#include <stdint.h>

Classes
struct	r2d_rvec2
	Vector struct. More...

struct	r2d_dvec2
	Integer vector struct for grid indexing. More...

struct	r2d_plane
	A plane. More...

struct	r2d_vertex
	A doubly-linked vertex. More...

struct	r2d_poly
	A polygon. More...

Macros
#define	R2D_MAX_VERTS 256

#define	R2D_NUM_MOMENTS(order) ((order+1)*(order+2)/2)
	Integrate a polynomial density over a polygon using simplicial decomposition. Uses the fast recursive method of Koehl (2012) to carry out the integration. More...

Typedefs
typedef double	r2d_real
	Real type specifying the precision to be used in calculations. More...

typedef int32_t	r2d_int
	Integer types used for indexing. More...

typedef int64_t	r2d_long

Functions
void	r2d_clip (r2d_poly poly, r2d_plane planes, r2d_int nplanes)
	Clip a polygon against an arbitrary number of clip planes (find its intersection with a set of half-spaces). More...

void	r2d_split (r2d_poly inpolys, r2d_int npolys, r2d_plane plane, r2d_poly out_pos, r2d_poly *out_neg)
	Splits a list of polygons across a single plane. More...

void	r2d_reduce (r2d_poly poly, r2d_real moments, r2d_int polyorder)

r2d_int	r2d_is_good (r2d_poly *poly)
	Checks a polygon to see if all vertices have two valid edges, that all vertices are pointed to by two other vertices, and that there are no vertices that point to themselves. More...

r2d_rvec2	r2d_poly_center (r2d_poly *poly)
	Calculates a center of a polygon. More...

void	r2d_shift_moments (r2d_real *moments, r2d_int polyorder, r2d_rvec2 vc)
	Adjust moments according to the shift of polygon vertices to the origin. More...

r2d_real	r2d_orient (r2d_rvec2 pa, r2d_rvec2 pb, r2d_rvec2 pc)
	Get the signed volume of the triangle defined by the input vertices. More...

void	r2d_print (r2d_poly *poly)
	Prints the vertices and connectivity of a polygon. For debugging. More...

void	r2d_rotate (r2d_poly *poly, r2d_real theta)
	Rotate a polygon about the origin. More...

void	r2d_translate (r2d_poly *poly, r2d_rvec2 shift)
	Translate a polygon. More...

void	r2d_scale (r2d_poly *poly, r2d_real scale)
	Scale a polygon. More...

void	r2d_shear (r2d_poly *poly, r2d_real shear, r2d_int axb, r2d_int axs)
	Shear a polygon. Each vertex undergoes the transformation `pos.xy[axb] += shear*pos.xy[axs]`. More...

void	r2d_affine (r2d_poly *poly, r2d_real mat[3][3])
	Apply a general affine transformation to a polygon. More...

void	r2d_init_box (r2d_poly poly, r2d_rvec2 rbounds)
	Initialize a polygon as an axis-aligned box. More...

void	r2d_init_poly (r2d_poly poly, r2d_rvec2 vertices, r2d_int numverts)
	Initialize a (simply-connected) general polygon from a list of vertices. Can use `r2d_is_good` to check that the output is valid. More...

void	r2d_box_faces_from_verts (r2d_plane faces, r2d_rvec2 rbounds)
	Get four faces (unit normals and distances to the origin) from a two-vertex description of an axis-aligned box. More...

void	r2d_poly_faces_from_verts (r2d_plane faces, r2d_rvec2 vertices, r2d_int numverts)
	Get all faces (unit normals and distances to the origin) from a general boundary description of a polygon. More...

Macro Definition Documentation

◆ R2D_MAX_VERTS

#define R2D_MAX_VERTS 256

◆ R2D_NUM_MOMENTS

#define R2D_NUM_MOMENTS ( order ) ((order+1)*(order+2)/2)

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

Parameters

[in]	poly	The polygon 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)/2` long. A conventient macro, `R2D_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`, `x^2`, `xy`, `y^2`, `x^3`, `x^2*y`...

Typedef Documentation

◆ r2d_int

typedef int32_t r2d_int

Integer types used for indexing.

◆ r2d_long

typedef int64_t r2d_long

◆ r2d_real

typedef double r2d_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

◆ r2d_affine()

void r2d_affine	(	r2d_poly *	poly,
		r2d_real	mat[3][3]
	)

Apply a general affine transformation to a polygon.

Parameters

[in,out]	poly	The polygon to transform.
[in]	mat	The 3x3 homogeneous transformation matrix by which to transform the vertices of the polygon.

◆ r2d_box_faces_from_verts()

void r2d_box_faces_from_verts	(	r2d_plane *	faces,
		r2d_rvec2 *	rbounds
	)

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

Parameters

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

◆ r2d_clip()

void r2d_clip	(	r2d_poly *	poly,
		r2d_plane *	planes,
		r2d_int	nplanes
	)

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

Parameters

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

◆ r2d_init_box()

void r2d_init_box	(	r2d_poly *	poly,
		r2d_rvec2 *	rbounds
	)

Initialize a polygon as an axis-aligned box.

Parameters

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

◆ r2d_init_poly()

void r2d_init_poly	(	r2d_poly *	poly,
		r2d_rvec2 *	vertices,
		r2d_int	numverts
	)

Initialize a (simply-connected) general polygon from a list of vertices. Can use r2d_is_good to check that the output is valid.

Parameters

[out]	poly	The polygon to initialize.
[in]	vertices	Array of length `numverts` giving the vertices of the input polygon, in counterclockwise order.
[in]	numverts	Number of vertices in the input polygon.

◆ r2d_is_good()

r2d_int r2d_is_good ( r2d_poly * poly )

Checks a polygon to see if all vertices have two valid edges, that all vertices are pointed to by two other vertices, and that there are no vertices that point to themselves.

Parameters

[in] poly The polygon to check.

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

◆ r2d_orient()

r2d_real r2d_orient	(	r2d_rvec2	pa,
		r2d_rvec2	pb,
		r2d_rvec2	pc
	)

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

Parameters

[in] pa,pb,pc Vertices defining a triangle from which to calculate an area.

Returns: The signed volume of the input triangle.

◆ r2d_poly_center()

r2d_rvec2 r2d_poly_center ( r2d_poly * poly )

Calculates a center of a polygon.

Parameters

[in] poly The polygon to check.

Returns: coordinates of a polygon center.

◆ r2d_poly_faces_from_verts()

void r2d_poly_faces_from_verts	(	r2d_plane *	faces,
		r2d_rvec2 *	vertices,
		r2d_int	numverts
	)

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

Parameters

[out]	faces	Array of planes of length `numverts` defining the faces of the polygon.
[in]	vertices	Array of length `numverts` giving the vertices of the input polygon, in counterclockwise order.
[in]	numverts	Number of vertices in the input polygon.

◆ r2d_print()

void r2d_print ( r2d_poly * poly )

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

Parameters

[in] poly The polygon to print.

◆ r2d_reduce()

void r2d_reduce	(	r2d_poly *	poly,
		r2d_real *	moments,
		r2d_int	polyorder
	)

◆ r2d_rotate()

void r2d_rotate	(	r2d_poly *	poly,
		r2d_real	theta
	)

Rotate a polygon about the origin.

Parameters

[in,out]	poly	The polygon to rotate.
[in]	theta	The angle, in radians, by which to rotate the polygon.

◆ r2d_scale()

void r2d_scale	(	r2d_poly *	poly,
		r2d_real	scale
	)

Scale a polygon.

Parameters

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

◆ r2d_shear()

void r2d_shear	(	r2d_poly *	poly,
		r2d_real	shear,
		r2d_int	axb,
		r2d_int	axs
	)

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

Parameters

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

◆ r2d_shift_moments()

void r2d_shift_moments	(	r2d_real *	moments,
		r2d_int	polyorder,
		r2d_rvec2	vc
	)

Adjust moments according to the shift of polygon 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.

◆ r2d_split()

void r2d_split	(	r2d_poly *	inpolys,
		r2d_int	npolys,
		r2d_plane	plane,
		r2d_poly *	out_pos,
		r2d_poly *	out_neg
	)

Splits a list of polygons across a single plane.

Parameters

[in]	inpolys	Array input polyhedra to be split
[in]	npolys	The number of input polygons
[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.

◆ r2d_translate()

void r2d_translate	(	r2d_poly *	poly,
		r2d_rvec2	shift
	)

Translate a polygon.

Parameters

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

Classes

Macros

Typedefs

Functions

Macro Definition Documentation

◆ R2D_MAX_VERTS

◆ R2D_NUM_MOMENTS

Typedef Documentation

◆ r2d_int

◆ r2d_long

◆ r2d_real

Function Documentation

◆ r2d_affine()

◆ r2d_box_faces_from_verts()

◆ r2d_clip()

◆ r2d_init_box()

◆ r2d_init_poly()

◆ r2d_is_good()

◆ r2d_orient()

◆ r2d_poly_center()

◆ r2d_poly_faces_from_verts()

◆ r2d_print()

◆ r2d_reduce()

◆ r2d_rotate()

◆ r2d_scale()

◆ r2d_shear()

◆ r2d_shift_moments()

◆ r2d_split()

◆ r2d_translate()