quadric.c

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/* SPDX-FileCopyrightText: 2001-2002 NaN Holding BV. All rights reserved.
 *
 * SPDX-License-Identifier: GPL-2.0-or-later */
 
#include <string.h>
 
#include "BLI_math_base.h"
#include "BLI_math_matrix.h"
#include "BLI_math_vector.h"
#include "BLI_quadric.h" /* own include */
 
#include "BLI_strict_flags.h" /* Keep last. */
 
#define QUADRIC_FLT_TOT (sizeof(Quadric) / sizeof(double))
 
void BLI_quadric_from_plane(Quadric *q, const double v[4])
{
  q->a2 = v[0] * v[0];
  q->b2 = v[1] * v[1];
  q->c2 = v[2] * v[2];
 
  q->ab = v[0] * v[1];
  q->ac = v[0] * v[2];
  q->bc = v[1] * v[2];
 
  q->ad = v[0] * v[3];
  q->bd = v[1] * v[3];
  q->cd = v[2] * v[3];
 
  q->d2 = v[3] * v[3];
}
 
#if 0 /* UNUSED */
 
static void quadric_to_tensor_m3(const Quadric *q, double m[3][3])
{
  m[0][0] = q->a2;
  m[0][1] = q->ab;
  m[0][2] = q->ac;
 
  m[1][0] = q->ab;
  m[1][1] = q->b2;
  m[1][2] = q->bc;
 
  m[2][0] = q->ac;
  m[2][1] = q->bc;
  m[2][2] = q->c2;
}
 
#endif
 
static bool quadric_to_tensor_m3_inverse(const Quadric *q, double m[3][3], double epsilon)
{
  const double det = (q->a2 * (q->b2 * q->c2 - q->bc * q->bc) -
                      q->ab * (q->ab * q->c2 - q->ac * q->bc) +
                      q->ac * (q->ab * q->bc - q->ac * q->b2));
 
  if (fabs(det) > epsilon) {
    const double invdet = 1.0 / det;
 
    m[0][0] = (q->b2 * q->c2 - q->bc * q->bc) * invdet;
    m[1][0] = (q->bc * q->ac - q->ab * q->c2) * invdet;
    m[2][0] = (q->ab * q->bc - q->b2 * q->ac) * invdet;
 
    m[0][1] = (q->ac * q->bc - q->ab * q->c2) * invdet;
    m[1][1] = (q->a2 * q->c2 - q->ac * q->ac) * invdet;
    m[2][1] = (q->ab * q->ac - q->a2 * q->bc) * invdet;
 
    m[0][2] = (q->ab * q->bc - q->ac * q->b2) * invdet;
    m[1][2] = (q->ac * q->ab - q->a2 * q->bc) * invdet;
    m[2][2] = (q->a2 * q->b2 - q->ab * q->ab) * invdet;
 
    return true;
  }
 
  return false;
}
 
void BLI_quadric_to_vector_v3(const Quadric *q, double v[3])
{
  v[0] = q->ad;
  v[1] = q->bd;
  v[2] = q->cd;
}
 
void BLI_quadric_clear(Quadric *q)
{
  memset(q, 0, sizeof(*q));
}
 
void BLI_quadric_add_qu_qu(Quadric *a, const Quadric *b)
{
  add_vn_vn_d((double *)a, (double *)b, QUADRIC_FLT_TOT);
}
 
void BLI_quadric_add_qu_ququ(Quadric *r, const Quadric *a, const Quadric *b)
{
  add_vn_vnvn_d((double *)r, (const double *)a, (const double *)b, QUADRIC_FLT_TOT);
}
 
void BLI_quadric_mul(Quadric *a, const double scalar)
{
  mul_vn_db((double *)a, QUADRIC_FLT_TOT, scalar);
}
 
double BLI_quadric_evaluate(const Quadric *q, const double v[3])
{
  const double v00 = v[0] * v[0], v01 = v[0] * v[1], v02 = v[0] * v[2];
  const double v11 = v[1] * v[1], v12 = v[1] * v[2];
  const double v22 = v[2] * v[2];
  return ((q->a2 * v00) + (q->ab * 2 * v01) + (q->ac * 2 * v02) + (q->ad * 2 * v[0]) + /* a */
          (q->b2 * v11) + (q->bc * 2 * v12) + (q->bd * 2 * v[1]) +                     /* b */
          (q->c2 * v22) + (q->cd * 2 * v[2]) +                                         /* c */
          (q->d2)                                                                      /* d */
  );
}
 
bool BLI_quadric_optimize(const Quadric *q, double v[3], const double epsilon)
{
  double m[3][3];
 
  if (quadric_to_tensor_m3_inverse(q, m, epsilon)) {
    BLI_quadric_to_vector_v3(q, v);
    mul_m3_v3_db(m, v);
    negate_v3_db(v);
    return true;
  }
 
  return false;
}