole number greater than or equal to 3.•
D round_radius :
default = 0.125 : the radius applied to round the lower and upper circular edges of the rpcylicone - a non-zero positive decimal number which must be less than both the lower and upper radii of the rpcylicone and less than half the length of the rpcylicone.•
I round_steps :
default = 8 : the number of steps used to round the lower and upper circular edges of the rpcylicone (i.e. the discretisation resolution) - a positive whole number greater than or equal to 1.→ [ length, round_radius ] > 0
→ segments >= 3
→ [ lower_radius, upper_radius ] > round_radius
→ length > ( round_radius * 2 )
→ round_steps >= 1
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( ( ( round_steps + 1 ) * 2 ) * segments ) + 2Polygon Count:→ |P| = ( round_steps * 2 + 1 + 2 ) * segmentsPractical Examples:return rpcylicone(); // returns the default zero-argument unit rpcylicone
Alias Formation Rules:Additional Notes: S-P-CONE : Generate 3D Sub-Divided-Polar-Cone
→ 'instantiates a 3D bi-linearly sub-divided polar conic solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { s_p_cone, s_polar_cone, s_pole_cone, s_polar_point_cone, sd_p_cone, sd_polar_cone, sd_pole_cone, sd_polar_point_cone, subd_p_cone, subd_polar_cone, subd_pole_cone, subd_polar_point_cone, ... (+8) };
Invocation Options:prefix G3 spcone ( I segments )prefix G3 spcone ( I xcount, I ycount )prefix G3 spcone ( I segments, I xcount, I ycount )prefix G3 spcone ( D radius, D length, I xcount, I ycount )prefix G3 spcone ( D radius, D length, I segments, I xcount, I ycount )Input Arguments:•
D radius :
default = 0.5 : the radius of the spcone (diameter = radius * 2) - a non-zero positive decimal number.•
D length :
default = 1 : the length of the spcone (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretistion resolution or the number of circular steps) - a positive whole number greater than or equal to 3.•
I xcount :
default = 4 : the number of sub-division partitions applied to the spcone along the x-axis (i.e. along the radius at its circular base) - a positive whole number greater than or equal to 1.•
I ycount :
default = 8 : the number of sub-division partitions applied to the spcone along the y-axis (i.e. along its length or vertical height) - a positive whole number greater than or equal to 1.→ [ radius, length ] > 0
→ segments >= 3
→ [ xcount, ycount ] >= 1
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( xcount * segments ) + ( ycount * segments ) + 2Polygon Count:→ |P| = ( xcount + ycount ) * segmentsPractical Examples:return spcone(); // returns the default zero-argument unit spcone
Alias Formation Rules:Additional Notes: S-P-CYLINDER : Generate 3D Sub-Divided-Polar-Cylinder
→ 'instantiates a 3D bi-linearly sub-divided polar cylindrical solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { s_p_cylinder, s_polar_cylinder, s_pole_cylinder, s_polar_point_cylinder, sd_p_cylinder, sd_polar_cylinder, sd_pole_cylinder, sd_polar_point_cylinder, subd_p_cylinder, subd_polar_cylinder, subd_pole_cylinder, subd_polar_point_cylinder, ... (+8) };
Invocation Options:prefix G3 spcylinder ( I segments )prefix G3 spcylinder ( I xcount, I ycount )prefix G3 spcylinder ( I segments, I xcount, I ycount )prefix G3 spcylinder ( D radius, D length, I xcount, I ycount )prefix G3 spcylinder ( D radius, D length, I segments, I xcount, I ycount )Input Arguments:•
D radius :
default = 0.5 : the radius of the spcylinder (diameter = radius * 2) - a non-zero positive decimal number.•
D length :
default = 1 : the length of the spcylinder (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretistion resolution or the number of circular steps) - a positive whole number greater than or equal to 3.•
I xcount :
default = 4 : the number of sub-division partitions applied to the spcylinder along the x-axis (i.e. along the radius at its circular base and top) - a positive whole number greater than or equal to 1.•
I ycount :
default = 8 : the number of sub-division partitions applied to the spcylinder along the y-axis (i.e. along its length or vertical height) - a positive whole number greater than or equal to 1.→ [ radius, length ] > 0
→ segments >= 3
→ [ xcount, ycount ] >= 1
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( xcount * segments * 2 ) + ( ( ycount + 1 ) * segments ) + 2Polygon Count:→ |P| = ( xcount * 2 + ycount ) * segmentsPractical Examples:return spcylinder(); // returns the default zero-argument unit spcylinder
Alias Formation Rules:Additional Notes: S-P-CYLICONE : Generate 3D Sub-Divided-Polar-Cylicone
→ 'instantiates a 3D bi-linearly sub-divided polar conic-cylindrical solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { s_p_cylicone, s_polar_cylicone, s_pole_cylicone, s_polar_point_cylicone, sd_p_cylicone, sd_polar_cylicone, sd_pole_cylicone, sd_polar_point_cylicone, subd_p_cylicone, subd_polar_cylicone, subd_pole_cylicone, subd_polar_point_cylicone, ... (+8) };
Invocation Options:prefix G3 spcylicone ( I segments )prefix G3 spcylicone ( D lower_radius, D upper_radius )prefix G3 spcylicone ( I lower_xcount, I upper_xcount, I ycount )prefix G3 spcylicone ( D lower_radius, D upper_radius, I lower_xcount, I upper_xcount, I ycount )prefix G3 spcylicone ( D lower_radius, D upper_radius, D length, I segments, I lower_xcount, I upper_xcount, I ycount )Input Arguments:•
D lower_radius :
default = 0.5 : the radius at the base of the spcylicone - a non-zero positive decimal number.•
D upper_radius :
default = 0.25 : the radius at the top of the spcylicone - a non-zero positive decimal number.•
D length :
default = 1 : the length of the spcylicone (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretistion resolution or the number of circular steps) - a positive whole number greater than or equal to 3.•
I lower_xcount :
default = 4 : the number of sub-division partitions applied to the spcylicone along the x-axis at its lower circular edge - a positive whole number greater than or equal to 1.•
I upper_xcount :
default = 2 : the number of sub-division partitions applied to the spcylicone along the x-axis at its upper circular edge - a positive whole number greater than or equal to 1.•
I ycount :
default = 8 : the number of sub-division partitions applied to the spcylicone along the y-axis (i.e. along its length or vertical height) - a positive whole number greater than or equal to 1.→ [ radius, length ] > 0
→ [ lower_radius, upper_radius ] >= 0
→ segments >= 3
→ [ lower_xcount, upper_xcount, ycount ] >= 1
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( xcount * segments * 2 ) + ( ( ycount + 1 ) * segments ) + 2Polygon Count:→ |P| = ( lower_xcount + upper_xcount + ycount ) * segmentsPractical Examples:return spcylicone(); // returns the default zero-argument unit spcylicone
Alias Formation Rules:Additional Notes: S-C-CAPSULE : Generate 3D Sub-Divided-Capped-Capsule
→ 'instantiates a 3D bi-linearly sub-divided flat-topped (capped) capsule solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { s_c_capsule, s_c_cap_3D, s_c_capsule_3D, s_cap_capsule, s_cap_cap_3D, s_cap_capsule_3D, s_capped_capsule, s_capped_cap_3D, s_capped_capsule_3D, sd_c_capsule, sd_c_cap_3D, sd_c_capsule_3D, ... (+33) };
Invocation Options:prefix G3 sccapsule ( I sub_divide_count )prefix G3 sccapsule ( D radius, D length, I sub_divide_count )prefix G3 sccapsule ( D radius, D length, I segments, I steps, I sub_divide_count )Input Arguments:•
D radius :
default = 0.25 : the radius of the sccapsule's hemispheres - a non-zero positive decimal number.•
D length :
default = 0.5 : the length of the sccapsule's straight-edge section (i.e. its cylindrical portion's height along the y-axis between its north and south hemispheres) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal slices (i.e. the discretisation resolution or the number of circular steps about the y-axis) - a positive whole number greater than or equal to 3.•
I steps :
default = 16 : the number of latitudinal stacks (i.e. the discretisation resolution or the number of quarter-circle steps from each of the sccapsule's hemisphere's poles, to their equators) - a positive whole number greater than or equal to 2.•
I sub_divide_count :
default = 8 : the number of sub-division partitions applied to the sccapsule's straight-edge section along the y-axis - a positive whole number greater than or equal to 2.→ [ radius, length ] > 0
→ segments >= 3
→ steps >= 2
→ sub_divide_count >= 2
Topology Types:→ [ quadrilaterals, N-gons: where N = slices ]Vertex Count:→ |V| = ( segments * steps * 2 ) + 2 + ( ( sub_divide_count - 1 ) * segments )Polygon Count:→ |P| = ( segments * steps * 2 ) + ( sub_divide_count * segments )Practical Examples:return sccapsule(); // returns the default zero-argument unit sccapsule
Alias Formation Rules:Additional Notes:If the sub_divide_count argument is less than 2 (i.e. 1) then the s-c-capsule is equivalent to a c-capsule.
S-B-CUBE : Generate 3D Sub-Divided-Beveled-Cuboid
→ 'instantiates a 3D bi-linearly sub-divided beveled (chamfered-edge) cuboidal solid'
Classification:→ { instantiative };
Alias & Synonyms:→ { s_b_cube, s_b_box_3D, s_b_cuboid, s_bevel_cube, s_bevel_box_3D, s_bevel_cuboid, s_beveled_cube, s_beveled_box_3D, s_beveled_cuboid, s_bevelled_cube, s_bevelled_box_3D, s_bevelled_cuboid, ... (+78) };
Invocation Options:prefix G3 sbcube ( D bevel_distance )prefix G3 sbcube ( D size, D bevel_distance )prefix G3 sbcube ( D size, D bevel_distance, I ncount )prefix G3 sbcube ( D width, D height, D depth, D bevel_distance )prefix G3 sbcube ( D width, D height, D depth, D bevel_distance, I bcount, I xcount, I ycount, I zcount )prefix G3 sbcube ( D x, D y, D z, D width, D height, D depth, D bevel_distance, I bcount, I xcount, I ycount, I zcount )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the sbcube - a non-zero positive decimal.•
D x :
default = -0.5 * width : the axis-aligned bounding-box minimum x-coordinate position of the sbcube - a decimal number.•
D y :
default = -0.5 * height : the axis-aligned bounding-box minimum y-coordinate position of the sbcube - a decimal number.•
D z :
default = -0.5 * depth : the axis-aligned bounding-box minimum z-coordinate position of the sbcube - a decimal number.•
D width :
default = 1 : the x-axis extent of the sbcube - a non-zero positive decimal.•
D height :
default = 1 : the y-axis extent of the sbcube - a non-zero positive decimal.•
D depth :
default = 1 : the z-axis extent of the sbcube - a non-zero positive decimal.•
D bevel_distance :
default = 0.125 : the projective-inset distance (i.e. the perpandicular chamfer or bevel length) applied to the corners and edges of the sbcube - a non-zero positive decimal number which must be less than half of the minimum of the sbcube's width, height, depth or uniform size.•
I bcount :
default = 1 : the number of sub-division partitions applied to the sbcube's beveled region - a positive integer greater than or equal to 1.•
I ncount :
default = 4 : the uniform number of sub-division partitions applied to the sbcube along the x-axis, y-axis and z-axis - a positive integer greater than or equal to 1.•
I xcount :
default = 4 : the number of sub-division partitions applied to the sbcube along the x-axis (i.e. along the sbcube's width) - a positive integer greater than or equal to 1.•
I ycount :
default = 4 : the number of sub-division partitions applied to the sbcube along the y-axis (i.e. along the sbcube's height) - a positive integer greater than or equal to 1.•
I zcount :
default = 4 : the number of sub-division partitions applied to the sbcube along the z-axis (i.e. along the sbcube's depth) - a positive integer greater than or equal to 1.→ [ width, height, depth, size, bevel_distance ] > 0
→ [ bcount, ncount, xcount, ycount, zcount ] >= 1
→ [ width, height, depth, size ] > ( bevel_distance * 2 )
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( ( xcount + 1 ) * ( ycount + 1 ) * 2 ) + ( ( xcount + 1 ) * ( zcount + 1 ) * 2 ) + ( ( ycount + 1 ) * ( zcount + 1 ) * 2 ) + ( ( bcount + 1 ) * ( xcount + 1 + ycount + 1 + zcount + 1 ) * 4 ) + ( ( bcount * 3 + 1 ) * 8 )Polygon Count:→ |P| = ( xcount * ycount * 2 ) + ( xcount * zcount * 2 ) + ( ycount * zcount * 2 ) + ( bcount * ( xcount + ycount + zcount ) * 4 ) + ( bcount * 3 * 8 )Practical Examples:return sbcube(); // returns the default zero-argument unit sbcube
Alias Formation Rules:Additional Notes: S-B-CONE : Generate 3D Sub-Divided-Beveled-Cone
→ 'instantiates a 3D bi-linearly sub-divided beveled (chamfered-edge) conic solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { s_b_cone, s_bevel_cone, s_beveled_cone, s_bevelled_cone, s_chamfer_cone, s_chamfered_cone, sd_b_cone, sd_bevel_cone, sd_beveled_cone, sd_bevelled_cone, sd_chamfer_cone, sd_chamfered_cone, ... (+18) };
Invocation Options:prefix G3 sbcone ( D radius, D length, I segments, D bevel_distance, I bcount, I xcount, I ycount )Input Arguments:•
D radius :
default = 0.5 : the radius of the sbcone - a non-zero positive decimal.•
D length :
default = 1 : the length of the sbcone (i.e. its height along the y-axis - or its vertical extent) - a non-zero positive decimal.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretisation resolution or number of circular steps) - a positive integer greater than or equal to 3.•
D bevel_distance :
default = 0.125 : the projective-inset distance (i.e. the perpandicular chamfer or bevel length) applied to the sbcone - a non-zero positive decimal which must be less than the sbcone's radius and less than the sbcone's length.•
I bcount :
default = 1 : the number of sub-division partitions applied to the sbcone's beveled region - a positive integer greater than or equal to 1.•
I xcount :
default = 4 : the number of sub-division partitions applied to the sbcone along the x-axis (i.e. along the radius at its circular base) - a positive integer greater than or equal to 1.•
I ycount :
default = 8 : the number of sub-division partitions apploed to the sbcone along the y-axis (i.e. along its length or vertical height) - a positive integer greater than or equal to 1.→ [ radius, length, bevel_distance ] > 0
→ segments >= 3
→ [ bcount, xcount, ycount ] >= 1
→ [ radius, length ] > bevel_distance
Topology Types:→ [ triangles, quadrilaterals, N-gons: where N = segments ]Vertex Count:→ |V| = ( xcount * segments ) + ( ycount * segments ) + ( ( bcount + 1 ) * segments ) + 2Polygon Count:→ |P| = ( ( ( xcount - 1 ) + ycount + bcount ) * segments ) + 1Practical Examples:return sbcone(); // returns the default zero-argument unit sbcone
Alias Formation Rules:Additional Notes: S-B-CYLINDER : Generate 3D Sub-Divided-Beveled-Cylinder
→ 'instantiates a 3D bi-linearly sub-divided beveled (chamfered-edge) cylinderical solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { s_b_cylinder, s_bevel_cylinder, s_beveled_cylinder, s_bevelled_cylinder, s_chamfer_cylinder, s_chamfered_cylinder, sd_b_cylinder, sd_bevel_cylinder, sd_beveled_cylinder, sd_bevelled_cylinder, sd_chamfer_cylinder, sd_chamfered_cylinder, ... (+18) };
Invocation Options:prefix G3 sbcylinder ( D radius, D length, I segments, D bevel_distance, I bcount, I xcount, I ycount )Input Arguments:•
D radius :
default = 0.5 : the radius of the sbcylinder - a non-zero positive decimal.•
D length :
default = 1 : the length of the sbcylinder (i.e. its height along the y-axis - or its vertical extent) - a non-zero positive decimal.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretisation resolution or number of circular steps) - a positive integer greater than or equal to 3.•
D bevel_distance :
default = 0.125 : the projective-inset distance (i.e. the perdandicular chamfer of bevel length) applied to the sbcylinder - a non-zero positive decimal which must be less than the sbcylinder's radius and less than half of the sbcylinder's length.•
I bcount :
default = 1 : the number of sub-division partitions applied to the sbcylinder's beveled regions - a positive integer greater than or equal to 1.•
I xcount :
default = 4 : the number of sub-division partitions applied to the sbcylinder along the x-axis (i.e. along the radius at its circular base and top) - a positive integer greater than or equal to 1.•
I ycount :
default = 8 : the number of sub-division partitions applied to the sbyclinder along the y-axis (i.e. along its length pr vertical height) - a positive integer greater than or equal to 1.→ [ radius, length, bevel_distance ] > 0
→ segments >= 3
→ [ bcount, xcount, ycount ] >= 1
→ radius > bevel_distance
→ length > ( bevel_distance * 2 )
Topology Types:→ [ quadrilaterals, N-gons: where N = segments ]Vertex Count:→ |V| = ( xcount * segments * 2 ) + ( ( ycount + 1 ) * segments ) + ( ( bcount + 1 ) * segments * 2 ) + 2Polygon Count:→ |P| = ( ( ( xcount - 1 ) * 2 ) + ycount + ( bcount * 2 ) ) * segments + 2Practical Examples:return sbcylinder(); // returns the default zero-argument unit sbcylinder
Alias Formation Rules:Additional Notes: S-B-CYLICONE : Generate 3D Sub-Divided-Beveled-Cylicone
→ 'instantiates a 3D bi-linearly sub-divided beveled (chamfered-edge) conic-cylindrical solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { s_b_cylicone, s_bevel_cylicone, s_beveled_cylicone, s_bevelled_cylicone, s_chamfer_cylicone, s_chamfered_cylicone, sd_b_cylicone, sd_bevel_cylicone, sd_beveled_cylicone, sd_bevelled_cylicone, sd_chamfer_cylicone, sd_chamfered_cylicone, ... (+18) };
Invocation Options:prefix G3 sbcylicone ( D lower_radius, D upper_radius, D length, I segments, D bevel_distance, I bcount, I lower_xcount, I upper_xcount, I ycount )Input Arguments:•
D lower_radius :
default = 0.5 : the radius at the base of the sbcylicone - a positive decimal greater than zero and greater than the beveling distance.•
D upper_radius :
default = 0.5 : the radius at the top of the sbcylicone - a positive decimal greater than zero and greater than the beveling distance.•
D length :
default = 1 : the length of the sbcylicone (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretisation resolution or the number circular steps) - a positive integer greater than or equal to 3.•
D bevel_distance :
default = 0.125 : the projective-inset distance (i.e. the perpandicular chamfer or bevel length) applied to the sbcylicone (both its lower and upper circular edges) - a non-zero positive decimal number - which must be less than the sbcylicone's lower and upper radii and less than half of the sbcylicone's length.•
I bcount :
default = 1 : the number of sub-division partitions applied to the sbcylicone's beveled regions - a positive integer greater than or equal to 1.•
I lower_xcount :
default = 4 : the number of sub-division partitions applied to the sbcylicone along the x-axis at its lower circular edge - a positive integer greater than or equal to 1.•
I upper_xcount :
default = 2 : the number of sub-division partitions applied to the sbcylicone along the x-axis at its upper circular edge - a positive integer greater than or equal to 1.•
I ycount :
default = 8 : the number of sub-division partitions applied to the sbcylicone along the y-axis (i.e. along its length or vertical height) - a positive integer greater than or equal to 1.→ [ length, bevel_distance ] > 0
→ [ lower_radius, upper_radius ] >= 0
→ segments >= 3
→ [ bcount, lower_xcount, upper_xcount, ycount ] >= 1
→ [ lower_radius, upper_radius ] > bevel_distance
→ length > ( bevel_distance * 2 )
Topology Types:→ [ triangles, quadrilaterals, N-gons: where N = segments ]Vertex Count:→ |V| = ( lower_xcount * segments ) + ( upper_xcount * segments ) + ( ( ycount + 1 ) * segments ) + ( ( bcount + 1 ) * segments * 2 ) + 2Polygon Count:→ |P| = ( ( lower_xcount - 1 ) + ( upper_xcount - 1 ) + ycount + ( bcount * 2 ) ) * segments + 2Practical Examples:return sbcylicone(); // returns the default zero-argument unit sbcylicone
Alias Formation Rules:Additional Notes: S-R-CUBE : Generate 3D Sub-Divided-Rounded-Cuboid
→ 'instantiates a 3D bi-linearly sub-divided rounded (smooth-edged) cuboidal solid'
Classification:→ { instantiative };
Alias & Synonyms:→ { s_r_cube, s_r_box_3D, s_r_cuboid, s_rnd_cube, s_rnd_box_3D, s_rnd_cuboid, s_round_cube, s_round_box_3D, s_round_cuboid, s_rounded_cube, s_rounded_box_3D, s_rounded_cuboid, ... (+48) };
Invocation Options:prefix G3 srcube ( D round_radius, I round_steps )prefix G3 srcube ( D size, D round_radius, I round_steps )prefix G3 srcube ( D size, D round_radius, I round_steps, I ncount )prefix G3 srcube ( D width, D height, D depth, D round_radius, I round_steps )prefix G3 srcube ( D width, D height, D depth, D round_radius, I round_steps, I xcount, I ycount, I zcount )prefix G3 srcube ( D x, D y, D z, D width, D height, D depth, D round_radius, I round_steps, I xcount, I ycount, I zcount )Input Arguments:•
D size :
default = 1 : the uniform scale factor applied to the srcube - a non-zero positive decimal.•
D x :
default = -0.5 * width : the bounding-box minimum x-coordinate position of the srcube.•
D y :
default = -0.5 * height : the bounding-box minimum y-coordinate position of the srcube.•
D z :
default = -0.5 * depth : the bounding-box minimum z-coordinate position of the srcube.•
D width :
default = 1 : the x-axis extent of the srcube - a non-zero positive decimal.•
D height :
default = 1 : the y-axis extent of the srcube - a non-zero positive decimal.•
D depth :
default = 1 : the z-axis extent of the srcube - a non-zero positive decimal.•
D round_radius :
default = 0.125 : the radius applied to round the corners and edges of the srcube - a non-zero positive decimal which should be less than half of the minimum of the srcube's width, height, depth or uniform size factor.•
I round_steps :
default = 8 : the number of discretisation steps used to round the corners and edges of the srcube - a positive whole number greater than or equal to 1.•
I ncount :
default = 4 : the uniform number of sub-division partitions applied to the srcube along the x-axis, y-axis and z-axis - a positive integer greater than or equal to 1.•
I xcount :
default = 4 : the number of sub-division partitions applied to the srcube along the x-axis (i.e. along the srcube's width) - a positive integer greater than or equal to 1.•
I ycount :
default = 4 : the number of sub-division partitions applied to the srcube along the y-axis (i.e. along the srcube's height) - a positive integer greater than or equal to 1.•
I zcount :
default = 4 : the number of sub-division partitions applied to the srcube along the z-axis (i.e. along the srcube's depth) - a positive integer greater than or equal to 1.→ [ width, height, depth, size, round_radius ] > 0
→ [ round_steps, ncount, xcount, ycount, zcount ] >= 1
→ [ width, height, depth, size ] > ( round_radius * 2 )
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( ( xcount + 1 ) * ( ycount + 1 ) * 2 ) + ( ( xcount + 1 ) * ( zcount + 1 ) * 2 ) + ( ( ycount + 1 ) * ( zcount + 1 ) * 2 ) + ( ( round_steps + 1 ) * ( xcount + 1 + ycount + 1 + zcount + 1 ) * 4 ) + ( ( ( round_steps + 1 ) * round_steps + 1 ) * 8 )Polygon Count:→ |P| = ( xcount * ycount * 2 ) + ( xcount * zcount * 2 ) + ( ycount * zcount * 2 ) + ( round_steps * ( xcount + ycount + zcount ) * 4 ) + ( round_steps * round_steps * 8 )Practical Examples:return srcube(); // returns the default zero-argument unit srcube
Alias Formation Rules:Additional Notes: S-R-CONE : Generate 3D Sub-Divided-Rounded-Cone
→ 'instantiates a 3D bi-linearly sub-divided rounded (smooth-edged) conic solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { s_r_cone, s_rnd_cone, s_round_cone, s_rounded_cone, sd_r_cone, sd_rnd_cone, sd_round_cone, sd_rounded_cone, subd_r_cone, subd_rnd_cone, subd_round_cone, subd_rounded_cone, ... (+8) };
Invocation Options:prefix G3 srcone ( D radius, D length, I segments, D round_radius, I round_steps, I xcount, I ycount )Input Arguments:•
D radius :
default = 0.5 : the radius of the srcone - a non-zero positive decimal.•
D length :
default = 1 : the length of the srcone - (i.e. its height along the y-axis - or its vertical extent) - a non-zero positive decimal.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretisation resolution or number of circular steps) - a positive integer greater than or equal to 3.•
D round_radius :
default = 0.125 : the radius applied to round the circular edge of the srcone - a non-zero positive decimal which should be less than both the srcone's radius and length.•
I round_steps :
default = 8 : the number of discretisation steps used to round the circle edge of the srcone - a positive whole number greater than or equal to 1.•
I xcount :
default = 4 : the number of sub-division partitions applied to the srcone along the x-axis (i.e. along the radius at its circular base) - a positive integer greater than or equal to 1.•
I ycount :
default = 8 : the number of sub-division partitions applied to the srcone along the y-axis (i.e. along its length or vertical height) - a positive integer greater than or equal to 1.→ [ radius, length, round_radius ] > 0
→ segments >= 3
→ [ round_steps, xcount, ycount ] >= 1
→ [ radius, length ] > round_radius
Topology Types:→ [ triangles, quadrilaterals, N-gons: where N = segments ]Vertex Count:→ |V| = ( xcount * segments ) + ( ycount * segments ) + ( ( round_steps + 1 ) * segments ) + 2Polygon Count:→ |P| = ( ( ( xcount - 1 ) + ycount + round_steps ) * segments ) + 1Practical Examples:return srcone(); // returns the default zero-argument unit srcone
Alias Formation Rules:Additional Notes: S-R-CYLINDER : Generate 3D Sub-Divided-Rounded-Cylinder
→ 'instantiates a 3D bi-linearly sub-divided rounded (smooth-edged) cylindrical solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { s_r_cylinder, s_rnd_cylinder, s_round_cylinder, s_rounded_cylinder, sd_r_cylinder, sd_rnd_cylinder, sd_round_cylinder, sd_rounded_cylinder, subd_r_cylinder, subd_rnd_cylinder, subd_round_cylinder, subd_rounded_cylinder, ... (+8) };
Invocation Options:prefix G3 srcylinder ( D radius, D length, I segments, D round_radius, I round_steps, I xcount, I ycount )Input Arguments:•
D radius :
default = 0.5 : the radius of the srcylinder - a non-zero positive decimal.•
D length :
default = 1 : the length of the srcylinder - (i.e. its height along the y-axis - or its vertical extent) - a non-zero positive decimal.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretisation resolution or number of circular steps) - a positive integer greater than or equal to 3.•
D round_radius :
default = 0.125 : the radius applied to round the circular edges of the srcylinder - a non-zero positive decimal which should be less than the srcylinder's radius and less than half of the srcylinder's length.•
I round_steps :
default = 8 : the number of discretisation steps used to round the circular edges of the srcylinder - a positive integer greater than or equal to 1.•
I xcount :
default = 4 : the number of sub-division partitions applied to the srcylinder along the x-axis (i.e. along the radius at its circular base and top) - a positive integer greater than or equal to 1.•
I ycount :
default = 8 : the number of sub-division partitions applied to the srcylinder along the y-axis (i.e. along its length or vertical height) - a positive integer greater than or equal to 1.→ [ radius, length, round_radius ] > 0
→ segments >= 3
→ [ round_steps, xcount, ycount ] >= 1
→ radius > round_radius
→ length > ( round_radius * 2 )
Topology Types:→ [ quadrilaterals, N-gons: where N = segments ]Vertex Count:→ |V| = ( xcount * segments * 2 ) + ( ( ycount + 1 ) * segments ) + ( ( round_steps + 1 ) * segments * 2 ) + 2Polygon Count:→ |P| = ( ( ( xcount - 1 ) * 2 ) + ycount + ( round_steps * 2 ) ) * segments + 2Practical Examples:return srcylinder(); // returns the default zero-argument unit srcylinder
Alias Formation Rules:Additional Notes: S-R-CYLICONE : Generate 3D Sub-Divided-Rounded-Cylicone
→ 'instantiates a 3D bi-linearly sub-divided rounded (smooth-edged) conic-cylindrical solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { s_r_cylicone, s_rnd_cylicone, s_round_cylicone, s_rounded_cylicone, sd_r_cylicone, sd_rnd_cylicone, sd_round_cylicone, sd_rounded_cylicone, subd_r_cylicone, subd_rnd_cylicone, subd_round_cylicone, subd_rounded_cylicone, ... (+8) };
Invocation Options:prefix G3 srcylicone ( D lower_radius, D upper_radius, D length, I segments, D round_radius, I round_steps, I lower_xcount, I upper_xcount, I ycount )Input Arguments:•
D lower_radius :
default = 0.5 : the radius at the base of the srcylicone - a positive decimal greater than zero and greater than the rounding radius.•
D upper_radius :
default = 0.5 : the radius at the top of the srcylicone - a positive decimal greater than zero and greater than the rounding radius.•
D length :
default = 1 : the length of the srcylicone (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretisation resolution or the number of circular steps) - a positive integer greater than or equal to 3.•
D round_radius :
default = 0.125 : the radius applied to round the circular edges of the srcylicone - a non-zero positive decimal which should be less than the srcylicone's lower and upper radii and less than half of the srcylicone's length.•
I round_steps :
default = 8 : the number of discretisation steps used to round the circular edges of the srcylicone - a positive integer greater than or equal to 1.•
I lower_xcount :
default = 4 : the number of sub-division partitions applied to the srcylicone along the x-axis at its lower circular edge - a positive integer greater than or equal to 1.•
I upper_xcount :
default = 2 : the number of sub-division partitions applied to the srcylicone along the x-axis at its upper circular edge - a positive integer greater than or equal to 1.•
I ycount :
default = 8 : the number of sub-division partitions applied to the srcylicone along the y-axis (i.e. along its length or vertical height) - a positive integer greater than or equal to 1.→ [ length, round_radius ] > 0
→ [ lower_radius, upper_radius ] >= 0
→ segments >= 3
→ [ round_steps, lower_xcount, upper_xcount, ycount ] >= 1
→ [ lower_radius, upper_radius ] > round_radius
→ length > ( round_radius * 2 )
Topology Types:→ [ triangles, quadrilaterals, N-gons: where N = segments ]Vertex Count:→ |V| = ( lower_xcount * segments ) + ( upper_xcount * segments ) + ( ( ycount + 1 ) * segments ) + ( ( round_steps + 1 ) * segments * 2 ) + 2Polygon Count:→ |P| = ( ( lower_xcount - 1 ) + ( upper_xcount - 1 ) + ycount + ( round_steps * 2 ) ) * segments + 2Practical Examples:return srcylicone(); // returns the default zero-argument unit srcylicone
Alias Formation Rules:Additional Notes: S-B-P-CONE : Generate 3D Sub-Divided-Beveled-Polar-Cone
→ 'instantiates a 3D bi-linearly sub-divided beveled (chamfered-edge) polar conic solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { s_b_p_cone, s_b_polar_cone, s_b_pole_cone, s_b_polar_point_cone, s_bevel_p_cone, s_bevel_polar_cone, s_bevel_pole_cone, s_bevel_polar_point_cone, s_beveled_p_cone, s_beveled_polar_cone, s_beveled_pole_cone, s_beveled_polar_point_cone, ... (+108) };
Invocation Options:prefix G3 sbpcone ( D radius, D length, I segments, D bevel_distance, I bcount, I xcount, I ycount )Input Arguments:•
D radius :
default = 0.5 : the radius of the sbpcone - a non-zero positive decimal.•
D length :
default = 1 : the length of the sbpcone (i.e. its height along the y-axis - or its vertical extent) - a non-zero positive decimal.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretisation resolution or number of circular steps) - a positive integer greater than or equal to 3.•
D bevel_distance :
default = 0.125 : the projective-inset distance (i.e. the perpandicular chamfer or bevel length) applied to the sbpcone - a non-zero positive decimal which must be less than the sbpcone's radius and less than the sbpcone's length.•
I bcount :
default = 1 : the number of sub-division partitions applied to the sbpcone's beveled region - a positive integer greater than or equal to 1.•
I xcount :
default = 4 : the number of sub-division partitions applied to the sbpcone along the x-axis (i.e. along the radius at its circular base) - a positive integer greater than or equal to 1.•
I ycount :
default = 8 : the number of sub-division partitions apploed to the sbpcone along the y-axis (i.e. along its length or vertical height) - a positive integer greater than or equal to 1.→ [ radius, length, bevel_distance ] > 0
→ segments >= 3
→ [ bcount, xcount, ycount ] >= 1
→ [ radius, length ] > bevel_distance
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( xcount * segments ) + ( ycount * segments ) + ( ( bcount + 1 ) * segments ) + 2Polygon Count:→ |P| = ( xcount + ycount + bcount ) * segmentsPractical Examples:return sbpcone(); // returns the default zero-argument unit sbpcone
Alias Formation Rules:Additional Notes: S-B-P-CYLINDER : Generate 3D Sub-Divided-Beveled-Polar-Cylinder
→ 'instantiates a 3D bi-linearly sub-divided beveled (chamfered-edge) polar cylindrical solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { s_b_p_cylinder, s_b_polar_cylinder, s_b_pole_cylinder, s_b_polar_point_cylinder, s_bevel_p_cylinder, s_bevel_polar_cylinder, s_bevel_pole_cylinder, s_bevel_polar_point_cylinder, s_beveled_p_cylinder, s_beveled_polar_cylinder, s_beveled_pole_cylinder, s_beveled_polar_point_cylinder, ... (+108) };
Invocation Options:prefix G3 sbpcylinder ( D radius, D length, I segments, D bevel_distance, I bcount, I xcount, I ycount )Input Arguments:•
D radius :
default = 0.5 : the radius of the sbpcylinder - a non-zero positive decimal.•
D length :
default = 1 : the length of the sbpcylinder (i.e. its height along the y-axis - or its vertical extent) - a non-zero positive decimal.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretisation resolution or number of circular steps) - a positive integer greater than or equal to 3.•
D bevel_distance :
default = 0.125 : the projective-inset distance (i.e. the perdandicular chamfer of bevel length) applied to the sbpcylinder - a non-zero positive decimal which must be less than the sbpcylinder's radius and less than half of the sbpcylinder's length.•
I bcount :
default = 1 : the number of sub-division partitions applied to the sbpcylinder's beveled regions - a positive integer greater than or equal to 1.•
I xcount :
default = 4 : the number of sub-division partitions applied to the sbpcylinder along the x-axis (i.e. along the radius at its circular base and top) - a positive integer greater than or equal to 1.•
I ycount :
default = 8 : the number of sub-division partitions applied to the sbyclinder along the y-axis (i.e. along its length pr vertical height) - a positive integer greater than or equal to 1.→ [ radius, length, bevel_distance ] > 0
→ segments >= 3
→ [ bcount, xcount, ycount ] >= 1
→ radius > bevel_distance
→ length > ( bevel_distance * 2 )
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( xcount * segments * 2 ) + ( ( ycount + 1 ) * segments ) + ( ( bcount + 1 ) * segments * 2 ) + 2Polygon Count:→ |P| = ( ( xcount * 2 ) + ycount + ( bcount * 2 ) ) * segmentsPractical Examples:return sbpcylinder(); // returns the default zero-argument unit sbpcylinder
Alias Formation Rules:Additional Notes: S-B-P-CYLICONE : Generate 3D Sub-Divided-Beveled-Polar-Cylicone
→ 'instantiates a 3D bi-linearly sub-divided beveled (chamfered-edge) polar conic-cylindrical solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { s_b_p_cylicone, s_b_polar_cylicone, s_b_pole_cylicone, s_b_polar_point_cylicone, s_bevel_p_cylicone, s_bevel_polar_cylicone, s_bevel_pole_cylicone, s_bevel_polar_point_cylicone, s_beveled_p_cylicone, s_beveled_polar_cylicone, s_beveled_pole_cylicone, s_beveled_polar_point_cylicone, ... (+108) };
Invocation Options:prefix G3 sbpcylicone ( D lower_radius, D upper_radius, D length, I segments, D bevel_distance, I bcount, I lower_xcount, I upper_xcount, I ycount )Input Arguments:•
D lower_radius :
default = 0.5 : the radius at the base of the sbpcylicone - a positive decimal greater than zero and greater than the beveling distance.•
D upper_radius :
default = 0.5 : the radius at the top of the sbpcylicone - a positive decimal greater than zero and greater than the beveling distance.•
D length :
default = 1 : the length of the sbpcylicone (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretisation resolution or the number circular steps) - a positive integer greater than or equal to 3.•
D bevel_distance :
default = 0.125 : the projective-inset distance (i.e. the perpandicular chamfer or bevel length) applied to the sbpcylicone (both its lower and upper circular edges) - a non-zero positive decimal number - which must be less than the sbpcylicone's lower and upper radii and less than half of the sbpcylicone's length.•
I bcount :
default = 1 : the number of sub-division partitions applied to the sbpcylicone's beveled regions - a positive integer greater than or equal to 1.•
I lower_xcount :
default = 4 : the number of sub-division partitions applied to the sbpcylicone along the x-axis at its lower circular edge - a positive integer greater than or equal to 1.•
I upper_xcount :
default = 2 : the number of sub-division partitions applied to the sbpcylicone along the x-axis at its upper circular edge - a positive integer greater than or equal to 1.•
I ycount :
default = 8 : the number of sub-division partitions applied to the sbpcylicone along the y-axis (i.e. along its length or vertical height) - a positive integer greater than or equal to 1.→ [ length, bevel_distance ] > 0
→ [ lower_radius, upper_radius ] >= 0
→ segments >= 3
→ [ bcount, lower_xcount, upper_xcount, ycount ] >= 1
→ [ lower_radius, upper_radius ] > bevel_distance
→ length > ( bevel_distance * 2 )
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( lower_xcount * segments ) + ( upper_xcount * segments ) + ( ( ycount + 1 ) * segments ) + ( ( bcount + 1 ) * segments * 2 ) + 2Polygon Count:→ |P| = ( lower_xcount + upper_xcount + ycount + ( bcount * 2 ) ) * segmentsPractical Examples:return sbpcylicone(); // returns the default zero-argument unit sbpcylicone
Alias Formation Rules:Additional Notes: S-R-P-CONE : Generate 3D Sub-Divided-Rounded-Polar-Cone
→ 'instantiates a 3D bi-linearly sub-divided rounded (smooth-edged) polar conic solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { s_r_p_cone, s_r_polar_cone, s_r_pole_cone, s_r_polar_point_cone, s_rnd_p_cone, s_rnd_polar_cone, s_rnd_pole_cone, s_rnd_polar_point_cone, s_round_p_cone, s_round_polar_cone, s_round_pole_cone, s_round_polar_point_cone, ... (+68) };
Invocation Options:prefix G3 srpcone ( D radius, D length, I segments, D round_radius, I round_steps, I xcount, I ycount )Input Arguments:•
D radius :
default = 0.5 : the radius of the srpcone - a non-zero positive decimal.•
D length :
default = 1 : the length of the srpcone - (i.e. its height along the y-axis - or its vertical extent) - a non-zero positive decimal.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretisation resolution or number of circular steps) - a positive integer greater than or equal to 3.•
D round_radius :
default = 0.125 : the radius applied to round the circular edge of the srpcone - a non-zero positive decimal which should be less than both the srpcone's radius and length.•
I round_steps :
default = 8 : the number of discretisation steps used to round the circle edge of the srpcone - a positive whole number greater than or equal to 1.•
I xcount :
default = 4 : the number of sub-division partitions applied to the srpcone along the x-axis (i.e. along the radius at its circular base) - a positive integer greater than or equal to 1.•
I ycount :
default = 8 : the number of sub-division partitions applied to the srpcone along the y-axis (i.e. along its length or vertical height) - a positive integer greater than or equal to 1.→ [ radius, length, round_radius ] > 0
→ segments >= 3
→ [ round_steps, xcount, ycount ] >= 1
→ [ radius, length ] > round_radius
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( xcount * segments ) + ( ycount * segments ) + ( ( round_steps + 1 ) * segments ) + 2Polygon Count:→ |P| = ( xcount + ycount + round_steps ) * segmentsPractical Examples:return srpcone(); // returns the default zero-argument unit srpcone
Alias Formation Rules:Additional Notes: S-R-P-CYLINDER : Generate 3D Sub-Divided-Rounded-Polar-Cylinder
→ 'instantiates a 3D bi-linearly sub-divided rounded (smooth-edge) polar cylindrical solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { s_r_p_cylinder, s_r_polar_cylinder, s_r_pole_cylinder, s_r_polar_point_cylinder, s_rnd_p_cylinder, s_rnd_polar_cylinder, s_rnd_pole_cylinder, s_rnd_polar_point_cylinder, s_round_p_cylinder, s_round_polar_cylinder, s_round_pole_cylinder, s_round_polar_point_cylinder, ... (+68) };
Invocation Options:prefix G3 srpcylinder ( D radius, D length, I segments, D round_radius, I round_steps, I xcount, I ycount )Input Arguments:•
D radius :
default = 0.5 : the radius of the srpcylinder - a non-zero positive decimal.•
D length :
default = 1 : the length of the srpcylinder - (i.e. its height along the y-axis - or its vertical extent) - a non-zero positive decimal.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretisation resolution or number of circular steps) - a positive integer greater than or equal to 3.•
D round_radius :
default = 0.125 : the radius applied to round the circular edges of the srpcylinder - a non-zero positive decimal which should be less than the srpcylinder's radius and less than half of the srpcylinder's length.•
I round_steps :
default = 8 : the number of discretisation steps used to round the circular edges of the srpcylinder - a positive integer greater than or equal to 1.•
I xcount :
default = 4 : the number of sub-division partitions applied to the srpcylinder along the x-axis (i.e. along the radius at its circular base and top) - a positive integer greater than or equal to 1.•
I ycount :
default = 8 : the number of sub-division partitions applied to the srpcylinder along the y-axis (i.e. along its length or vertical height) - a positive integer greater than or equal to 1.→ [ radius, length, round_radius ] > 0
→ segments >= 3
→ [ round_steps, xcount, ycount ] >= 1
→ radius > round_radius
→ length > ( round_radius * 2 )
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( xcount * segments * 2 ) + ( ( ycount + 1 ) * segments ) + ( ( round_steps + 1 ) * segments * 2 ) + 2Polygon Count:→ |P| = ( ( xcount * 2 ) + ycount + ( round_steps * 2 ) ) * segmentsPractical Examples:return srpcylinder(); // returns the default zero-argument unit srpcylinder
Alias Formation Rules:Additional Notes: S-R-P-CYLICONE : Generate 3D Sub-Divided-Rounded-Polar-Cylicone
→ 'instantiates a 3D bi-linearly sub-divided rounded (smooth-edge) polar conic-cylindrical solid centered at the origin (0,0,0)'
Classification:→ { instantiative };
Alias & Synonyms:→ { s_r_p_cylicone, s_r_polar_cylicone, s_r_pole_cylicone, s_r_polar_point_cylicone, s_rnd_p_cylicone, s_rnd_polar_cylicone, s_rnd_pole_cylicone, s_rnd_polar_point_cylicone, s_round_p_cylicone, s_round_polar_cylicone, s_round_pole_cylicone, s_round_polar_point_cylicone, ... (+68) };
Invocation Options:prefix G3 srpcylicone ( D lower_radius, D upper_radius, D length, I segments, D round_radius, I round_steps, I lower_xcount, I upper_xcount, I ycount )Input Arguments:•
D lower_radius :
default = 0.5 : the radius at the base of the srpcylicone - a positive decimal greater than zero and greater than the rounding radius.•
D upper_radius :
default = 0.5 : the radius at the top of the srpcylicone - a positive decimal greater than zero and greater than the rounding radius.•
D length :
default = 1 : the length of the srpcylicone (i.e. its height along the y-axis or its vertical extent) - a non-zero positive decimal number.•
I segments :
default = 32 : the number of longitudinal segments (i.e. the discretisation resolution or the number of circular steps) - a positive integer greater than or equal to 3.•
D round_radius :
default = 0.125 : the radius applied to round the circular edges of the srpcylicone - a non-zero positive decimal which should be less than the srpcylicone's lower and upper radii and less than half of the srpcylicone's length.•
I round_steps :
default = 8 : the number of discretisation steps used to round the circular edges of the srpcylicone - a positive integer greater than or equal to 1.•
I lower_xcount :
default = 4 : the number of sub-division partitions applied to the srpcylicone along the x-axis at its lower circular edge - a positive integer greater than or equal to 1.•
I upper_xcount :
default = 2 : the number of sub-division partitions applied to the srpcylicone along the x-axis at its upper circular edge - a positive integer greater than or equal to 1.•
I ycount :
default = 8 : the number of sub-division partitions applied to the srpcylicone along the y-axis (i.e. along its length or vertical height) - a positive integer greater than or equal to 1.→ [ length, round_radius ] > 0
→ [ lower_radius, upper_radius ] >= 0
→ segments >= 3
→ [ round_steps, lower_xcount, upper_xcount, ycount ] >= 1
→ [ lower_radius, upper_radius ] > round_radius
→ length > ( round_radius * 2 )
Topology Types:→ [ triangles, quadrilaterals ]Vertex Count:→ |V| = ( lower_xcount * segments ) + ( upper_xcount * segments ) + ( ( ycount + 1 ) * segments ) + ( ( round_steps + 1 ) * segments * 2 ) + 2Polygon Count:→ |P| = ( lower_xcount + upper_xcount + ycount + ( bcount * 2 ) ) * segmentsPractical Examples:return srpcylicone(); // returns the default zero-argument unit srpcylicone
Alias Formation Rules:Additional Notes: 
