BLI_math_geom.h

Go to the documentation of this file.

/*
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * as published by the Free Software Foundation; either version 2
 * of the License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
 *
 * The Original Code is Copyright (C) 2001-2002 by NaN Holding BV.
 * All rights reserved.
 *
 * The Original Code is: some of this file.
 */
 
#pragma once
 
#include "BLI_compiler_attrs.h"
#include "BLI_math_inline.h"
 
#ifdef BLI_MATH_GCC_WARN_PRAGMA
#  pragma GCC diagnostic push
#  pragma GCC diagnostic ignored "-Wredundant-decls"
#endif
 
#ifdef __cplusplus
extern "C" {
#endif
 
/********************************** Polygons *********************************/
 
float normal_tri_v3(float n[3], const float v1[3], const float v2[3], const float v3[3]);
float normal_quad_v3(
    float n[3], const float v1[3], const float v2[3], const float v3[3], const float v4[3]);
float normal_poly_v3(float n[3], const float verts[][3], unsigned int nr);
 
MINLINE float area_tri_v2(const float v1[2], const float v2[2], const float v3[2]);
MINLINE float area_squared_tri_v2(const float v1[2], const float v2[2], const float v3[2]);
MINLINE float area_tri_signed_v2(const float v1[2], const float v2[2], const float v3[2]);
float area_tri_v3(const float v1[3], const float v2[3], const float v3[3]);
float area_squared_tri_v3(const float v1[3], const float v2[3], const float v3[3]);
float area_tri_signed_v3(const float v1[3],
                         const float v2[3],
                         const float v3[3],
                         const float normal[3]);
float area_quad_v3(const float v1[3], const float v2[3], const float v3[3], const float v4[3]);
float area_squared_quad_v3(const float v1[3],
                           const float v2[3],
                           const float v3[3],
                           const float v4[3]);
float area_poly_v3(const float verts[][3], unsigned int nr);
float area_poly_v2(const float verts[][2], unsigned int nr);
float area_squared_poly_v3(const float verts[][3], unsigned int nr);
float area_squared_poly_v2(const float verts[][2], unsigned int nr);
float area_poly_signed_v2(const float verts[][2], unsigned int nr);
float cotangent_tri_weight_v3(const float v1[3], const float v2[3], const float v3[3]);
 
void cross_tri_v3(float n[3], const float v1[3], const float v2[3], const float v3[3]);
MINLINE float cross_tri_v2(const float v1[2], const float v2[2], const float v3[2]);
void cross_poly_v3(float n[3], const float verts[][3], unsigned int nr);
float cross_poly_v2(const float verts[][2], unsigned int nr);
 
/********************************* Planes **********************************/
 
void plane_from_point_normal_v3(float r_plane[4],
                                const float plane_co[3],
                                const float plane_no[3]);
void plane_to_point_vector_v3(const float plane[4], float r_plane_co[3], float r_plane_no[3]);
void plane_to_point_vector_v3_normalized(const float plane[4],
                                         float r_plane_co[3],
                                         float r_plane_no[3]);
 
MINLINE float plane_point_side_v3(const float plane[4], const float co[3]);
 
/********************************* Volume **********************************/
 
float volume_tetrahedron_v3(const float v1[3],
                            const float v2[3],
                            const float v3[3],
                            const float v4[3]);
float volume_tetrahedron_signed_v3(const float v1[3],
                                   const float v2[3],
                                   const float v3[3],
                                   const float v4[3]);
 
float volume_tri_tetrahedron_signed_v3_6x(const float v1[3], const float v2[3], const float v3[3]);
float volume_tri_tetrahedron_signed_v3(const float v1[3], const float v2[3], const float v3[3]);
 
bool is_edge_convex_v3(const float v1[3], const float v2[3], const float v3[3], const float v4[3]);
bool is_quad_convex_v3(const float v1[3], const float v2[3], const float v3[3], const float v4[3]);
bool is_quad_convex_v2(const float v1[2], const float v2[2], const float v3[2], const float v4[2]);
bool is_poly_convex_v2(const float verts[][2], unsigned int nr);
int is_quad_flip_v3(const float v1[3], const float v2[3], const float v3[3], const float v4[3]);
bool is_quad_flip_v3_first_third_fast(const float v1[3],
                                      const float v2[3],
                                      const float v3[3],
                                      const float v4[3]);
 
/********************************* Distance **********************************/
 
float dist_squared_to_line_v2(const float p[2], const float l1[2], const float l2[2]);
float dist_to_line_v2(const float p[2], const float l1[2], const float l2[2]);
float dist_squared_to_line_segment_v2(const float p[2], const float l1[2], const float l2[2]);
float dist_to_line_segment_v2(const float p[2], const float l1[2], const float l2[2]);
 
float dist_signed_squared_to_plane_v3(const float p[3], const float plane[4]);
float dist_squared_to_plane_v3(const float p[3], const float plane[4]);
float dist_signed_to_plane_v3(const float p[3], const float plane[4]);
float dist_to_plane_v3(const float p[3], const float plane[4]);
 
/* plane3 versions */
float dist_signed_squared_to_plane3_v3(const float p[3], const float plane[4]);
float dist_squared_to_plane3_v3(const float p[3], const float plane[4]);
float dist_signed_to_plane3_v3(const float p[3], const float plane[4]);
float dist_to_plane3_v3(const float p[3], const float plane[4]);
 
float dist_squared_to_line_segment_v3(const float p[3], const float l1[3], const float l2[3]);
float dist_to_line_segment_v3(const float p[3], const float l1[3], const float l2[3]);
float dist_squared_to_line_v3(const float p[3], const float l1[3], const float l2[3]);
float dist_to_line_v3(const float p[3], const float l1[3], const float l2[3]);
float dist_signed_squared_to_corner_v3v3v3(const float p[3],
                                           const float v1[3],
                                           const float v2[3],
                                           const float v3[3],
                                           const float axis_ref[3]);
float dist_squared_to_ray_v3_normalized(const float ray_origin[3],
                                        const float ray_direction[3],
                                        const float co[3]);
float dist_squared_ray_to_seg_v3(const float ray_origin[3],
                                 const float ray_direction[3],
                                 const float v0[3],
                                 const float v1[3],
                                 float r_point[3],
                                 float *r_depth);
 
void aabb_get_near_far_from_plane(const float plane_no[3],
                                  const float bbmin[3],
                                  const float bbmax[3],
                                  float bb_near[3],
                                  float bb_afar[3]);
 
struct DistRayAABB_Precalc {
  float ray_origin[3];
  float ray_direction[3];
  float ray_inv_dir[3];
};
void dist_squared_ray_to_aabb_v3_precalc(struct DistRayAABB_Precalc *neasrest_precalc,
                                         const float ray_origin[3],
                                         const float ray_direction[3]);
float dist_squared_ray_to_aabb_v3(const struct DistRayAABB_Precalc *data,
                                  const float bb_min[3],
                                  const float bb_max[3],
                                  float r_point[3],
                                  float *r_depth);
/* when there is no advantage to precalc. */
float dist_squared_ray_to_aabb_v3_simple(const float ray_origin[3],
                                         const float ray_direction[3],
                                         const float bb_min[3],
                                         const float bb_max[3],
                                         float r_point[3],
                                         float *r_depth);
 
struct DistProjectedAABBPrecalc {
  float ray_origin[3];
  float ray_direction[3];
  float ray_inv_dir[3];
  float pmat[4][4];
  float mval[2];
};
void dist_squared_to_projected_aabb_precalc(struct DistProjectedAABBPrecalc *precalc,
                                            const float projmat[4][4],
                                            const float winsize[2],
                                            const float mval[2]);
float dist_squared_to_projected_aabb(struct DistProjectedAABBPrecalc *data,
                                     const float bbmin[3],
                                     const float bbmax[3],
                                     bool r_axis_closest[3]);
float dist_squared_to_projected_aabb_simple(const float projmat[4][4],
                                            const float winsize[2],
                                            const float mval[2],
                                            const float bbmin[3],
                                            const float bbmax[3]);
 
float closest_to_ray_v3(float r_close[3],
                        const float p[3],
                        const float ray_orig[3],
                        const float ray_dir[3]);
float closest_to_line_v2(float r_close[2], const float p[2], const float l1[2], const float l2[2]);
double closest_to_line_v2_db(double r_close[2],
                             const double p[2],
                             const double l1[2],
                             const double l2[2]);
float closest_to_line_v3(float r_close[3], const float p[3], const float l1[3], const float l2[3]);
void closest_to_line_segment_v2(float r_close[2],
                                const float p[2],
                                const float l1[2],
                                const float l2[2]);
void closest_to_line_segment_v3(float r_close[3],
                                const float p[3],
                                const float l1[3],
                                const float l2[3]);
void closest_to_plane_normalized_v3(float r_close[3], const float plane[4], const float pt[3]);
void closest_to_plane_v3(float r_close[3], const float plane[4], const float pt[3]);
void closest_to_plane3_normalized_v3(float r_close[3], const float plane[3], const float pt[3]);
void closest_to_plane3_v3(float r_close[3], const float plane[3], const float pt[3]);
 
/* Set 'r' to the point in triangle (v1, v2, v3) closest to point 'p' */
void closest_on_tri_to_point_v3(
    float r[3], const float p[3], const float v1[3], const float v2[3], const float v3[3]);
 
float ray_point_factor_v3_ex(const float p[3],
                             const float ray_origin[3],
                             const float ray_direction[3],
                             const float epsilon,
                             const float fallback);
float ray_point_factor_v3(const float p[3],
                          const float ray_origin[3],
                          const float ray_direction[3]);
 
float line_point_factor_v3_ex(const float p[3],
                              const float l1[3],
                              const float l2[3],
                              const float epsilon,
                              const float fallback);
float line_point_factor_v3(const float p[3], const float l1[3], const float l2[3]);
 
float line_point_factor_v2_ex(const float p[2],
                              const float l1[2],
                              const float l2[2],
                              const float epsilon,
                              const float fallback);
float line_point_factor_v2(const float p[2], const float l1[2], const float l2[2]);
 
float line_plane_factor_v3(const float plane_co[3],
                           const float plane_no[3],
                           const float l1[3],
                           const float l2[3]);
 
void limit_dist_v3(float v1[3], float v2[3], const float dist);
 
/******************************* Intersection ********************************/
 
/* TODO int return value consistency */
 
/* line-line */
#define ISECT_LINE_LINE_COLINEAR -1
#define ISECT_LINE_LINE_NONE 0
#define ISECT_LINE_LINE_EXACT 1
#define ISECT_LINE_LINE_CROSS 2
 
int isect_seg_seg_v2(const float v1[2], const float v2[2], const float v3[2], const float v4[2]);
void isect_seg_seg_v3(const float a0[3],
                      const float a1[3],
                      const float b0[3],
                      const float b1[3],
                      float r_a[3],
                      float r_b[3]);
 
int isect_seg_seg_v2_int(const int v1[2], const int v2[2], const int v3[2], const int v4[2]);
int isect_seg_seg_v2_point_ex(const float v0[2],
                              const float v1[2],
                              const float v2[2],
                              const float v3[2],
                              const float endpoint_bias,
                              float vi[2]);
int isect_seg_seg_v2_point(
    const float v0[2], const float v1[2], const float v2[2], const float v3[2], float vi[2]);
bool isect_seg_seg_v2_simple(const float v1[2],
                             const float v2[2],
                             const float v3[2],
                             const float v4[2]);
int isect_seg_seg_v2_lambda_mu_db(const double v1[2],
                                  const double v2[2],
                                  const double v3[2],
                                  const double v4[2],
                                  double *r_lambda,
                                  double *r_mu);
int isect_line_sphere_v3(const float l1[3],
                         const float l2[3],
                         const float sp[3],
                         const float r,
                         float r_p1[3],
                         float r_p2[3]);
int isect_line_sphere_v2(const float l1[2],
                         const float l2[2],
                         const float sp[2],
                         const float r,
                         float r_p1[2],
                         float r_p2[2]);
 
int isect_line_line_v2_point(
    const float v0[2], const float v1[2], const float v2[2], const float v3[2], float r_vi[2]);
int isect_line_line_epsilon_v3(const float v1[3],
                               const float v2[3],
                               const float v3[3],
                               const float v4[3],
                               float i1[3],
                               float i2[3],
                               const float epsilon);
int isect_line_line_v3(const float v1[3],
                       const float v2[3],
                       const float v3[3],
                       const float v4[3],
                       float r_i1[3],
                       float r_i2[3]);
bool isect_line_line_strict_v3(const float v1[3],
                               const float v2[3],
                               const float v3[3],
                               const float v4[3],
                               float vi[3],
                               float *r_lambda);
bool isect_ray_ray_epsilon_v3(const float ray_origin_a[3],
                              const float ray_direction_a[3],
                              const float ray_origin_b[3],
                              const float ray_direction_b[3],
                              const float epsilon,
                              float *r_lambda_a,
                              float *r_lambda_b);
bool isect_ray_ray_v3(const float ray_origin_a[3],
                      const float ray_direction_a[3],
                      const float ray_origin_b[3],
                      const float ray_direction_b[3],
                      float *r_lambda_a,
                      float *r_lambda_b);
 
bool isect_ray_plane_v3(const float ray_origin[3],
                        const float ray_direction[3],
                        const float plane[4],
                        float *r_lambda,
                        const bool clip);
 
bool isect_point_planes_v3(float (*planes)[4], int totplane, const float p[3]);
bool isect_point_planes_v3_negated(const float (*planes)[4], const int totplane, const float p[3]);
 
bool isect_line_plane_v3(float r_isect_co[3],
                         const float l1[3],
                         const float l2[3],
                         const float plane_co[3],
                         const float plane_no[3]) ATTR_WARN_UNUSED_RESULT;
 
bool isect_plane_plane_plane_v3(const float plane_a[4],
                                const float plane_b[4],
                                const float plane_c[4],
                                float r_isect_co[3]) ATTR_WARN_UNUSED_RESULT;
bool isect_plane_plane_v3(const float plane_a[4],
                          const float plane_b[4],
                          float r_isect_co[3],
                          float r_isect_no[3]) ATTR_WARN_UNUSED_RESULT;
 
bool isect_planes_v3_fn(
    const float planes[][4],
    const int planes_len,
    const float eps_coplanar,
    const float eps_isect,
    void (*callback_fn)(const float co[3], int i, int j, int k, void *user_data),
    void *user_data);
 
/* line/ray triangle */
bool isect_line_segment_tri_v3(const float p1[3],
                               const float p2[3],
                               const float v0[3],
                               const float v1[3],
                               const float v2[3],
                               float *r_lambda,
                               float r_uv[2]);
bool isect_line_segment_tri_epsilon_v3(const float p1[3],
                                       const float p2[3],
                                       const float v0[3],
                                       const float v1[3],
                                       const float v2[3],
                                       float *r_lambda,
                                       float r_uv[2],
                                       const float epsilon);
bool isect_axial_line_segment_tri_v3(const int axis,
                                     const float p1[3],
                                     const float p2[3],
                                     const float v0[3],
                                     const float v1[3],
                                     const float v2[3],
                                     float *r_lambda);
 
bool isect_ray_tri_v3(const float ray_origin[3],
                      const float ray_direction[3],
                      const float v0[3],
                      const float v1[3],
                      const float v2[3],
                      float *r_lambda,
                      float r_uv[2]);
bool isect_ray_tri_threshold_v3(const float ray_origin[3],
                                const float ray_direction[3],
                                const float v0[3],
                                const float v1[3],
                                const float v2[3],
                                float *r_lambda,
                                float r_uv[2],
                                const float threshold);
bool isect_ray_tri_epsilon_v3(const float ray_origin[3],
                              const float ray_direction[3],
                              const float v0[3],
                              const float v1[3],
                              const float v2[3],
                              float *r_lambda,
                              float r_uv[2],
                              const float epsilon);
bool isect_tri_tri_v3_ex(const float tri_a[3][3],
                         const float tri_b[3][3],
                         float r_i1[3],
                         float r_i2[3],
                         int *r_tri_a_edge_isect_count);
bool isect_tri_tri_v3(const float t_a0[3],
                      const float t_a1[3],
                      const float t_a2[3],
                      const float t_b0[3],
                      const float t_b1[3],
                      const float t_b2[3],
                      float r_i1[3],
                      float r_i2[3]);
 
bool isect_tri_tri_v2(const float p1[2],
                      const float q1[2],
                      const float r1[2],
                      const float p2[2],
                      const float q2[2],
                      const float r2[2]);
 
/* water-tight raycast (requires pre-calculation) */
struct IsectRayPrecalc {
  /* Maximal dimension kz, and orthogonal dimensions. */
  int kx, ky, kz;
 
  /* Shear constants. */
  float sx, sy, sz;
};
 
void isect_ray_tri_watertight_v3_precalc(struct IsectRayPrecalc *isect_precalc,
                                         const float ray_direction[3]);
bool isect_ray_tri_watertight_v3(const float ray_origin[3],
                                 const struct IsectRayPrecalc *isect_precalc,
                                 const float v0[3],
                                 const float v1[3],
                                 const float v2[3],
                                 float *r_dist,
                                 float r_uv[2]);
/* slower version which calculates IsectRayPrecalc each time */
bool isect_ray_tri_watertight_v3_simple(const float ray_origin[3],
                                        const float ray_direction[3],
                                        const float v0[3],
                                        const float v1[3],
                                        const float v2[3],
                                        float *r_lambda,
                                        float r_uv[2]);
 
bool isect_ray_seg_v2(const float ray_origin[2],
                      const float ray_direction[2],
                      const float v0[2],
                      const float v1[2],
                      float *r_lambda,
                      float *r_u);
 
bool isect_ray_line_v3(const float ray_origin[3],
                       const float ray_direction[3],
                       const float v0[3],
                       const float v1[3],
                       float *r_lambda);
 
/* point in polygon */
bool isect_point_poly_v2(const float pt[2],
                         const float verts[][2],
                         const unsigned int nr,
                         const bool use_holes);
bool isect_point_poly_v2_int(const int pt[2],
                             const int verts[][2],
                             const unsigned int nr,
                             const bool use_holes);
 
int isect_point_quad_v2(
    const float p[2], const float v1[2], const float v2[2], const float v3[2], const float v4[2]);
 
int isect_point_tri_v2(const float pt[2], const float v1[2], const float v2[2], const float v3[2]);
bool isect_point_tri_v2_cw(const float pt[2],
                           const float v1[2],
                           const float v2[2],
                           const float v3[2]);
int isect_point_tri_v2_int(
    const int x1, const int y1, const int x2, const int y2, const int a, const int b);
bool isect_point_tri_prism_v3(const float p[3],
                              const float v1[3],
                              const float v2[3],
                              const float v3[3]);
bool isect_point_tri_v3(const float p[3],
                        const float v1[3],
                        const float v2[3],
                        const float v3[3],
                        float r_isect_co[3]);
 
/* axis-aligned bounding box */
bool isect_aabb_aabb_v3(const float min1[3],
                        const float max1[3],
                        const float min2[3],
                        const float max2[3]);
 
struct IsectRayAABB_Precalc {
  float ray_origin[3];
  float ray_inv_dir[3];
  int sign[3];
};
 
void isect_ray_aabb_v3_precalc(struct IsectRayAABB_Precalc *data,
                               const float ray_origin[3],
                               const float ray_direction[3]);
bool isect_ray_aabb_v3(const struct IsectRayAABB_Precalc *data,
                       const float bb_min[3],
                       const float bb_max[3],
                       float *tmin);
bool isect_ray_aabb_v3_simple(const float orig[3],
                              const float dir[3],
                              const float bb_min[3],
                              const float bb_max[3],
                              float *tmin,
                              float *tmax);
 
/* other */
#define ISECT_AABB_PLANE_BEHIND_ANY 0
#define ISECT_AABB_PLANE_CROSS_ANY 1
#define ISECT_AABB_PLANE_IN_FRONT_ALL 2
 
int isect_aabb_planes_v3(const float (*planes)[4],
                         const int totplane,
                         const float bbmin[3],
                         const float bbmax[3]);
 
bool isect_sweeping_sphere_tri_v3(const float p1[3],
                                  const float p2[3],
                                  const float radius,
                                  const float v0[3],
                                  const float v1[3],
                                  const float v2[3],
                                  float *r_lambda,
                                  float ipoint[3]);
 
bool clip_segment_v3_plane(
    const float p1[3], const float p2[3], const float plane[4], float r_p1[3], float r_p2[3]);
bool clip_segment_v3_plane_n(const float p1[3],
                             const float p2[3],
                             const float plane_array[][4],
                             const int plane_tot,
                             float r_p1[3],
                             float r_p2[3]);
 
bool point_in_slice_seg(float p[3], float l1[3], float l2[3]);
 
/****************************** Interpolation ********************************/
void interp_weights_tri_v3(
    float w[3], const float v1[3], const float v2[3], const float v3[3], const float co[3]);
void interp_weights_quad_v3(float w[4],
                            const float v1[3],
                            const float v2[3],
                            const float v3[3],
                            const float v4[3],
                            const float co[3]);
void interp_weights_poly_v3(float w[], float v[][3], const int n, const float co[3]);
void interp_weights_poly_v2(float w[], float v[][2], const int n, const float co[2]);
 
void interp_cubic_v3(float x[3],
                     float v[3],
                     const float x1[3],
                     const float v1[3],
                     const float x2[3],
                     const float v2[3],
                     const float t);
 
int interp_sparse_array(float *array, const int list_size, const float skipval);
 
void transform_point_by_tri_v3(float pt_tar[3],
                               float const pt_src[3],
                               const float tri_tar_p1[3],
                               const float tri_tar_p2[3],
                               const float tri_tar_p3[3],
                               const float tri_src_p1[3],
                               const float tri_src_p2[3],
                               const float tri_src_p3[3]);
void transform_point_by_seg_v3(float p_dst[3],
                               const float p_src[3],
                               const float l_dst_p1[3],
                               const float l_dst_p2[3],
                               const float l_src_p1[3],
                               const float l_src_p2[3]);
 
void barycentric_weights_v2(
    const float v1[2], const float v2[2], const float v3[2], const float co[2], float w[3]);
void barycentric_weights_v2_clamped(
    const float v1[2], const float v2[2], const float v3[2], const float co[2], float w[3]);
void barycentric_weights_v2_persp(
    const float v1[4], const float v2[4], const float v3[4], const float co[2], float w[3]);
void barycentric_weights_v2_quad(const float v1[2],
                                 const float v2[2],
                                 const float v3[2],
                                 const float v4[2],
                                 const float co[2],
                                 float w[4]);
 
bool barycentric_coords_v2(
    const float v1[2], const float v2[2], const float v3[2], const float co[2], float w[3]);
int barycentric_inside_triangle_v2(const float w[3]);
 
void resolve_tri_uv_v2(
    float r_uv[2], const float st[2], const float st0[2], const float st1[2], const float st2[2]);
void resolve_tri_uv_v3(
    float r_uv[2], const float st[3], const float st0[3], const float st1[3], const float st2[3]);
void resolve_quad_uv_v2(float r_uv[2],
                        const float st[2],
                        const float st0[2],
                        const float st1[2],
                        const float st2[2],
                        const float st3[2]);
void resolve_quad_uv_v2_deriv(float r_uv[2],
                              float r_deriv[2][2],
                              const float st[2],
                              const float st0[2],
                              const float st1[2],
                              const float st2[2],
                              const float st3[2]);
float resolve_quad_u_v2(const float st[2],
                        const float st0[2],
                        const float st1[2],
                        const float st2[2],
                        const float st3[2]);
 
/* use to find the point of a UV on a face */
void interp_bilinear_quad_v3(float data[4][3], float u, float v, float res[3]);
void interp_barycentric_tri_v3(float data[3][3], float u, float v, float res[3]);
 
/***************************** View & Projection *****************************/
 
void lookat_m4(
    float mat[4][4], float vx, float vy, float vz, float px, float py, float pz, float twist);
void polarview_m4(float mat[4][4], float dist, float azimuth, float incidence, float twist);
 
void perspective_m4(float mat[4][4],
                    const float left,
                    const float right,
                    const float bottom,
                    const float top,
                    const float nearClip,
                    const float farClip);
void perspective_m4_fov(float mat[4][4],
                        const float angle_left,
                        const float angle_right,
                        const float angle_up,
                        const float angle_down,
                        const float nearClip,
                        const float farClip);
void orthographic_m4(float mat[4][4],
                     const float left,
                     const float right,
                     const float bottom,
                     const float top,
                     const float nearClip,
                     const float farClip);
void window_translate_m4(float winmat[4][4], float perspmat[4][4], const float x, const float y);
 
void planes_from_projmat(const float mat[4][4],
                         float left[4],
                         float right[4],
                         float top[4],
                         float bottom[4],
                         float near[4],
                         float far[4]);
 
void projmat_dimensions(const float projmat[4][4],
                        float *r_left,
                        float *r_right,
                        float *r_bottom,
                        float *r_top,
                        float *r_near,
                        float *r_far);
void projmat_dimensions_db(const float projmat[4][4],
                           double *r_left,
                           double *r_right,
                           double *r_bottom,
                           double *r_top,
                           double *r_near,
                           double *r_far);
 
void projmat_from_subregion(const float projmat[4][4],
                            const int win_size[2],
                            const int x_min,
                            const int x_max,
                            const int y_min,
                            const int y_max,
                            float r_projmat[4][4]);
 
int box_clip_bounds_m4(float boundbox[2][3], const float bounds[4], float winmat[4][4]);
void box_minmax_bounds_m4(float min[3], float max[3], float boundbox[2][3], float mat[4][4]);
 
/********************************** Mapping **********************************/
 
void map_to_tube(float *r_u, float *r_v, const float x, const float y, const float z);
void map_to_sphere(float *r_u, float *r_v, const float x, const float y, const float z);
void map_to_plane_v2_v3v3(float r_co[2], const float co[3], const float no[3]);
void map_to_plane_axis_angle_v2_v3v3fl(float r_co[2],
                                       const float co[3],
                                       const float axis[3],
                                       const float angle);
 
/********************************** Normals **********************************/
 
void accumulate_vertex_normals_tri_v3(float n1[3],
                                      float n2[3],
                                      float n3[3],
                                      const float f_no[3],
                                      const float co1[3],
                                      const float co2[3],
                                      const float co3[3]);
 
void accumulate_vertex_normals_v3(float n1[3],
                                  float n2[3],
                                  float n3[3],
                                  float n4[3],
                                  const float f_no[3],
                                  const float co1[3],
                                  const float co2[3],
                                  const float co3[3],
                                  const float co4[3]);
 
void accumulate_vertex_normals_poly_v3(float **vertnos,
                                       const float polyno[3],
                                       const float **vertcos,
                                       float vdiffs[][3],
                                       const int nverts);
 
/********************************* Tangents **********************************/
 
void tangent_from_uv_v3(const float uv1[2],
                        const float uv2[2],
                        const float uv3[2],
                        const float co1[3],
                        const float co2[3],
                        const float co3[3],
                        const float n[3],
                        float r_tang[3]);
 
/******************************** Vector Clouds ******************************/
 
void vcloud_estimate_transform_v3(const int list_size,
                                  const float (*pos)[3],
                                  const float *weight,
                                  const float (*rpos)[3],
                                  const float *rweight,
                                  float lloc[3],
                                  float rloc[3],
                                  float lrot[3][3],
                                  float lscale[3][3]);
 
/****************************** Spherical Harmonics *************************/
 
/* Uses 2nd order SH => 9 coefficients, stored in this order:
 * 0 = (0, 0),
 * 1 = (1, -1), 2 = (1, 0), 3 = (1, 1),
 * 4 = (2, -2), 5 = (2, -1), 6 = (2, 0), 7 = (2, 1), 8 = (2, 2) */
 
MINLINE void zero_sh(float r[9]);
MINLINE void copy_sh_sh(float r[9], const float a[9]);
MINLINE void mul_sh_fl(float r[9], const float f);
MINLINE void add_sh_shsh(float r[9], const float a[9], const float b[9]);
MINLINE float dot_shsh(const float a[9], const float b[9]);
 
MINLINE float eval_shv3(float r[9], const float v[3]);
MINLINE float diffuse_shv3(float r[9], const float v[3]);
MINLINE void vec_fac_to_sh(float r[9], const float v[3], const float f);
MINLINE void madd_sh_shfl(float r[9], const float sh[3], const float f);
 
/********************************* Form Factor *******************************/
 
float form_factor_quad(const float p[3],
                       const float n[3],
                       const float q0[3],
                       const float q1[3],
                       const float q2[3],
                       const float q3[3]);
bool form_factor_visible_quad(const float p[3],
                              const float n[3],
                              const float v0[3],
                              const float v1[3],
                              const float v2[3],
                              float q0[3],
                              float q1[3],
                              float q2[3],
                              float q3[3]);
float form_factor_hemi_poly(
    float p[3], float n[3], float v1[3], float v2[3], float v3[3], float v4[3]);
 
void axis_dominant_v3_to_m3_negate(float r_mat[3][3], const float normal[3]);
void axis_dominant_v3_to_m3(float r_mat[3][3], const float normal[3]);
 
MINLINE void axis_dominant_v3(int *r_axis_a, int *r_axis_b, const float axis[3]);
MINLINE float axis_dominant_v3_max(int *r_axis_a,
                                   int *r_axis_b,
                                   const float axis[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE int axis_dominant_v3_single(const float vec[3]);
MINLINE int axis_dominant_v3_ortho_single(const float vec[3]);
 
MINLINE int max_axis_v3(const float vec[3]);
MINLINE int min_axis_v3(const float vec[3]);
 
MINLINE int poly_to_tri_count(const int poly_count, const int corner_count);
 
MINLINE float shell_angle_to_dist(const float angle);
MINLINE float shell_v3v3_normalized_to_dist(const float a[3], const float b[3]);
MINLINE float shell_v2v2_normalized_to_dist(const float a[2], const float b[2]);
MINLINE float shell_v3v3_mid_normalized_to_dist(const float a[3], const float b[3]);
MINLINE float shell_v2v2_mid_normalized_to_dist(const float a[2], const float b[2]);
 
/********************************* Cubic (Bezier) *******************************/
 
float cubic_tangent_factor_circle_v3(const float tan_l[3], const float tan_r[3]);
 
/********************************** Geodesics *********************************/
 
float geodesic_distance_propagate_across_triangle(
    const float v0[3], const float v1[3], const float v2[3], const float dist1, const float dist2);
 
/**************************** Inline Definitions ******************************/
 
#if BLI_MATH_DO_INLINE
#  include "intern/math_geom_inline.c"
#endif
 
#ifdef BLI_MATH_GCC_WARN_PRAGMA
#  pragma GCC diagnostic pop
#endif
 
#ifdef __cplusplus
}
#endif