Interface for rNd. More...

#include <stdint.h>

Classes
struct	rNd_rvec
	A N-vector. More...

struct	rNd_dvec
	An integer N-vector for grid indexing. More...

struct	rNd_plane
	A hyperplane. More...

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

struct	rNd_poly
	An `RND_DIM`-dimensional polytope. More...

Macros
#define	RND_DIM 4

#define	RND_MAX_VERTS 1024

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

typedef int32_t	rNd_int
	Integer type used for indexing. More...

typedef int64_t	rNd_long

Functions
void	rNd_clip (rNd_poly poly, rNd_plane planes, rNd_int nplanes)
	Clip a polytope against an arbitrary number of hyperplanes (find its intersection with a set of half-spaces). More...

void	rNd_reduce (rNd_poly poly, rNd_real moments, rNd_int polyorder)
	Integrate a polynomial density over a polytope. Still under development. More...

rNd_int	rNd_is_good (rNd_poly *poly)
	Checks a polytope to see if it is a valid `RND_DIM`-polyhedral graph, by testing compliance with Balinski's theorem. More...

rNd_real	rNd_orient (rNd_rvec verts[RND_DIM+1])
	Get the signed volume of the `RND_DIM`-simplex defined by the input vertices. More...

void	rNd_print (rNd_poly *poly)
	Prints the vertices and connectivity of a polytope. For debugging. More...

void	rNd_rotate (rNd_poly *poly, rNd_real theta, rNd_int ax1, rNd_int ax2)
	Rotate a polytope about one axis. More...

void	rNd_translate (rNd_poly *poly, rNd_rvec shift)
	Translate a polytope. More...

void	rNd_scale (rNd_poly *poly, rNd_rvec scale)
	Scale a polytope. More...

void	rNd_shear (rNd_poly *poly, rNd_real shear, rNd_int axb, rNd_int axs)
	Shear a polytope. Each vertex undergoes the transformation `pos.xyz[axb] += shear*pos.xyz[axs]`. More...

void	rNd_affine (rNd_poly *poly, rNd_real mat[RND_DIM+1][RND_DIM+1])
	Apply a general affine transformation to a polytope. More...

void	rNd_init_simplex (rNd_poly *poly, rNd_rvec verts[RND_DIM+1])
	Initialize a polytope as an `RND_DIM`-simplex. More...

void	rNd_init_box (rNd_poly *poly, rNd_rvec rbounds[2])
	Initialize a polytope as an axis-aligned hyperrectangle. More...

Detailed Description

Interface for rNd.

Author: Devon Powell

Date: 31 August 2015

Macro Definition Documentation

◆ RND_DIM

#define RND_DIM 4

◆ RND_MAX_VERTS

#define RND_MAX_VERTS 1024

Typedef Documentation

◆ rNd_int

typedef int32_t rNd_int

Integer type used for indexing.

◆ rNd_long

typedef int64_t rNd_long

◆ rNd_real

typedef double rNd_real

Real type specifying the precision to be used in calculations.

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

Function Documentation

◆ rNd_affine()

void rNd_affine	(	rNd_poly *	poly,
		rNd_real	mat[RND_DIM+1][RND_DIM+1]
	)

Apply a general affine transformation to a polytope.

Parameters

[in,out]	poly	The polytope to transform.
[in]	mat	The `(RND_DIM+1)*(RND_DIM+1)` homogeneous transformation matrix.

◆ rNd_clip()

void rNd_clip	(	rNd_poly *	poly,
		rNd_plane *	planes,
		rNd_int	nplanes
	)

Clip a polytope against an arbitrary number of hyperplanes (find its intersection with a set of half-spaces).

Parameters

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

◆ rNd_init_box()

void rNd_init_box	(	rNd_poly *	poly,
		rNd_rvec	rbounds[2]
	)

Initialize a polytope as an axis-aligned hyperrectangle.

Parameters

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

◆ rNd_init_simplex()

void rNd_init_simplex	(	rNd_poly *	poly,
		rNd_rvec	verts[RND_DIM+1]
	)

Initialize a polytope as an RND_DIM-simplex.

Parameters

[out]	poly	The polytope to initialize.
[in]	verts	An array of `RND_DIM+1` vectors, giving the vertices of the simplex.

◆ rNd_is_good()

rNd_int rNd_is_good ( rNd_poly * poly )

Checks a polytope to see if it is a valid RND_DIM-polyhedral graph, by testing compliance with Balinski's theorem.

Parameters

[in] poly The polytope to check.

Returns: 1 if the polytope is valid, 0 if not.

◆ rNd_orient()

rNd_real rNd_orient ( rNd_rvec verts[RND_DIM+1] )

Get the signed volume of the RND_DIM-simplex defined by the input vertices.

Parameters

[in] verts RND_DIM+1 vertices defining a simplex from which to calculate a volume.

Returns: The signed volume of the input simplex.

◆ rNd_print()

void rNd_print ( rNd_poly * poly )

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

Parameters

[in] poly The polytope to print.

◆ rNd_reduce()

void rNd_reduce	(	rNd_poly *	poly,
		rNd_real *	moments,
		rNd_int	polyorder
	)

Integrate a polynomial density over a polytope. Still under development.

Parameters

[in]	poly	The polytope over which to integrate.
[in]	polyorder	Order of the polynomial density field. 0 for constant (1 moment), 1 for linear (`RND_DIM+1` moments), etc.
[in,out]	moments	Array to be filled with the integration results, up to the specified `polyorder`. Order of moments is row-major.

◆ rNd_rotate()

void rNd_rotate	(	rNd_poly *	poly,
		rNd_real	theta,
		rNd_int	ax1,
		rNd_int	ax2
	)

Rotate a polytope about one axis.

Parameters

[in,out]	poly	The polytope to rotate.
[in]	theta	The angle, in radians, by which to rotate the polytope.
[in]	ax1	Along with `ax2`, the plane in which to rotate the polytope.
[in]	ax2	Along with `ax1`, the plane in which to rotate the polytope.

◆ rNd_scale()

void rNd_scale	(	rNd_poly *	poly,
		rNd_rvec	scale
	)

Scale a polytope.

Parameters

[in,out]	poly	The polytope to scale.
[in]	scale	The factor by which to scale the polytope along each dimension.

◆ rNd_shear()

void rNd_shear	(	rNd_poly *	poly,
		rNd_real	shear,
		rNd_int	axb,
		rNd_int	axs
	)

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

Parameters

[in,out]	poly	The polytope to shear.
[in]	shear	The factor by which to shear the polytope.
[in]	axb	The axis along which to shear the polytope.
[in]	axs	The axis across which to shear the polytope.

◆ rNd_translate()

void rNd_translate	(	rNd_poly *	poly,
		rNd_rvec	shift
	)

Translate a polytope.

Parameters

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

Classes

Macros

Typedefs

Functions

Detailed Description

Macro Definition Documentation

◆ RND_DIM

◆ RND_MAX_VERTS

Typedef Documentation

◆ rNd_int

◆ rNd_long

◆ rNd_real

Function Documentation

◆ rNd_affine()

◆ rNd_clip()

◆ rNd_init_box()

◆ rNd_init_simplex()

◆ rNd_is_good()

◆ rNd_orient()

◆ rNd_print()

◆ rNd_reduce()

◆ rNd_rotate()

◆ rNd_scale()

◆ rNd_shear()

◆ rNd_translate()