math_geom_inline.c

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/*
 * 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.
 */
 
#ifndef __MATH_GEOM_INLINE_C__
#define __MATH_GEOM_INLINE_C__
 
#include "BLI_math.h"
#include "BLI_math_vector.h"
 
#include <string.h>
 
/* A few small defines. Keep'em local! */
#define SMALL_NUMBER 1.e-8f
 
/********************************** Polygons *********************************/
 
MINLINE float cross_tri_v2(const float v1[2], const float v2[2], const float v3[2])
{
  return (v1[0] - v2[0]) * (v2[1] - v3[1]) + (v1[1] - v2[1]) * (v3[0] - v2[0]);
}
 
MINLINE float area_tri_signed_v2(const float v1[2], const float v2[2], const float v3[2])
{
  return 0.5f * ((v1[0] - v2[0]) * (v2[1] - v3[1]) + (v1[1] - v2[1]) * (v3[0] - v2[0]));
}
 
MINLINE float area_tri_v2(const float v1[2], const float v2[2], const float v3[2])
{
  return fabsf(area_tri_signed_v2(v1, v2, v3));
}
 
MINLINE float area_squared_tri_v2(const float v1[2], const float v2[2], const float v3[2])
{
  float area = area_tri_signed_v2(v1, v2, v3);
  return area * area;
}
 
/****************************** Spherical Harmonics **************************/
 
MINLINE void zero_sh(float r[9])
{
  memset(r, 0, sizeof(float[9]));
}
 
MINLINE void copy_sh_sh(float r[9], const float a[9])
{
  memcpy(r, a, sizeof(float[9]));
}
 
MINLINE void mul_sh_fl(float r[9], const float f)
{
  int i;
 
  for (i = 0; i < 9; i++) {
    r[i] *= f;
  }
}
 
MINLINE void add_sh_shsh(float r[9], const float a[9], const float b[9])
{
  int i;
 
  for (i = 0; i < 9; i++) {
    r[i] = a[i] + b[i];
  }
}
 
MINLINE float dot_shsh(const float a[9], const float b[9])
{
  float r = 0.0f;
  int i;
 
  for (i = 0; i < 9; i++) {
    r += a[i] * b[i];
  }
 
  return r;
}
 
MINLINE float diffuse_shv3(float sh[9], const float v[3])
{
  /* See formula (13) in:
   * "An Efficient Representation for Irradiance Environment Maps" */
  static const float c1 = 0.429043f, c2 = 0.511664f, c3 = 0.743125f;
  static const float c4 = 0.886227f, c5 = 0.247708f;
  float x, y, z, sum;
 
  x = v[0];
  y = v[1];
  z = v[2];
 
  sum = c1 * sh[8] * (x * x - y * y);
  sum += c3 * sh[6] * z * z;
  sum += c4 * sh[0];
  sum += -c5 * sh[6];
  sum += 2.0f * c1 * (sh[4] * x * y + sh[7] * x * z + sh[5] * y * z);
  sum += 2.0f * c2 * (sh[3] * x + sh[1] * y + sh[2] * z);
 
  return sum;
}
 
MINLINE void vec_fac_to_sh(float r[9], const float v[3], const float f)
{
  /* See formula (3) in:
   * "An Efficient Representation for Irradiance Environment Maps" */
  float sh[9], x, y, z;
 
  x = v[0];
  y = v[1];
  z = v[2];
 
  sh[0] = 0.282095f;
 
  sh[1] = 0.488603f * y;
  sh[2] = 0.488603f * z;
  sh[3] = 0.488603f * x;
 
  sh[4] = 1.092548f * x * y;
  sh[5] = 1.092548f * y * z;
  sh[6] = 0.315392f * (3.0f * z * z - 1.0f);
  sh[7] = 1.092548f * x * z;
  sh[8] = 0.546274f * (x * x - y * y);
 
  mul_sh_fl(sh, f);
  copy_sh_sh(r, sh);
}
 
MINLINE float eval_shv3(float sh[9], const float v[3])
{
  float tmp[9];
 
  vec_fac_to_sh(tmp, v, 1.0f);
  return dot_shsh(tmp, sh);
}
 
MINLINE void madd_sh_shfl(float r[9], const float sh[9], const float f)
{
  float tmp[9];
 
  copy_sh_sh(tmp, sh);
  mul_sh_fl(tmp, f);
  add_sh_shsh(r, r, tmp);
}
 
/* get the 2 dominant axis values, 0==X, 1==Y, 2==Z */
MINLINE void axis_dominant_v3(int *r_axis_a, int *r_axis_b, const float axis[3])
{
  const float xn = fabsf(axis[0]);
  const float yn = fabsf(axis[1]);
  const float zn = fabsf(axis[2]);
 
  if (zn >= xn && zn >= yn) {
    *r_axis_a = 0;
    *r_axis_b = 1;
  }
  else if (yn >= xn && yn >= zn) {
    *r_axis_a = 0;
    *r_axis_b = 2;
  }
  else {
    *r_axis_a = 1;
    *r_axis_b = 2;
  }
}
 
/* same as axis_dominant_v3 but return the max value */
MINLINE float axis_dominant_v3_max(int *r_axis_a, int *r_axis_b, const float axis[3])
{
  const float xn = fabsf(axis[0]);
  const float yn = fabsf(axis[1]);
  const float zn = fabsf(axis[2]);
 
  if (zn >= xn && zn >= yn) {
    *r_axis_a = 0;
    *r_axis_b = 1;
    return zn;
  }
  else if (yn >= xn && yn >= zn) {
    *r_axis_a = 0;
    *r_axis_b = 2;
    return yn;
  }
  else {
    *r_axis_a = 1;
    *r_axis_b = 2;
    return xn;
  }
}
 
/* get the single dominant axis value, 0==X, 1==Y, 2==Z */
MINLINE int axis_dominant_v3_single(const float vec[3])
{
  const float x = fabsf(vec[0]);
  const float y = fabsf(vec[1]);
  const float z = fabsf(vec[2]);
  return ((x > y) ? ((x > z) ? 0 : 2) : ((y > z) ? 1 : 2));
}
 
/* the dominant axis of an orthogonal vector */
MINLINE int axis_dominant_v3_ortho_single(const float vec[3])
{
  const float x = fabsf(vec[0]);
  const float y = fabsf(vec[1]);
  const float z = fabsf(vec[2]);
  return ((x < y) ? ((x < z) ? 0 : 2) : ((y < z) ? 1 : 2));
}
 
MINLINE int max_axis_v3(const float vec[3])
{
  const float x = vec[0];
  const float y = vec[1];
  const float z = vec[2];
  return ((x > y) ? ((x > z) ? 0 : 2) : ((y > z) ? 1 : 2));
}
 
MINLINE int min_axis_v3(const float vec[3])
{
  const float x = vec[0];
  const float y = vec[1];
  const float z = vec[2];
  return ((x < y) ? ((x < z) ? 0 : 2) : ((y < z) ? 1 : 2));
}
 
MINLINE int poly_to_tri_count(const int poly_count, const int corner_count)
{
  BLI_assert(!poly_count || corner_count > poly_count * 2);
  return corner_count - (poly_count * 2);
}
 
MINLINE float plane_point_side_v3(const float plane[4], const float co[3])
{
  return dot_v3v3(co, plane) + plane[3];
}
 
/* useful to calculate an even width shell, by taking the angle between 2 planes.
 * The return value is a scale on the offset.
 * no angle between planes is 1.0, as the angle between the 2 planes approaches 180d
 * the distance gets very high, 180d would be inf, but this case isn't valid */
MINLINE float shell_angle_to_dist(const float angle)
{
  return (UNLIKELY(angle < SMALL_NUMBER)) ? 1.0f : fabsf(1.0f / cosf(angle));
}
MINLINE float shell_v3v3_normalized_to_dist(const float a[3], const float b[3])
{
  const float angle_cos = fabsf(dot_v3v3(a, b));
  BLI_ASSERT_UNIT_V3(a);
  BLI_ASSERT_UNIT_V3(b);
  return (UNLIKELY(angle_cos < SMALL_NUMBER)) ? 1.0f : (1.0f / angle_cos);
}
MINLINE float shell_v2v2_normalized_to_dist(const float a[2], const float b[2])
{
  const float angle_cos = fabsf(dot_v2v2(a, b));
  BLI_ASSERT_UNIT_V2(a);
  BLI_ASSERT_UNIT_V2(b);
  return (UNLIKELY(angle_cos < SMALL_NUMBER)) ? 1.0f : (1.0f / angle_cos);
}
 
MINLINE float shell_v3v3_mid_normalized_to_dist(const float a[3], const float b[3])
{
  float angle_cos;
  float ab[3];
  BLI_ASSERT_UNIT_V3(a);
  BLI_ASSERT_UNIT_V3(b);
  add_v3_v3v3(ab, a, b);
  angle_cos = (normalize_v3(ab) != 0.0f) ? fabsf(dot_v3v3(a, ab)) : 0.0f;
  return (UNLIKELY(angle_cos < SMALL_NUMBER)) ? 1.0f : (1.0f / angle_cos);
}
 
MINLINE float shell_v2v2_mid_normalized_to_dist(const float a[2], const float b[2])
{
  float angle_cos;
  float ab[2];
  BLI_ASSERT_UNIT_V2(a);
  BLI_ASSERT_UNIT_V2(b);
  add_v2_v2v2(ab, a, b);
  angle_cos = (normalize_v2(ab) != 0.0f) ? fabsf(dot_v2v2(a, ab)) : 0.0f;
  return (UNLIKELY(angle_cos < SMALL_NUMBER)) ? 1.0f : (1.0f / angle_cos);
}
 
#undef SMALL_NUMBER
 
#endif /* __MATH_GEOM_INLINE_C__ */