// added helper for common subexpression elimination by eihrul, and other optimizations by div0
int Matrix4x4_Invert_Full (matrix4x4_t *out, const matrix4x4_t *in1)
{
- float det;
-
- // note: orientation does not matter, as transpose(invert(transpose(m))) == invert(m), proof:
- // transpose(invert(transpose(m))) * m
- // = transpose(invert(transpose(m))) * transpose(transpose(m))
- // = transpose(transpose(m) * invert(transpose(m)))
- // = transpose(identity)
- // = identity
-
- // this seems to help gcc's common subexpression elimination, and also makes the code look nicer
- float m00 = in1->m[0][0], m01 = in1->m[0][1], m02 = in1->m[0][2], m03 = in1->m[0][3],
- m10 = in1->m[1][0], m11 = in1->m[1][1], m12 = in1->m[1][2], m13 = in1->m[1][3],
- m20 = in1->m[2][0], m21 = in1->m[2][1], m22 = in1->m[2][2], m23 = in1->m[2][3],
- m30 = in1->m[3][0], m31 = in1->m[3][1], m32 = in1->m[3][2], m33 = in1->m[3][3];
-
- // calculate the adjoint
- out->m[0][0] = (m11*(m22*m33 - m23*m32) - m21*(m12*m33 - m13*m32) + m31*(m12*m23 - m13*m22));
- out->m[0][1] = -(m01*(m22*m33 - m23*m32) - m21*(m02*m33 - m03*m32) + m31*(m02*m23 - m03*m22));
- out->m[0][2] = (m01*(m12*m33 - m13*m32) - m11*(m02*m33 - m03*m32) + m31*(m02*m13 - m03*m12));
- out->m[0][3] = -(m01*(m12*m23 - m13*m22) - m11*(m02*m23 - m03*m22) + m21*(m02*m13 - m03*m12));
- out->m[1][0] = -(m10*(m22*m33 - m23*m32) - m20*(m12*m33 - m13*m32) + m30*(m12*m23 - m13*m22));
- out->m[1][1] = (m00*(m22*m33 - m23*m32) - m20*(m02*m33 - m03*m32) + m30*(m02*m23 - m03*m22));
- out->m[1][2] = -(m00*(m12*m33 - m13*m32) - m10*(m02*m33 - m03*m32) + m30*(m02*m13 - m03*m12));
- out->m[1][3] = (m00*(m12*m23 - m13*m22) - m10*(m02*m23 - m03*m22) + m20*(m02*m13 - m03*m12));
- out->m[2][0] = (m10*(m21*m33 - m23*m31) - m20*(m11*m33 - m13*m31) + m30*(m11*m23 - m13*m21));
- out->m[2][1] = -(m00*(m21*m33 - m23*m31) - m20*(m01*m33 - m03*m31) + m30*(m01*m23 - m03*m21));
- out->m[2][2] = (m00*(m11*m33 - m13*m31) - m10*(m01*m33 - m03*m31) + m30*(m01*m13 - m03*m11));
- out->m[2][3] = -(m00*(m11*m23 - m13*m21) - m10*(m01*m23 - m03*m21) + m20*(m01*m13 - m03*m11));
- out->m[3][0] = -(m10*(m21*m32 - m22*m31) - m20*(m11*m32 - m12*m31) + m30*(m11*m22 - m12*m21));
- out->m[3][1] = (m00*(m21*m32 - m22*m31) - m20*(m01*m32 - m02*m31) + m30*(m01*m22 - m02*m21));
- out->m[3][2] = -(m00*(m11*m32 - m12*m31) - m10*(m01*m32 - m02*m31) + m30*(m01*m12 - m02*m11));
- out->m[3][3] = (m00*(m11*m22 - m12*m21) - m10*(m01*m22 - m02*m21) + m20*(m01*m12 - m02*m11));
-
- // calculate the determinant (as inverse == 1/det * adjoint, adjoint * m == identity * det, so this calculates the det)
- det = m00*out->m[0][0] + m10*out->m[0][1] + m20*out->m[0][2] + m30*out->m[0][3];
- if (det == 0.0f)
- return 0;
-
- // multiplications are faster than divisions, usually
- det = 1.0f / det;
-
- // manually unrolled loop to multiply all matrix elements by 1/det
- out->m[0][0] *= det; out->m[0][1] *= det; out->m[0][2] *= det; out->m[0][3] *= det;
- out->m[1][0] *= det; out->m[1][1] *= det; out->m[1][2] *= det; out->m[1][3] *= det;
- out->m[2][0] *= det; out->m[2][1] *= det; out->m[2][2] *= det; out->m[2][3] *= det;
- out->m[3][0] *= det; out->m[3][1] *= det; out->m[3][2] *= det; out->m[3][3] *= det;
-
- return 1;
+ float det;
+
+ // note: orientation does not matter, as transpose(invert(transpose(m))) == invert(m), proof:
+ // transpose(invert(transpose(m))) * m
+ // = transpose(invert(transpose(m))) * transpose(transpose(m))
+ // = transpose(transpose(m) * invert(transpose(m)))
+ // = transpose(identity)
+ // = identity
+
+ // this seems to help gcc's common subexpression elimination, and also makes the code look nicer
+ float m00 = in1->m[0][0], m01 = in1->m[0][1], m02 = in1->m[0][2], m03 = in1->m[0][3],
+ m10 = in1->m[1][0], m11 = in1->m[1][1], m12 = in1->m[1][2], m13 = in1->m[1][3],
+ m20 = in1->m[2][0], m21 = in1->m[2][1], m22 = in1->m[2][2], m23 = in1->m[2][3],
+ m30 = in1->m[3][0], m31 = in1->m[3][1], m32 = in1->m[3][2], m33 = in1->m[3][3];
+
+ // calculate the adjoint
+ out->m[0][0] = (m11*(m22*m33 - m23*m32) - m21*(m12*m33 - m13*m32) + m31*(m12*m23 - m13*m22));
+ out->m[0][1] = -(m01*(m22*m33 - m23*m32) - m21*(m02*m33 - m03*m32) + m31*(m02*m23 - m03*m22));
+ out->m[0][2] = (m01*(m12*m33 - m13*m32) - m11*(m02*m33 - m03*m32) + m31*(m02*m13 - m03*m12));
+ out->m[0][3] = -(m01*(m12*m23 - m13*m22) - m11*(m02*m23 - m03*m22) + m21*(m02*m13 - m03*m12));
+ out->m[1][0] = -(m10*(m22*m33 - m23*m32) - m20*(m12*m33 - m13*m32) + m30*(m12*m23 - m13*m22));
+ out->m[1][1] = (m00*(m22*m33 - m23*m32) - m20*(m02*m33 - m03*m32) + m30*(m02*m23 - m03*m22));
+ out->m[1][2] = -(m00*(m12*m33 - m13*m32) - m10*(m02*m33 - m03*m32) + m30*(m02*m13 - m03*m12));
+ out->m[1][3] = (m00*(m12*m23 - m13*m22) - m10*(m02*m23 - m03*m22) + m20*(m02*m13 - m03*m12));
+ out->m[2][0] = (m10*(m21*m33 - m23*m31) - m20*(m11*m33 - m13*m31) + m30*(m11*m23 - m13*m21));
+ out->m[2][1] = -(m00*(m21*m33 - m23*m31) - m20*(m01*m33 - m03*m31) + m30*(m01*m23 - m03*m21));
+ out->m[2][2] = (m00*(m11*m33 - m13*m31) - m10*(m01*m33 - m03*m31) + m30*(m01*m13 - m03*m11));
+ out->m[2][3] = -(m00*(m11*m23 - m13*m21) - m10*(m01*m23 - m03*m21) + m20*(m01*m13 - m03*m11));
+ out->m[3][0] = -(m10*(m21*m32 - m22*m31) - m20*(m11*m32 - m12*m31) + m30*(m11*m22 - m12*m21));
+ out->m[3][1] = (m00*(m21*m32 - m22*m31) - m20*(m01*m32 - m02*m31) + m30*(m01*m22 - m02*m21));
+ out->m[3][2] = -(m00*(m11*m32 - m12*m31) - m10*(m01*m32 - m02*m31) + m30*(m01*m12 - m02*m11));
+ out->m[3][3] = (m00*(m11*m22 - m12*m21) - m10*(m01*m22 - m02*m21) + m20*(m01*m12 - m02*m11));
+
+ // calculate the determinant (as inverse == 1/det * adjoint, adjoint * m == identity * det, so this calculates the det)
+ det = m00*out->m[0][0] + m10*out->m[0][1] + m20*out->m[0][2] + m30*out->m[0][3];
+ if (det == 0.0f)
+ return 0;
+
+ // multiplications are faster than divisions, usually
+ det = 1.0f / det;
+
+ // manually unrolled loop to multiply all matrix elements by 1/det
+ out->m[0][0] *= det; out->m[0][1] *= det; out->m[0][2] *= det; out->m[0][3] *= det;
+ out->m[1][0] *= det; out->m[1][1] *= det; out->m[1][2] *= det; out->m[1][3] *= det;
+ out->m[2][0] *= det; out->m[2][1] *= det; out->m[2][2] *= det; out->m[2][3] *= det;
+ out->m[3][0] *= det; out->m[3][1] *= det; out->m[3][2] *= det; out->m[3][3] *= det;
+
+ return 1;
}
#elif 1
// Adapted from code contributed to Mesa by David Moore (Mesa 7.6 under SGI Free License B - which is MIT/X11-type)
#endif
}
+// see http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm
+void Matrix4x4_ToOrigin3Quat4Float(const matrix4x4_t *m, float *origin, float *quat)
+{
+#if 0
+ float s;
+ quat[3] = sqrt(1.0f + m->m[0][0] + m->m[1][1] + m->m[2][2]) * 0.5f;
+ s = 0.25f / quat[3];
+#ifdef MATRIX4x4_OPENGLORIENTATION
+ origin[0] = m->m[3][0];
+ origin[1] = m->m[3][1];
+ origin[2] = m->m[3][2];
+ quat[0] = (m->m[1][2] - m->m[2][1]) * s;
+ quat[1] = (m->m[2][0] - m->m[0][2]) * s;
+ quat[2] = (m->m[0][1] - m->m[1][0]) * s;
+#else
+ origin[0] = m->m[0][3];
+ origin[1] = m->m[1][3];
+ origin[2] = m->m[2][3];
+ quat[0] = (m->m[2][1] - m->m[1][2]) * s;
+ quat[1] = (m->m[0][2] - m->m[2][0]) * s;
+ quat[2] = (m->m[1][0] - m->m[0][1]) * s;
+#endif
+
+#else
+
+#ifdef MATRIX4x4_OPENGLORIENTATION
+ float trace = m->m[0][0] + m->m[1][1] + m->m[2][2];
+ origin[0] = m->m[3][0];
+ origin[1] = m->m[3][1];
+ origin[2] = m->m[3][2];
+ if(trace > 0)
+ {
+ float r = sqrt(1.0f + trace), inv = 0.5f / r;
+ quat[0] = (m->m[1][2] - m->m[2][1]) * inv;
+ quat[1] = (m->m[2][0] - m->m[0][2]) * inv;
+ quat[2] = (m->m[0][1] - m->m[1][0]) * inv;
+ quat[3] = 0.5f * r;
+ }
+ else if(m->m[0][0] > m->m[1][1] && m->m[0][0] > m->m[2][2])
+ {
+ float r = sqrt(1.0f + m->m[0][0] - m->m[1][1] - m->m[2][2]), inv = 0.5f / r;
+ quat[0] = 0.5f * r;
+ quat[1] = (m->m[0][1] + m->m[1][0]) * inv;
+ quat[2] = (m->m[2][0] + m->m[0][2]) * inv;
+ quat[3] = (m->m[1][2] - m->m[2][1]) * inv;
+ }
+ else if(m->m[1][1] > m->m[2][2])
+ {
+ float r = sqrt(1.0f + m->m[1][1] - m->m[0][0] - m->m[2][2]), inv = 0.5f / r;
+ quat[0] = (m->m[0][1] + m->m[1][0]) * inv;
+ quat[1] = 0.5f * r;
+ quat[2] = (m->m[1][2] + m->m[2][1]) * inv;
+ quat[3] = (m->m[2][0] - m->m[0][2]) * inv;
+ }
+ else
+ {
+ float r = sqrt(1.0f + m->m[2][2] - m->m[0][0] - m->m[1][1]), inv = 0.5f / r;
+ quat[0] = (m->m[2][0] + m->m[0][2]) * inv;
+ quat[1] = (m->m[1][2] + m->m[2][1]) * inv;
+ quat[2] = 0.5f * r;
+ quat[3] = (m->m[0][1] - m->m[1][0]) * inv;
+ }
+#else
+ float trace = m->m[0][0] + m->m[1][1] + m->m[2][2];
+ origin[0] = m->m[0][3];
+ origin[1] = m->m[1][3];
+ origin[2] = m->m[2][3];
+ if(trace > 0)
+ {
+ float r = sqrt(1.0f + trace), inv = 0.5f / r;
+ quat[0] = (m->m[2][1] - m->m[1][2]) * inv;
+ quat[1] = (m->m[0][2] - m->m[2][0]) * inv;
+ quat[2] = (m->m[1][0] - m->m[0][1]) * inv;
+ quat[3] = 0.5f * r;
+ }
+ else if(m->m[0][0] > m->m[1][1] && m->m[0][0] > m->m[2][2])
+ {
+ float r = sqrt(1.0f + m->m[0][0] - m->m[1][1] - m->m[2][2]), inv = 0.5f / r;
+ quat[0] = 0.5f * r;
+ quat[1] = (m->m[1][0] + m->m[0][1]) * inv;
+ quat[2] = (m->m[0][2] + m->m[2][0]) * inv;
+ quat[3] = (m->m[2][1] - m->m[1][2]) * inv;
+ }
+ else if(m->m[1][1] > m->m[2][2])
+ {
+ float r = sqrt(1.0f + m->m[1][1] - m->m[0][0] - m->m[2][2]), inv = 0.5f / r;
+ quat[0] = (m->m[1][0] + m->m[0][1]) * inv;
+ quat[1] = 0.5f * r;
+ quat[2] = (m->m[2][1] + m->m[1][2]) * inv;
+ quat[3] = (m->m[0][2] - m->m[2][0]) * inv;
+ }
+ else
+ {
+ float r = sqrt(1.0f + m->m[2][2] - m->m[0][0] - m->m[1][1]), inv = 0.5f / r;
+ quat[0] = (m->m[0][2] + m->m[2][0]) * inv;
+ quat[1] = (m->m[2][1] + m->m[1][2]) * inv;
+ quat[2] = 0.5f * r;
+ quat[3] = (m->m[1][0] - m->m[0][1]) * inv;
+ }
+#endif
+
+#endif
+}
+
// LordHavoc: I got this code from:
//http://www.doom3world.org/phpbb2/viewtopic.php?t=2884
void Matrix4x4_FromDoom3Joint(matrix4x4_t *m, double ox, double oy, double oz, double x, double y, double z)
{
- double w = 1.0 - (x*x+y*y+z*z);
- w = w > 0.0 ? -sqrt(w) : 0.0;
+ double w = 1.0f - (x*x+y*y+z*z);
+ w = w > 0.0f ? -sqrt(w) : 0.0f;
#ifdef MATRIX4x4_OPENGLORIENTATION
m->m[0][0]=1-2*(y*y+z*z);m->m[1][0]= 2*(x*y-z*w);m->m[2][0]= 2*(x*z+y*w);m->m[3][0]=ox;
m->m[0][1]= 2*(x*y+z*w);m->m[1][1]=1-2*(x*x+z*z);m->m[2][1]= 2*(y*z-x*w);m->m[3][1]=oy;
#endif
}
+void Matrix4x4_FromBonePose7s(matrix4x4_t *m, float originscale, const short *pose7s)
+{
+ float origin[3];
+ float quat[4];
+ float quatscale = pose7s[6] > 0 ? -1.0f / 32767.0f : 1.0f / 32767.0f;
+ origin[0] = pose7s[0] * originscale;
+ origin[1] = pose7s[1] * originscale;
+ origin[2] = pose7s[2] * originscale;
+ quat[0] = pose7s[3] * quatscale;
+ quat[1] = pose7s[4] * quatscale;
+ quat[2] = pose7s[5] * quatscale;
+ quat[3] = pose7s[6] * quatscale;
+ Matrix4x4_FromOriginQuat(m, origin[0], origin[1], origin[2], quat[0], quat[1], quat[2], quat[3]);
+}
+
+void Matrix4x4_ToBonePose7s(const matrix4x4_t *m, float origininvscale, short *pose7s)
+{
+ float origin[3];
+ float quat[4];
+ float quatscale;
+ Matrix4x4_ToOrigin3Quat4Float(m, origin, quat);
+ // normalize quaternion so that it is unit length
+ quatscale = quat[0]*quat[0]+quat[1]*quat[1]+quat[2]*quat[2]+quat[3]*quat[3];
+ if (quatscale)
+ quatscale = (quat[3] >= 0 ? -32767.0f : 32767.0f) / sqrt(quatscale);
+ // use a negative scale on the quat because the above function produces a
+ // positive quat[3] and canonical quaternions have negative quat[3]
+ pose7s[0] = origin[0] * origininvscale;
+ pose7s[1] = origin[1] * origininvscale;
+ pose7s[2] = origin[2] * origininvscale;
+ pose7s[3] = quat[0] * quatscale;
+ pose7s[4] = quat[1] * quatscale;
+ pose7s[5] = quat[2] * quatscale;
+ pose7s[6] = quat[3] * quatscale;
+}
+
void Matrix4x4_Blend (matrix4x4_t *out, const matrix4x4_t *in1, const matrix4x4_t *in2, double blend)
{
double iblend = 1 - blend;
#endif
}
+// transforms a positive distance plane (A*x+B*y+C*z-D=0) through a rotation or translation matrix
void Matrix4x4_TransformPositivePlane(const matrix4x4_t *in, float x, float y, float z, float d, float *o)
{
float scale = sqrt(in->m[0][0] * in->m[0][0] + in->m[0][1] * in->m[0][1] + in->m[0][2] * in->m[0][2]);
#endif
}
+// transforms a standard plane (A*x+B*y+C*z+D=0) through a rotation or translation matrix
void Matrix4x4_TransformStandardPlane(const matrix4x4_t *in, float x, float y, float z, float d, float *o)
{
float scale = sqrt(in->m[0][0] * in->m[0][0] + in->m[0][1] * in->m[0][1] + in->m[0][2] * in->m[0][2]);
void Matrix4x4_Abs (matrix4x4_t *out)
{
- out->m[0][0] = fabs(out->m[0][0]);
- out->m[0][1] = fabs(out->m[0][1]);
- out->m[0][2] = fabs(out->m[0][2]);
- out->m[1][0] = fabs(out->m[1][0]);
- out->m[1][1] = fabs(out->m[1][1]);
- out->m[1][2] = fabs(out->m[1][2]);
- out->m[2][0] = fabs(out->m[2][0]);
- out->m[2][1] = fabs(out->m[2][1]);
- out->m[2][2] = fabs(out->m[2][2]);
+ out->m[0][0] = fabs(out->m[0][0]);
+ out->m[0][1] = fabs(out->m[0][1]);
+ out->m[0][2] = fabs(out->m[0][2]);
+ out->m[1][0] = fabs(out->m[1][0]);
+ out->m[1][1] = fabs(out->m[1][1]);
+ out->m[1][2] = fabs(out->m[1][2]);
+ out->m[2][0] = fabs(out->m[2][0]);
+ out->m[2][1] = fabs(out->m[2][1]);
+ out->m[2][2] = fabs(out->m[2][2]);
}