-static GLboolean invert_matrix_general( GLmatrix *mat )
-{
- const GLfloat *m = mat->m;
- GLfloat *out = mat->inv;
- GLfloat wtmp[4][8];
- GLfloat m0, m1, m2, m3, s;
- GLfloat *r0, *r1, *r2, *r3;
-
- r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];
-
- r0[0] = MAT(m,0,0), r0[1] = MAT(m,0,1),
- r0[2] = MAT(m,0,2), r0[3] = MAT(m,0,3),
- r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0,
-
- r1[0] = MAT(m,1,0), r1[1] = MAT(m,1,1),
- r1[2] = MAT(m,1,2), r1[3] = MAT(m,1,3),
- r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0,
-
- r2[0] = MAT(m,2,0), r2[1] = MAT(m,2,1),
- r2[2] = MAT(m,2,2), r2[3] = MAT(m,2,3),
- r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0,
-
- r3[0] = MAT(m,3,0), r3[1] = MAT(m,3,1),
- r3[2] = MAT(m,3,2), r3[3] = MAT(m,3,3),
- r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0;
-
- /* choose pivot - or die */
- if (fabs(r3[0])>fabs(r2[0])) SWAP_ROWS(r3, r2);
- if (fabs(r2[0])>fabs(r1[0])) SWAP_ROWS(r2, r1);
- if (fabs(r1[0])>fabs(r0[0])) SWAP_ROWS(r1, r0);
- if (0.0 == r0[0]) return GL_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 != 0.0) { r1[4] -= m1 * s; r2[4] -= m2 * s; r3[4] -= m3 * s; }
- s = r0[5];
- if (s != 0.0) { r1[5] -= m1 * s; r2[5] -= m2 * s; r3[5] -= m3 * s; }
- s = r0[6];
- if (s != 0.0) { r1[6] -= m1 * s; r2[6] -= m2 * s; r3[6] -= m3 * s; }
- s = r0[7];
- if (s != 0.0) { r1[7] -= m1 * s; r2[7] -= m2 * s; r3[7] -= m3 * s; }
-
- /* choose pivot - or die */
- if (fabs(r3[1])>fabs(r2[1])) SWAP_ROWS(r3, r2);
- if (fabs(r2[1])>fabs(r1[1])) SWAP_ROWS(r2, r1);
- if (0.0 == r1[1]) return GL_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 (0.0 != s) { r2[4] -= m2 * s; r3[4] -= m3 * s; }
- s = r1[5]; if (0.0 != s) { r2[5] -= m2 * s; r3[5] -= m3 * s; }
- s = r1[6]; if (0.0 != s) { r2[6] -= m2 * s; r3[6] -= m3 * s; }
- s = r1[7]; if (0.0 != s) { r2[7] -= m2 * s; r3[7] -= m3 * s; }
-
- /* choose pivot - or die */
- if (fabs(r3[2])>fabs(r2[2])) SWAP_ROWS(r3, r2);
- if (0.0 == r2[2]) return GL_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 (0.0 == r3[3]) return GL_FALSE;
-
- s = 1.0/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 = 1.0/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 = 1.0/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 = 1.0/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);
-
- MAT(out,0,0) = r0[4]; MAT(out,0,1) = r0[5],
- MAT(out,0,2) = r0[6]; MAT(out,0,3) = r0[7],
- MAT(out,1,0) = r1[4]; MAT(out,1,1) = r1[5],
- MAT(out,1,2) = r1[6]; MAT(out,1,3) = r1[7],
- MAT(out,2,0) = r2[4]; MAT(out,2,1) = r2[5],
- MAT(out,2,2) = r2[6]; MAT(out,2,3) = r2[7],
- MAT(out,3,0) = r3[4]; MAT(out,3,1) = r3[5],
- MAT(out,3,2) = r3[6]; MAT(out,3,3) = r3[7];
-
- return GL_TRUE;
-}
-#undef SWAP_ROWS
-
-/* Adapted from graphics gems II.
- */
-GLboolean invert_matrix_3d_general( GLmatrix *mat )
-{
- const GLfloat *in = mat->m;
- GLfloat *out = mat->inv;
- GLfloat pos, neg, t;
- GLfloat det;
-
- /* Calculate the determinant of upper left 3x3 submatrix and
- * determine if the matrix is singular.
- */
- pos = neg = 0.0;
- t = MAT(in,0,0) * MAT(in,1,1) * MAT(in,2,2);
- if (t >= 0.0) pos += t; else neg += t;
-
- t = MAT(in,1,0) * MAT(in,2,1) * MAT(in,0,2);
- if (t >= 0.0) pos += t; else neg += t;
-
- t = MAT(in,2,0) * MAT(in,0,1) * MAT(in,1,2);
- if (t >= 0.0) pos += t; else neg += t;
-
- t = -MAT(in,2,0) * MAT(in,1,1) * MAT(in,0,2);
- if (t >= 0.0) pos += t; else neg += t;
-
- t = -MAT(in,1,0) * MAT(in,0,1) * MAT(in,2,2);
- if (t >= 0.0) pos += t; else neg += t;
-
- t = -MAT(in,0,0) * MAT(in,2,1) * MAT(in,1,2);
- if (t >= 0.0) pos += t; else neg += t;
-
- det = pos + neg;
-
- if (det*det < 1e-25)
- return GL_FALSE;
-
- det = 1.0 / det;
- MAT(out,0,0) = ( (MAT(in,1,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,1,2) )*det);
- MAT(out,0,1) = (- (MAT(in,0,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,0,2) )*det);
- MAT(out,0,2) = ( (MAT(in,0,1)*MAT(in,1,2) - MAT(in,1,1)*MAT(in,0,2) )*det);
- MAT(out,1,0) = (- (MAT(in,1,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,1,2) )*det);
- MAT(out,1,1) = ( (MAT(in,0,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,0,2) )*det);
- MAT(out,1,2) = (- (MAT(in,0,0)*MAT(in,1,2) - MAT(in,1,0)*MAT(in,0,2) )*det);
- MAT(out,2,0) = ( (MAT(in,1,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,1,1) )*det);
- MAT(out,2,1) = (- (MAT(in,0,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,0,1) )*det);
- MAT(out,2,2) = ( (MAT(in,0,0)*MAT(in,1,1) - MAT(in,1,0)*MAT(in,0,1) )*det);
-
- /* Do the translation part */
- MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) +
- MAT(in,1,3) * MAT(out,0,1) +
- MAT(in,2,3) * MAT(out,0,2) );
- MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) +
- MAT(in,1,3) * MAT(out,1,1) +
- MAT(in,2,3) * MAT(out,1,2) );
- MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) +
- MAT(in,1,3) * MAT(out,2,1) +
- MAT(in,2,3) * MAT(out,2,2) );
-
- return GL_TRUE;
-}
-
-
-static GLboolean invert_matrix_3d( GLmatrix *mat )
-{
- const GLfloat *in = mat->m;
- GLfloat *out = mat->inv;
-
- if (!TEST_MAT_FLAGS(mat, MAT_FLAGS_ANGLE_PRESERVING))
- {
- return invert_matrix_3d_general( mat );
- }
-
- if (mat->flags & MAT_FLAG_UNIFORM_SCALE)
- {
- GLfloat scale = (MAT(in,0,0) * MAT(in,0,0) +
- MAT(in,0,1) * MAT(in,0,1) +
- MAT(in,0,2) * MAT(in,0,2));
-
- if (scale == 0.0)
- return GL_FALSE;
-
- scale = 1.0 / scale;
-
- /* Transpose and scale the 3 by 3 upper-left submatrix. */
- MAT(out,0,0) = scale * MAT(in,0,0);
- MAT(out,1,0) = scale * MAT(in,0,1);
- MAT(out,2,0) = scale * MAT(in,0,2);
- MAT(out,0,1) = scale * MAT(in,1,0);
- MAT(out,1,1) = scale * MAT(in,1,1);
- MAT(out,2,1) = scale * MAT(in,1,2);
- MAT(out,0,2) = scale * MAT(in,2,0);
- MAT(out,1,2) = scale * MAT(in,2,1);
- MAT(out,2,2) = scale * MAT(in,2,2);
- }
- else if (mat->flags & MAT_FLAG_ROTATION)
- {
- /* Transpose the 3 by 3 upper-left submatrix. */
- MAT(out,0,0) = MAT(in,0,0);
- MAT(out,1,0) = MAT(in,0,1);
- MAT(out,2,0) = MAT(in,0,2);
- MAT(out,0,1) = MAT(in,1,0);
- MAT(out,1,1) = MAT(in,1,1);
- MAT(out,2,1) = MAT(in,1,2);
- MAT(out,0,2) = MAT(in,2,0);
- MAT(out,1,2) = MAT(in,2,1);
- MAT(out,2,2) = MAT(in,2,2);
- }
- else /* pure translation */
- {
- MEMCPY( out, Identity, sizeof(Identity) );
- MAT(out,0,3) = - MAT(in,0,3);
- MAT(out,1,3) = - MAT(in,1,3);
- MAT(out,2,3) = - MAT(in,2,3);
- return GL_TRUE;
- }
-
- if (mat->flags & MAT_FLAG_TRANSLATION)
- {
- /* Do the translation part */
- MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) +
- MAT(in,1,3) * MAT(out,0,1) +
- MAT(in,2,3) * MAT(out,0,2) );
- MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) +
- MAT(in,1,3) * MAT(out,1,1) +
- MAT(in,2,3) * MAT(out,1,2) );
- MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) +
- MAT(in,1,3) * MAT(out,2,1) +
- MAT(in,2,3) * MAT(out,2,2) );
- }
- else
- {
- MAT(out,0,3) = MAT(out,1,3) = MAT(out,2,3) = 0.0;
- }
-
- return GL_TRUE;
-}
-
-
-
-static GLboolean invert_matrix_identity( GLmatrix *mat )