Polyhedrons

Polyhedron mathematical functions; 3-polytope. More...

Collaboration diagram for Polyhedrons:

Files
file	polyhedron.scad
	Polyhedron shapes, conversions, properties, and tests functions..

Properties
function	polyhedron_area (c, f)
	Compute the surface area of a polyhedron in a Euclidean 3d-space. More...
function	polyhedron_tf_volume (c, f)
	Compute the volume of a triangulated polyhedron in a Euclidean 3d-space. More...
function	polyhedron_tf_centroid (c, f)
	Compute the center of mass of a triangulated polyhedron in a Euclidean 3d-space. More...

Detailed Description

Polyhedron mathematical functions; 3-polytope.

Requires:
include <omdl-base.scad>;

Function Documentation

polyhedron_area()

function polyhedron_area	(	c	,
		f
	)

Compute the surface area of a polyhedron in a Euclidean 3d-space.

Parameters

c	<coords-3d> A list of 3d cartesian coordinates [[x, y, z], ...].
f	<integer-list-list> A list of faces that enclose the shape where each face is a list of coordinate indexes.

Returns

<decimal> The surface area of the given polyhedron.

polyhedron_tf_centroid()

function polyhedron_tf_centroid	(	c	,
		f
	)

Compute the center of mass of a triangulated polyhedron in a Euclidean 3d-space.

Parameters

c	<coords-3d> A list of 3d cartesian coordinates [[x, y, z], ...].
f	<integer-list-3-list> A list of triangular faces that enclose the polyhedron where each face is a list of three coordinate indexes.

Returns

<point-3d> The center of mass of the given polyhedron.

See Wikipedia for more information on centroid determined via the divergence theorem and midpoint quadrature.

Note

All faces are assumed to be a union of triangles oriented clockwise from the outside inwards.

polyhedron_tf_volume()

function polyhedron_tf_volume	(	c	,
		f
	)

Compute the volume of a triangulated polyhedron in a Euclidean 3d-space.

Parameters

c	<coords-3d> A list of 3d cartesian coordinates [[x, y, z], ...].
f	<integer-list-3-list> A list of triangular faces that enclose the polyhedron where each face is a list of three coordinate indexes.

Returns

<decimal> The volume of the given polyhedron.

See Wikipedia for more information on volumes determined using the divergence theorem.

Note

All faces are assumed to be a union of triangles oriented clockwise from the outside inwards.