// Returns true if the distance between f0 and f1 is smaller than epsilon
public bool CompareApproximately(FP f0, FP f1, FP epsilon)
{
FP dist = (f0 - f1);
dist = FPMath.Abs(dist);
return(dist < epsilon);
}
private static FP ManhattanDistance(Vector2Int p0, Vector2Int p1)
{
var dx = FPMath.Abs(p0.x - p1.x);
var dy = FPMath.Abs(p0.y - p1.y);
return(dx + dy);
}
public bool InvertMatrix4x4_Full(ref FPMatrix4x4 m, out FPMatrix4x4 output)
{
output = new FPMatrix4x4();
output.Clear();
FP[,] wtmp = new FP[4, 8];
FP m0, m1, m2, m3, s;
FP[] r0 = new FP[8];
FP[] r1 = new FP[8];
FP[] r2 = new FP[8];
FP[] r3 = new FP[8];
r0[0] = m.m00; r0[1] = m.m01;
r0[2] = m.m02; r0[3] = m.m03;
r0[4] = 1.0; r0[5] = r0[6] = r0[7] = 0.0;
r1[0] = m.m00; r1[1] = m.m01;
r1[2] = m.m02; r1[3] = m.m03;
r1[5] = 1.0; r1[4] = r1[6] = r1[7] = 0.0;
r2[0] = m.m00; r2[1] = m.m01;
r2[2] = m.m02; r2[3] = m.m03;
r2[6] = 1.0; r2[4] = r2[5] = r2[7] = 0.0;
r3[0] = m.m00; r3[1] = m.m01;
r3[2] = m.m02; r3[3] = m.m03;
r3[7] = 1.0; r3[4] = r3[5] = r3[6] = 0.0;
/* choose pivot - or die */
if (FPMath.Abs(r3[0]) > FPMath.Abs(r2[0]))
{
swap_rows(ref r3, ref r2);
}
if (FPMath.Abs(r2[0]) > FPMath.Abs(r1[0]))
{
swap_rows(ref r2, ref r1);
}
if (FPMath.Abs(r1[0]) > FPMath.Abs(r0[0]))
{
swap_rows(ref r1, ref r0);
}
if (0.0F == r0[0])
{
return(false);
}
/* eliminate first variable */
m1 = r1[0] / r0[0]; m2 = r2[0] / r0[0]; m3 = r3[0] / r0[0];
s = r0[1]; r1[1] -= m1 * s; r2[1] -= m2 * s; r3[1] -= m3 * s;
s = r0[2]; r1[2] -= m1 * s; r2[2] -= m2 * s; r3[2] -= m3 * s;
s = r0[3]; r1[3] -= m1 * s; r2[3] -= m2 * s; r3[3] -= m3 * s;
s = r0[4];
if (s != 0)
{
r1[4] -= m1 * s; r2[4] -= m2 * s; r3[4] -= m3 * s;
}
s = r0[5];
if (s != 0)
{
r1[5] -= m1 * s; r2[5] -= m2 * s; r3[5] -= m3 * s;
}
s = r0[6];
if (s != 0)
{
r1[6] -= m1 * s; r2[6] -= m2 * s; r3[6] -= m3 * s;
}
s = r0[7];
if (s != 0)
{
r1[7] -= m1 * s; r2[7] -= m2 * s; r3[7] -= m3 * s;
}
/* choose pivot - or die */
if (FPMath.Abs(r3[1]) > FPMath.Abs(r2[1]))
{
swap_rows(ref r3, ref r2);
}
if (FPMath.Abs(r2[1]) > FPMath.Abs(r1[1]))
{
swap_rows(ref r2, ref r1);
}
if (0 == r1[1])
{
return(false);
}
/* eliminate second variable */
m2 = r2[1] / r1[1]; m3 = r3[1] / r1[1];
r2[2] -= m2 * r1[2]; r3[2] -= m3 * r1[2];
r2[3] -= m2 * r1[3]; r3[3] -= m3 * r1[3];
s = r1[4]; if (0.0F != s)
{
r2[4] -= m2 * s; r3[4] -= m3 * s;
}
s = r1[5]; if (0.0F != s)
{
r2[5] -= m2 * s; r3[5] -= m3 * s;
}
s = r1[6]; if (0.0F != s)
{
r2[6] -= m2 * s; r3[6] -= m3 * s;
}
s = r1[7]; if (0.0F != s)
{
r2[7] -= m2 * s; r3[7] -= m3 * s;
}
/* choose pivot - or die */
if (FPMath.Abs(r3[2]) > FPMath.Abs(r2[2]))
{
swap_rows(ref r3, ref r2);
}
if (0.0F == r2[2])
{
return(false);
}
/* eliminate third variable */
m3 = r3[2] / r2[2];
r3[3] -= m3 * r2[3]; r3[4] -= m3 * r2[4];
r3[5] -= m3 * r2[5]; r3[6] -= m3 * r2[6];
r3[7] -= m3 * r2[7];
/* last check */
if (0.0F == r3[3])
{
return(false);
}
s = 1.0F / r3[3]; /* now back substitute row 3 */
r3[4] *= s; r3[5] *= s; r3[6] *= s; r3[7] *= s;
m2 = r2[3]; /* now back substitute row 2 */
s = 1.0F / r2[2];
r2[4] = s * (r2[4] - r3[4] * m2); r2[5] = s * (r2[5] - r3[5] * m2);
r2[6] = s * (r2[6] - r3[6] * m2); r2[7] = s * (r2[7] - r3[7] * m2);
m1 = r1[3];
r1[4] -= r3[4] * m1; r1[5] -= r3[5] * m1;
r1[6] -= r3[6] * m1; r1[7] -= r3[7] * m1;
m0 = r0[3];
r0[4] -= r3[4] * m0; r0[5] -= r3[5] * m0;
r0[6] -= r3[6] * m0; r0[7] -= r3[7] * m0;
m1 = r1[2]; /* now back substitute row 1 */
s = 1.0F / r1[1];
r1[4] = s * (r1[4] - r2[4] * m1); r1[5] = s * (r1[5] - r2[5] * m1);
r1[6] = s * (r1[6] - r2[6] * m1); r1[7] = s * (r1[7] - r2[7] * m1);
m0 = r0[2];
r0[4] -= r2[4] * m0; r0[5] -= r2[5] * m0;
r0[6] -= r2[6] * m0; r0[7] -= r2[7] * m0;
m0 = r0[1]; /* now back substitute row 0 */
s = 1.0F / r0[0];
r0[4] = s * (r0[4] - r1[4] * m0); r0[5] = s * (r0[5] - r1[5] * m0);
r0[6] = s * (r0[6] - r1[6] * m0); r0[7] = s * (r0[7] - r1[7] * m0);
output.m00 = r0[4]; output.m01 = r0[5]; output.m02 = r0[6]; output.m03 = r0[7];
output.m10 = r1[4]; output.m11 = r1[5]; output.m12 = r1[6]; output.m13 = r1[7];
output.m20 = r2[4]; output.m21 = r2[5]; output.m22 = r2[6]; output.m23 = r2[7];
output.m30 = r3[4]; output.m31 = r3[5]; output.m32 = r3[6]; output.m33 = r3[7];
return(true);
}
