Polytope

Polygon and polyhedron tools. More...

Collaboration diagram for Polytope:

Files
file	polytope.scad
	Polygon and polyhedron tools.

Functions
module	polytope_number (c, f, e, vi=true, fi=true, ei=true, sp=false, ts, th, to, tr=0)
	Label the vertices, paths, and edges of a polytope. More...
module	polytope_frame (c, f, e, vi=true, fi=true, ei=true, vc=1, fc=2, ec=0)
	Assemble a polytope skeletal frame using child objects. More...
module	polytope_bounding_box (c, f, a)
	The 3d or 2d bounding box shape for a polytope. More...

Detailed Description

Polygon and polyhedron tools.

Requires:
include <omdl-base.scad>;
include <tools/align.scad>;
include <tools/polytope.scad>;

Function Documentation

polytope_bounding_box()

module polytope_bounding_box	(	c	,
		f	,
		a
	)

The 3d or 2d bounding box shape for a polytope.

Parameters

c	<coords-3d | coords-2d> A list of 3d or 2d coordinate points.
f	<<integer-list>-list> A list of faces (or paths) that enclose the shape where each face is a list of coordinate indexes.
a	<decimal-list-1:3 | decimal> The box padding. A list of lengths to equally pad the box dimensions.

Generates: (1) the 3d box shape that completely encloses the defined 3d polyhedron with the box sides oriented parallel to the coordinate axes. Or: (2) the 2d box shape that exactly encloses the defined 2d polygon with the box sides oriented parallel to the coordinate axes. When f is not given, the listed order of the coordinates c establishes the path.

Bounding box example script

    include <omdl-base.scad>;
    include <database/geometry/polyhedra/archimedean.scad>;
    include <tools/polytope.scad>;
 
    tc = dtc_polyhedra_archimedean;
    tr = dtr_polyhedra_archimedean;
    id = "truncated_cuboctahedron";
 
    c = table_get_value(tr, tc, id, "c");
    f = table_get_value(tr, tc, id, "f");
 
    polyhedron(c, f);
    %polytope_bounding_box(c,f );
 
    // end_include

Bounding box example diagram

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See also

polytope_limits for warning about secondary Shapes.

Definition at line 1028 of file polytope.scad.

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polytope_frame()

module polytope_frame	(	c	,
		f	,
		e	,
		vi	= true,
		fi	= true,
		ei	= true,
		vc	= 1,
		fc	= 2,
		ec	= 0
	)

Assemble a polytope skeletal frame using child objects.

Parameters

c	<coords-3d | coords-2d> A list of 3d or 2d coordinate points.
f	<<integer-list>-list> A list of faces (or paths) that enclose the shape where each face is a list of coordinate indexes.
e	<<integer-list-2>-list> A list of edges where each edge is a list of two coordinate indexes.
vi	<index> Vertex index. An index sequence specification.
fi	<index> Face index. An index sequence specification.
ei	<index> Edge index. An index sequence specification.
vc	<integer> Vertex child object index.
fc	<integer> Face child object index.
ec	<integer> Edge child object index.

Construct a skeletal frame for a given polytope. A 2d child object is linearly extruded along specified edges of the polytope to form the frame. Additional 3d child objects can be centered on specified vertices and/or the mean coordinates of specified faces.

To disable a child assignment to the vertices, faces, or edges, use an index that is less than zero or greater than the number of children. Parameter f is optional for polygons. When it is not given, the listed order of the coordinates c establishes the polygon path. When e is not specified, it is computed from f using polytope_faces2edges().

A. Framing example script

    include <omdl-base.scad>;
    include <tools/align.scad>;
    include <units/coordinate.scad>;
    include <database/geometry/polyhedra/cupolas.scad>;
    include <tools/polytope.scad>;
 
    tc = dtc_polyhedra_cupolas;
    tr = dtr_polyhedra_cupolas;
    id = "pentagonal_cupola";
 
    c = table_get_value(tr, tc, id, "c");
    f = table_get_value(tr, tc, id, "f");
 
    v1 = coordinate_scale3d_csc(c, 100);
    v2 = coordinate_scale3d_csc(c, 100, true);
 
    repeat_grid(2, 225, center=true, $fn=36)
    {
      polytope_frame(v1, f) {circle(r=4); color("grey") sphere(r=6);}
      polytope_frame(v2, f) {circle(r=4); color("grey") sphere(r=6);}
    }
 
    // end_include

A. Framing example diagram

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B. Framing example script

    include <omdl-base.scad>;
    include <tools/align.scad>;
    include <units/coordinate.scad>;
    include <database/geometry/polyhedra/archimedean.scad>;
    include <tools/polytope.scad>;
 
    tc = dtc_polyhedra_archimedean;
    tr = dtr_polyhedra_archimedean;
    id = "truncated_cuboctahedron";
 
    c = table_get_value(tr, tc, id, "c");
    f = table_get_value(tr, tc, id, "f");
    v = coordinate_scale3d_csc(c, 100);
 
    polytope_frame(v, f, fi="even", $fn = 36)
    {
      circle(r=2);
      color("grey") sphere(r=4);
      color("red") star3d(20);
    }
 
    polytope_frame(v, f, fi="odd", fc=0, vc=-1, ec=-1)
    color("blue") star3d(20);
 
    %polyhedron(v, f);
 
    // end_include

B. Framing example diagram

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Definition at line 788 of file polytope.scad.

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polytope_number()

module polytope_number	(	c	,
		f	,
		e	,
		vi	= true,
		fi	= true,
		ei	= true,
		sp	= false,
		ts	,
		th	,
		to	,
		tr	= 0
	)

Label the vertices, paths, and edges of a polytope.

Parameters

c	<coords-3d | coords-2d> A list of 3d or 2d coordinate points.
f	<<integer-list>-list> A list of faces (or paths) that enclose the shape where each face is a list of coordinate indexes.
e	<<integer-list-2>-list> A list of edges where each edge is a list of two coordinate indexes.
vi	<index> Vertex index. An index sequence specification.
fi	<index> Face index. An index sequence specification.
ei	<index> Edge index. An index sequence specification.
sp	<boolean> Show polyhedron shape.
ts	<decimal> The text size override.
th	<decimal> The text extrusion height override.
to	<vector-3d | vector-2d> The text offset override.
tr	<decimal-list-1:3 | decimal> The text rotation (in degrees).

Label the vertices, paths, and edges of a polytope. Parameter f is optional for polygons. When it is not given, the listed order of the coordinates c establishes the polygon path. When e is not specified, it is computed from f using polytope_faces2edges().

Numbering example script

    include <omdl-base.scad>;
    include <tools/align.scad>;
    include <units/coordinate.scad>;
    include <database/geometry/polyhedra/johnson.scad>;
    include <tools/polytope.scad>;
 
    tc = dtc_polyhedra_johnson;
    tr = dtr_polyhedra_johnson;
    id = "metagyrate_diminished_rhombicosidodecahedron";
 
    c = table_get_value(tr, tc, id, "c");
    f = table_get_value(tr, tc, id, "f");
    v = coordinate_scale3d_csc(c, 100);
 
    polytope_number(v, f, sp=true, $fn = 36);
 
    // end_include

Numbering example diagram

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Definition at line 347 of file polytope.scad.

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