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r3d.h
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r3d.h
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/*
*
* r3d.h
*
* Routines for fast, geometrically robust clipping operations
* and analytic volume/moment computations over polyhedra in 3D.
*
* Devon Powell
* 31 August 2015
*
* This program was prepared by Los Alamos National Security, LLC at Los Alamos National
* Laboratory (LANL) under contract No. DE-AC52-06NA25396 with the U.S. Department of Energy (DOE).
* All rights in the program are reserved by the DOE and Los Alamos National Security, LLC.
* Permission is granted to the public to copy and use this software without charge, provided that
* this Notice and any statement of authorship are reproduced on all copies. Neither the U.S.
* Government nor LANS makes any warranty, express or implied, or assumes any liability
* or responsibility for the use of this software.
*
*/
#ifndef _R3D_H_
#define _R3D_H_
#include <stdint.h>
/**
* \file r3d.h
* \author Devon Powell
* \date 31 August 2015
* \brief Interface for r3d
*/
/**
* \brief Real type specifying the precision to be used in calculations
*
* Default is `double`. `float` precision is enabled by
* compiling with `-DSINGLE_PRECISION`.
*/
#ifdef SINGLE_PRECISION
typedef float r3d_real;
#else
typedef double r3d_real;
#endif
/**
* \brief Integer types used for indexing
*/
typedef int32_t r3d_int;
typedef int64_t r3d_long;
/** \struct r3d_rvec3
* \brief A 3-vector.
*/
typedef union {
struct {
r3d_real x, /*!< \f$x\f$-component. */
y, /*!< \f$y\f$-component. */
z; /*!< \f$z\f$-component. */
};
r3d_real xyz[3]; /*!< Index-based access to components. */
} r3d_rvec3;
/** \struct r3d_dvec3
* \brief An integer 3-vector for grid indexing.
*/
typedef union {
struct {
r3d_int i, /*!< \f$x\f$-component. */
j, /*!< \f$y\f$-component. */
k; /*!< \f$z\f$-component. */
};
r3d_int ijk[3]; /*!< Index-based access to components. */
} r3d_dvec3;
/** \struct r3d_plane
* \brief A plane.
*/
typedef struct {
r3d_rvec3 n; /*!< Unit-length normal vector. */
r3d_real d; /*!< Signed perpendicular distance to the origin. */
} r3d_plane;
/** \struct r3d_vertex
* \brief A doubly-linked vertex.
*/
typedef struct {
r3d_int pnbrs[3]; /*!< Neighbor indices. */
r3d_rvec3 pos; /*!< Vertex position. */
} r3d_vertex;
/** \struct r3d_poly
* \brief A polyhedron. Can be convex, nonconvex, even multiply-connected.
*/
typedef struct {
r3d_vertex* verts; /*!< Vertex buffer. */
r3d_int nverts; /*!< Number of vertices in the buffer. */
} r3d_poly;
/**
* \brief Clip a polyhedron against an arbitrary number of clip planes (find its intersection with a set of half-spaces).
*
* \param [in, out] poly
* The polyehdron to be clipped.
*
* \param [in] planes
* An array of planes against which to clip this polyhedron.
*
* \param[in] nplanes
* The number of planes in the input array.
*
*/
void r3d_clip(r3d_poly* poly, r3d_plane* planes, r3d_int nplanes);
/**
* \brief Integrate a polynomial density over a polyhedron using simplicial decomposition.
* Uses the fast recursive method of Koehl (2012) to carry out the integration.
*
* \param [in] poly
* The polyhedron over which to integrate.
*
* \param [in] polyorder
* Order of the polynomial density field. 0 for constant (1 moment), 1 for linear
* (4 moments), 2 for quadratic (10 moments), etc.
*
* \param [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`,
* `x*y`, `x*z`, `y^2`, `y*z`, `z^2`, `x^3`, `x^2*y`...
*
*/
#define R3D_NUM_MOMENTS(order) ((order+1)*(order+2)*(order+3)/6)
void r3d_reduce(r3d_poly* poly, r3d_real* moments, r3d_int polyorder);
/**
* \brief 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.
*
* \param [in] poly
* The polyhedron to check.
*
* \return
* 1 if the polyhedron is good, 0 if not.
*
*/
r3d_int r3d_is_good(r3d_poly* poly);
/**
* \brief Get the signed volume of the tetrahedron defined by the input vertices.
*
* \param [in] verts
* Four vertices defining a tetrahedron from which to calculate a volume.
*
* \return
* The signed volume of the input tetrahedron.
*
*/
r3d_real r3d_orient(r3d_rvec3* verts);
/**
* \brief Prints the vertices and connectivity of a polyhedron. For debugging.
*
* \param [in] poly
* The polyhedron to print.
*
*/
void r3d_print(r3d_poly* poly);
/**
* \brief Rotate a polyhedron about one axis.
*
* \param [in, out] poly
* The polyehdron to rotate.
*
* \param [in] theta
* The angle, in radians, by which to rotate the polyhedron.
*
* \param [in] axis
* The axis (0, 1, or 2 corresponding to x, y, or z)
* about which to rotate the polyhedron.
*
*/
void r3d_rotate(r3d_poly* poly, r3d_real theta, r3d_int axis);
/**
* \brief Translate a polyhedron.
*
* \param [in, out] poly
* The polyhedron to translate.
*
* \param [in] shift
* The vector by which to translate the polyhedron.
*
*/
void r3d_translate(r3d_poly* poly, r3d_rvec3 shift);
/**
* \brief Scale a polyhedron.
*
* \param [in, out] poly
* The polyhedron to scale.
*
* \param [in] shift
* The factor by which to scale the polyhedron.
*
*/
void r3d_scale(r3d_poly* poly, r3d_real scale);
/**
* \brief Shear a polyhedron. Each vertex undergoes the transformation
* `pos.xyz[axb] += shear*pos.xyz[axs]`.
*
* \param [in, out] poly
* The polyhedron to shear.
*
* \param [in] shear
* The factor by which to shear the polyhedron.
*
* \param [in] axb
* The axis (0, 1, or 2 corresponding to x, y, or z) along which to shear the polyhedron.
*
* \param [in] axs
* The axis (0, 1, or 2 corresponding to x, y, or z) across which to shear the polyhedron.
*
*/
void r3d_shear(r3d_poly* poly, r3d_real shear, r3d_int axb, r3d_int axs);
/**
* \brief Apply a general affine transformation to a polyhedron.
*
* \param [in, out] poly
* The polyhedron to transform.
*
* \param [in] mat
* The 4x4 homogeneous transformation matrix by which to transform
* the vertices of the polyhedron.
*
*/
void r3d_affine(r3d_poly* poly, r3d_real mat[4][4]);
/**
* \brief Initialize a polyhedron as a tetrahedron.
*
* \param [out] poly
* The polyhedron to initialize.
*
* \param [in] verts
* An array of four vectors, giving the vertices of the tetrahedron.
*
*/
void r3d_init_tet(r3d_poly* poly, r3d_rvec3* verts);
/**
* \brief Initialize an empty polyhedron.
*
* \return poly
* The empty polyhedron.
*
*/
r3d_poly r3d_init_empty_poly();
/**
* \brief Initialize a polyhedron as an axis-aligned cube.
*
* \param [out] poly
* The polyhedron to initialize.
*
* \param [in] rbounds
* An array of two vectors, giving the lower and upper corners of the box.
*
*/
void r3d_init_box(r3d_poly* poly, r3d_rvec3* rbounds);
/**
* \brief Initialize a general polyhedron from a full boundary description.
* Can use `r3d_is_good` to check that the output is valid.
*
* \param [out] poly
* The polyhedron to initialize.
*
* \param [in] vertices
* Array of length `numverts` giving the vertices of the input polyhedron.
*
* \param [in] numverts
* Number of vertices in the input polyhedron.
*
* \param [in] faceinds
* Connectivity array, giving the indices of vertices in the
* order they appear around each face of the input polyhedron.
*
* \param [in] numvertsperface
* An array of length `numfaces` giving the number of vertices for each face
* of the input polyhedron.
*
* \param [in] numfaces
* Number of faces in the input polyhedron.
*
*/
void r3d_init_poly(r3d_poly* poly, r3d_rvec3* vertices, r3d_int numverts,
r3d_int** faceinds, r3d_int* numvertsperface, r3d_int numfaces);
/**
* \brief Clean and deallocate any memory used by an r3d_poly.
*/
void r3d_free_poly(r3d_poly* poly);
/**
* \brief Copy an r3d_poly to a new instance. Does a deep copy of the vertex buffer.
*
* \param[out] topoly
* The polyhedron to be copied TO.
*
* \param[in] frompoly
* The polyhedron we're copying FROM.
*
*/
void r3d_copy_poly(r3d_poly* topoly, r3d_poly* frompoly);
/**
* \brief Get four faces (unit normals and distances to the origin)
* from a four-vertex description of a tetrahedron.
*
* \param [out] faces
* Array of four planes defining the faces of the tetrahedron.
*
* \param [in] verts
* Array of four vectors defining the vertices of the tetrahedron.
*
*/
void r3d_tet_faces_from_verts(r3d_plane* faces, r3d_rvec3* verts);
/**
* \brief Get six faces (unit normals and distances to the origin)
* from a two-vertex description of an axis-aligned box.
*
* \param [out] faces
* Array of six planes defining the faces of the box.
*
* \param [in] rbounds
* Array of two vectors defining the bounds of the axis-aligned box
*
*/
void r3d_box_faces_from_verts(r3d_plane* faces, r3d_rvec3* rbounds);
/**
* \brief Get all faces (unit normals and distances to the origin)
* from a full boundary description of a polyhedron.
*
* \param [out] faces
* Array of planes of length `numfaces` defining the faces of the polyhedron.
*
* \param [in] vertices
* Array of length `numverts` giving the vertices of the input polyhedron.
*
* \param [in] numverts
* Number of vertices in the input polyhedron.
*
* \param [in] faceinds
* Connectivity array, giving the indices of vertices in the
* order they appear around each face of the input polyhedron.
*
* \param [in] numvertsperface
* An array of length `numfaces` giving the number of vertices for each face
* of the input polyhedron.
*
* \param [in] numfaces
* Number of faces in the input polyhedron.
*
*/
void r3d_poly_faces_from_verts(r3d_plane* faces, r3d_rvec3* vertices, r3d_int numverts,
r3d_int** faceinds, r3d_int* numvertsperface, r3d_int numfaces);
#endif // _R3D_H_