#include <stdint.h>
#include <stdlib.h>

Classes
struct	r3d_rvec3
	Vector struct. More...

struct	r3d_dvec3
	Integer vector struct for grid indexing. More...

struct	r3d_plane
	A plane. More...

struct	r3d_vertex
	A doubly-linked vertex. More...

struct	r3d_poly
	A polyhedron. More...

struct	r3d_brep

Macros
#define	R3D_MAX_VERTS 512

#define	R3D_NUM_MOMENTS(order) ((order + 1) * (order + 2) * (order + 3) / 6)
	Integrate a polynomial density over a polyhedron using simplicial decomposition. Uses the fast recursive method of Koehl (2012) to carry out the integration. More...

Typedefs
typedef double	r3d_real
	Real type specifying the precision to be used in calculations. More...

typedef int32_t	r3d_int
	Integer types used for indexing. More...

typedef int64_t	r3d_long

typedef struct r3d_brep	r3d_brep

Functions
void	r3d_clip (r3d_poly poly, r3d_plane planes, r3d_int nplanes)
	Clip a polyhedron against an arbitrary number of clip planes (find its intersection with a set of half-spaces). More...

void	r3d_split (r3d_poly inpolys, r3d_int npolys, r3d_plane plane, r3d_poly out_pos, r3d_poly *out_neg)
	Splits a list of polyhedra across a single plane. More...

void	r3d_reduce (r3d_poly poly, r3d_real moments, r3d_int polyorder)

r3d_int	r3d_is_good (r3d_poly *poly)
	Checks a polyhedron to see if all vertices have three valid edges, that all vertices are pointed to by three other vertices, and that there are no sets of two vertices with more than one edge between them. Overall, checks that the graph is 3-vertex-connected (an `O(nverts^2)` operation), which is required by Steinitz' theorem to be a valid polyhedral graph. More...

r3d_rvec3	r3d_poly_center (r3d_poly *poly)
	Calculates a center of a polyhedron. More...

void	r3d_shift_moments (r3d_real *moments, r3d_int polyorder, r3d_rvec3 vc)
	Adjust moments according to the shift of polyhedron vertices to the origin. More...

r3d_real	r3d_orient (r3d_rvec3 *verts)
	Get the signed volume of the tetrahedron defined by the input vertices. More...

void	r3d_print (r3d_poly *poly)
	Prints the vertices and connectivity of a polyhedron. For debugging. More...

void	r3d_rotate (r3d_poly *poly, r3d_real theta, r3d_int axis)
	Rotate a polyhedron about one axis. More...

void	r3d_translate (r3d_poly *poly, r3d_rvec3 shift)
	Translate a polyhedron. More...

void	r3d_scale (r3d_poly *poly, r3d_real scale)
	Scale a polyhedron. More...

void	r3d_shear (r3d_poly *poly, r3d_real shear, r3d_int axb, r3d_int axs)
	Shear a polyhedron. Each vertex undergoes the transformation `pos.xyz[axb] += shear*pos.xyz[axs]`. More...

void	r3d_affine (r3d_poly *poly, r3d_real mat[4][4])
	Apply a general affine transformation to a polyhedron. More...

void	r3d_init_tet (r3d_poly poly, r3d_rvec3 verts)
	Initialize a polyhedron as a tetrahedron. More...

void	r3d_init_box (r3d_poly poly, r3d_rvec3 rbounds)
	Initialize a polyhedron as an axis-aligned cube. More...

void	r3d_init_poly (r3d_poly poly, r3d_rvec3 vertices, r3d_int numverts, r3d_int *faceinds, r3d_int numvertsperface, r3d_int numfaces)
	Initialize a general polyhedron from a full boundary description. Can use `r3d_is_good` to check that the output is valid. More...

void	r3d_tet_faces_from_verts (r3d_plane faces, r3d_rvec3 verts)
	Get four faces (unit normals and distances to the origin) from a four-vertex description of a tetrahedron. More...

void	r3d_box_faces_from_verts (r3d_plane faces, r3d_rvec3 rbounds)
	Get six faces (unit normals and distances to the origin) from a two-vertex description of an axis-aligned box. More...

void	r3d_poly_faces_from_verts (r3d_plane faces, r3d_rvec3 vertices, r3d_int numverts, r3d_int *faceinds, r3d_int numvertsperface, r3d_int numfaces)
	Get all faces (unit normals and distances to the origin) from a full boundary description of a polyhedron. More...

void	r3d_init_brep (r3d_poly poly, r3d_brep brep, r3d_int numcomponents)
	Convert from R3D's internal vertex-edge format to the boundary representation. More...

void	r3d_print_brep (r3d_brep **brep, r3d_int numcomponents)
	Prints the boundary representation of an array of polyhedons given in boundary representation form. For debugging. More...

void	r3d_free_brep (r3d_brep **brep, r3d_int numcomponents)
	Free all the memory associated with the boundary representation array. More...

Macro Definition Documentation

◆ R3D_MAX_VERTS

#define R3D_MAX_VERTS 512

◆ R3D_NUM_MOMENTS

#define R3D_NUM_MOMENTS ( order ) ((order + 1) * (order + 2) * (order + 3) / 6)

Integrate a polynomial density over a polyhedron using simplicial decomposition. Uses the fast recursive method of Koehl (2012) to carry out the integration.

Parameters

[in]	poly	The polyhedron over which to integrate.
[in]	polyorder	Order of the polynomial density field. 0 for constant (1 moment), 1 for linear (4 moments), 2 for quadratic (10 moments), etc.
[in,out]	moments	Array to be filled with the integration results, up to the specified `polyorder`. Must be at least `(polyorder+1)(polyorder+2)(polyorder+3)/6` long. A conventient macro, `R3D_NUM_MOMENTS()` is provided to compute the number of moments for a given order. Order of moments is row-major, i.e. `1`, `x`, `y`, `z`, `x^2`, `xy`, `xz`, `y^2`, `yz`, `z^2`, `x^3`, `x^2y`...

Typedef Documentation

◆ r3d_brep

typedef struct r3d_brep r3d_brep

create a type for the boundary representation

◆ r3d_int

typedef int32_t r3d_int

Integer types used for indexing.

◆ r3d_long

typedef int64_t r3d_long

◆ r3d_real

typedef double r3d_real

Real type specifying the precision to be used in calculations.

Default is double. float precision is enabled by compiling with -DSINGLE_PRECISION.

Function Documentation

◆ r3d_affine()

void r3d_affine	(	r3d_poly *	poly,
		r3d_real	mat[4][4]
	)

Apply a general affine transformation to a polyhedron.

Parameters

[in,out]	poly	The polyhedron to transform.
[in]	mat	The 4x4 homogeneous transformation matrix by which to transform the vertices of the polyhedron.

◆ r3d_box_faces_from_verts()

void r3d_box_faces_from_verts	(	r3d_plane *	faces,
		r3d_rvec3 *	rbounds
	)

Get six faces (unit normals and distances to the origin) from a two-vertex description of an axis-aligned box.

Parameters

[out]	faces	Array of six planes defining the faces of the box.
[in]	rbounds	Array of two vectors defining the bounds of the axis-aligned box

◆ r3d_clip()

void r3d_clip	(	r3d_poly *	poly,
		r3d_plane *	planes,
		r3d_int	nplanes
	)

Clip a polyhedron against an arbitrary number of clip planes (find its intersection with a set of half-spaces).

Parameters

[in,out]	poly	The polyehdron to be clipped.
[in]	planes	An array of planes against which to clip this polyhedron.
[in]	nplanes	The number of planes in the input array.

◆ r3d_free_brep()

void r3d_free_brep	(	r3d_brep **	brep,
		r3d_int	numcomponents
	)

Free all the memory associated with the boundary representation array.

Parameters

[in]	brep	Pointer to an array of boundary representations.
[in]	numcomponents	The number of disconnected components in the boundary representation array.

◆ r3d_init_box()

void r3d_init_box	(	r3d_poly *	poly,
		r3d_rvec3 *	rbounds
	)

Initialize a polyhedron as an axis-aligned cube.

Parameters

[out]	poly	The polyhedron to initialize.
[in]	rbounds	An array of two vectors, giving the lower and upper corners of the box.

◆ r3d_init_brep()

void r3d_init_brep	(	r3d_poly *	poly,
		r3d_brep **	brep,
		r3d_int *	numcomponents
	)

Convert from R3D's internal vertex-edge format to the boundary representation.

Parameters

[in]	poly	Pointer to a single R3D polyhedron.
[out]	brep	Pointer to an array of boundary representations that will hold the different boundary representations for the different components.
[out]	numcomponents	Pointer to an integer that will hold the number of determined components.

◆ r3d_init_poly()

void r3d_init_poly	(	r3d_poly *	poly,
		r3d_rvec3 *	vertices,
		r3d_int	numverts,
		r3d_int **	faceinds,
		r3d_int *	numvertsperface,
		r3d_int	numfaces
	)

Initialize a general polyhedron from a full boundary description. Can use r3d_is_good to check that the output is valid.

Parameters

[out]	poly	The polyhedron to initialize.
[in]	vertices	Array of length `numverts` giving the vertices of the input polyhedron.
[in]	numverts	Number of vertices in the input polyhedron.
[in]	faceinds	Connectivity array, giving the indices of vertices in the order they appear around each face of the input polyhedron.
[in]	numvertsperface	An array of length `numfaces` giving the number of vertices for each face of the input polyhedron.
[in]	numfaces	Number of faces in the input polyhedron.

◆ r3d_init_tet()

void r3d_init_tet	(	r3d_poly *	poly,
		r3d_rvec3 *	verts
	)

Initialize a polyhedron as a tetrahedron.

Parameters

[out]	poly	The polyhedron to initialize.
[in]	verts	An array of four vectors, giving the vertices of the tetrahedron.

◆ r3d_is_good()

r3d_int r3d_is_good ( r3d_poly * poly )

Checks a polyhedron to see if all vertices have three valid edges, that all vertices are pointed to by three other vertices, and that there are no sets of two vertices with more than one edge between them. Overall, checks that the graph is 3-vertex-connected (an O(nverts^2) operation), which is required by Steinitz' theorem to be a valid polyhedral graph.

Parameters

[in] poly The polyhedron to check.

Returns: 1 if the polyhedron is good, 0 if not.

◆ r3d_orient()

r3d_real r3d_orient ( r3d_rvec3 * verts )

Get the signed volume of the tetrahedron defined by the input vertices.

Parameters

[in] verts Four vertices defining a tetrahedron from which to calculate a volume.

Returns: The signed volume of the input tetrahedron.

◆ r3d_poly_center()

r3d_rvec3 r3d_poly_center ( r3d_poly * poly )

Calculates a center of a polyhedron.

Parameters

[in] poly The polygon to check.

Returns: coordinates of a polygon center.

◆ r3d_poly_faces_from_verts()

void r3d_poly_faces_from_verts	(	r3d_plane *	faces,
		r3d_rvec3 *	vertices,
		r3d_int	numverts,
		r3d_int **	faceinds,
		r3d_int *	numvertsperface,
		r3d_int	numfaces
	)

Get all faces (unit normals and distances to the origin) from a full boundary description of a polyhedron.

Parameters

[out]	faces	Array of planes of length `numfaces` defining the faces of the polyhedron.
[in]	vertices	Array of length `numverts` giving the vertices of the input polyhedron.
[in]	numverts	Number of vertices in the input polyhedron.
[in]	faceinds	Connectivity array, giving the indices of vertices in the order they appear around each face of the input polyhedron.
[in]	numvertsperface	An array of length `numfaces` giving the number of vertices for each face of the input polyhedron.
[in]	numfaces	Number of faces in the input polyhedron.

◆ r3d_print()

void r3d_print ( r3d_poly * poly )

Prints the vertices and connectivity of a polyhedron. For debugging.

Parameters

[in] poly The polyhedron to print.

◆ r3d_print_brep()

void r3d_print_brep	(	r3d_brep **	brep,
		r3d_int	numcomponents
	)

Prints the boundary representation of an array of polyhedons given in boundary representation form. For debugging.

Parameters

[in]	brep	Pointer to an array of boundary representations.
[in]	numcomponents	The number of disconnected components in the boundary representation array.

◆ r3d_reduce()

void r3d_reduce	(	r3d_poly *	poly,
		r3d_real *	moments,
		r3d_int	polyorder
	)

◆ r3d_rotate()

void r3d_rotate	(	r3d_poly *	poly,
		r3d_real	theta,
		r3d_int	axis
	)

Rotate a polyhedron about one axis.

Parameters

[in,out]	poly	The polyehdron to rotate.
[in]	theta	The angle, in radians, by which to rotate the polyhedron.
[in]	axis	The axis (0, 1, or 2 corresponding to x, y, or z) about which to rotate the polyhedron.

◆ r3d_scale()

void r3d_scale	(	r3d_poly *	poly,
		r3d_real	scale
	)

Scale a polyhedron.

Parameters

[in,out]	poly	The polyhedron to scale.
[in]	shift	The factor by which to scale the polyhedron.

◆ r3d_shear()

void r3d_shear	(	r3d_poly *	poly,
		r3d_real	shear,
		r3d_int	axb,
		r3d_int	axs
	)

Shear a polyhedron. Each vertex undergoes the transformation pos.xyz[axb] += shear*pos.xyz[axs].

Parameters

[in,out]	poly	The polyhedron to shear.
[in]	shear	The factor by which to shear the polyhedron.
[in]	axb	The axis (0, 1, or 2 corresponding to x, y, or z) along which to shear the polyhedron.
[in]	axs	The axis (0, 1, or 2 corresponding to x, y, or z) across which to shear the polyhedron.

◆ r3d_shift_moments()

void r3d_shift_moments	(	r3d_real *	moments,
		r3d_int	polyorder,
		r3d_rvec3	vc
	)

Adjust moments according to the shift of polyhedron vertices to the origin.

Parameters

[in,out]	moments	The moments of the shifted polygon.
[in]	polyorder	Order of the polygon.
[in]	vc	Coordinates of the polygon center, which are used to shift the polygon.

◆ r3d_split()

void r3d_split	(	r3d_poly *	inpolys,
		r3d_int	npolys,
		r3d_plane	plane,
		r3d_poly *	out_pos,
		r3d_poly *	out_neg
	)

Splits a list of polyhedra across a single plane.

Parameters

[in]	inpolys	Array of input polyhedra to be split
[in]	npolys	The number of input polyhedra
[in]	plane	The plane about which to split the input polys
[out]	out_pos	The output array of fragments on the positive side of the clip plane. Must be at least npolys long. out_pos[i] and out_neg[i] correspond to inpolys[i], where out_neg[i].nverts or out.pos[i].nverts are set to zero if the poly lies entirely in the positive or negative side of the plane, respectively.
[out]	out_neg	The output array of fragments on the negitive side of the clip plane. Must be at least npolys long.

◆ r3d_tet_faces_from_verts()

void r3d_tet_faces_from_verts	(	r3d_plane *	faces,
		r3d_rvec3 *	verts
	)

Get four faces (unit normals and distances to the origin) from a four-vertex description of a tetrahedron.

Parameters

[out]	faces	Array of four planes defining the faces of the tetrahedron.
[in]	verts	Array of four vectors defining the vertices of the tetrahedron.

◆ r3d_translate()

void r3d_translate	(	r3d_poly *	poly,
		r3d_rvec3	shift
	)

Translate a polyhedron.

Parameters

[in,out]	poly	The polyhedron to translate.
[in]	shift	The vector by which to translate the polyhedron.

Classes

Macros

Typedefs

Functions

Macro Definition Documentation

◆ R3D_MAX_VERTS

◆ R3D_NUM_MOMENTS

Typedef Documentation

◆ r3d_brep

◆ r3d_int

◆ r3d_long

◆ r3d_real

Function Documentation

◆ r3d_affine()

◆ r3d_box_faces_from_verts()

◆ r3d_clip()

◆ r3d_free_brep()

◆ r3d_init_box()

◆ r3d_init_brep()

◆ r3d_init_poly()

◆ r3d_init_tet()

◆ r3d_is_good()

◆ r3d_orient()

◆ r3d_poly_center()

◆ r3d_poly_faces_from_verts()

◆ r3d_print()

◆ r3d_print_brep()

◆ r3d_reduce()

◆ r3d_rotate()

◆ r3d_scale()

◆ r3d_shear()

◆ r3d_shift_moments()

◆ r3d_split()

◆ r3d_tet_faces_from_verts()

◆ r3d_translate()