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#include <math.h>
#include <float.h>
#include "find_tori_math.h"
// TODO: optimization potential to do in-place inverse for some places where this is used.
Matrix3x3 inverseM33(const Matrix3x3 mat)
{
Matrix3x3 newMat;
for (int a = 0; a < 3; a++)
{
for (int b = 0; b < 3; b++)
{
newMat.val[a][b] = mat.val[a][b];
}
}
for (int i = 0; i < 3; i++)
{
for (int j = i + 1; j < 3; j++)
{
double tmp = newMat.val[i][j];
newMat.val[i][j] = newMat.val[j][i];
newMat.val[j][i] = tmp;
}
}
return newMat;
}
double distance(Point a, Point b)
{
double x = a.x - b.x;
double y = a.y - b.y;
double z = a.z - b.z;
return sqrt(x*x + y*y + z*z);
}
//###################################
// The following code originally came from
// http://stackoverflow.com/questions/23166898/efficient-way-to-calculate-a-3x3-rotation-matrix-from-the-rotation-defined-by-tw
// Need to check up on license terms and give proper attribution
// I think we'll be good with proper attribution, but don't want to assume without checking.
/* -------------------------------------------------------------------- */
/* Math Lib declarations */
/* -------------------------------------------------------------------- */
/* Main function */
/**
* Calculate a rotation matrix from 2 normalized vectors.
*
* v1 and v2 must be unit length.
*/
void rotation_between_vecs_to_mat3(double m[3][3], const double v1[3], const double v2[3])
{
double axis[3];
/* avoid calculating the angle */
double angle_sin;
double angle_cos;
cross_v3_v3v3(axis, v1, v2);
angle_sin = normalize_v3(axis);
angle_cos = dot_v3v3(v1, v2);
if (angle_sin > FLT_EPSILON) {
axis_calc:
axis_angle_normalized_to_mat3_ex(m, axis, angle_sin, angle_cos);
}
else {
/* Degenerate (co-linear) vectors */
if (angle_cos > 0.0f) {
/* Same vectors, zero rotation... */
unit_m3(m);
}
else {
/* Colinear but opposed vectors, 180 rotation... */
ortho_v3_v3(axis, v1);
normalize_v3(axis);
angle_sin = 0.0f; /* sin(M_PI) */
angle_cos = -1.0f; /* cos(M_PI) */
goto axis_calc;
}
}
}
/* -------------------------------------------------------------------- */
/* Math Lib */
void unit_m3(double m[3][3])
{
m[0][0] = m[1][1] = m[2][2] = 1.0;
m[0][1] = m[0][2] = 0.0;
m[1][0] = m[1][2] = 0.0;
m[2][0] = m[2][1] = 0.0;
}
double dot_v3v3(const double a[3], const double b[3])
{
return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
}
void cross_v3_v3v3(double r[3], const double a[3], const double b[3])
{
r[0] = a[1] * b[2] - a[2] * b[1];
r[1] = a[2] * b[0] - a[0] * b[2];
r[2] = a[0] * b[1] - a[1] * b[0];
}
void mul_v3_v3fl(double r[3], const double a[3], double f)
{
r[0] = a[0] * f;
r[1] = a[1] * f;
r[2] = a[2] * f;
}
double normalize_v3_v3(double r[3], const double a[3])
{
double d = dot_v3v3(a, a);
if (d > 1.0e-35f) {
d = sqrtf((float)d);
mul_v3_v3fl(r, a, 1.0f / d);
}
else {
d = r[0] = r[1] = r[2] = 0.0f;
}
return d;
}
double normalize_v3(double n[3])
{
return normalize_v3_v3(n, n);
}
int axis_dominant_v3_single(const double vec[3])
{
const float x = fabsf((float)vec[0]);
const float y = fabsf((float)vec[1]);
const float z = fabsf((float)vec[2]);
return ((x > y) ?
((x > z) ? 0 : 2) :
((y > z) ? 1 : 2));
}
void ortho_v3_v3(double p[3], const double v[3])
{
const int axis = axis_dominant_v3_single(v);
switch (axis) {
case 0:
p[0] = -v[1] - v[2];
p[1] = v[0];
p[2] = v[0];
break;
case 1:
p[0] = v[1];
p[1] = -v[0] - v[2];
p[2] = v[1];
break;
case 2:
p[0] = v[2];
p[1] = v[2];
p[2] = -v[0] - v[1];
break;
}
}
/* axis must be unit length */
void axis_angle_normalized_to_mat3_ex(
double mat[3][3], const double axis[3],
const double angle_sin, const double angle_cos)
{
double nsi[3], ico;
double n_00, n_01, n_11, n_02, n_12, n_22;
ico = (1.0f - angle_cos);
nsi[0] = axis[0] * angle_sin;
nsi[1] = axis[1] * angle_sin;
nsi[2] = axis[2] * angle_sin;
n_00 = (axis[0] * axis[0]) * ico;
n_01 = (axis[0] * axis[1]) * ico;
n_11 = (axis[1] * axis[1]) * ico;
n_02 = (axis[0] * axis[2]) * ico;
n_12 = (axis[1] * axis[2]) * ico;
n_22 = (axis[2] * axis[2]) * ico;
mat[0][0] = n_00 + angle_cos;
mat[0][1] = n_01 + nsi[2];
mat[0][2] = n_02 - nsi[1];
mat[1][0] = n_01 - nsi[2];
mat[1][1] = n_11 + angle_cos;
mat[1][2] = n_12 + nsi[0];
mat[2][0] = n_02 + nsi[1];
mat[2][1] = n_12 - nsi[0];
mat[2][2] = n_22 + angle_cos;
}
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