bool ScreenProject::invertMatrix(const double * m, double * out) const
{
/*
* Compute inverse of 4x4 transformation matrix.
* Code contributed by Jacques Leroy [email protected]
* Return GL_TRUE for success, GL_FALSE for failure (singular matrix)
*/
// http://www.mesa3d.org/license.html
// http://webcvs.freedesktop.org/mesa/Mesa/src/glu/mesa/project.c?content-type=text%2Fplain&view=co
//static GLboolean invert_matrix(const GLdouble * m, GLdouble * out)
/* NB. OpenGL Matrices are COLUMN major. */
#define SWAP_ROWS(a, b) { GLdouble *_tmp = a; (a)=(b); (b)=_tmp; }
#define MAT(m,r,c) (m)[(c)*4+(r)]
double wtmp[4][8];
double m0, m1, m2, m3, s;
double *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 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 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 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 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 true;
#undef MAT
#undef SWAP_ROWS
}
compress_data (j_compress_ptr cinfo, JSAMPIMAGE input_buf)
{
j_lossless_c_ptr losslsc = (j_lossless_c_ptr) cinfo->codec;
c_diff_ptr diff = (c_diff_ptr) losslsc->diff_private;
JDIMENSION MCU_col_num; /* index of current MCU within row */
JDIMENSION MCU_count; /* number of MCUs encoded */
/* JDIMENSION last_MCU_col = cinfo->MCUs_per_row - 1; */
JDIMENSION last_iMCU_row = cinfo->total_iMCU_rows - 1;
int comp, ci, yoffset, samp_row, samp_rows, samps_across;
jpeg_component_info *compptr;
/* Loop to write as much as one whole iMCU row */
for (yoffset = diff->MCU_vert_offset; yoffset < diff->MCU_rows_per_iMCU_row;
yoffset++) {
MCU_col_num = diff->mcu_ctr;
/* Scale and predict each scanline of the MCU-row separately.
*
* Note: We only do this if we are at the start of a MCU-row, ie,
* we don't want to reprocess a row suspended by the output.
*/
if (MCU_col_num == 0) {
for (comp = 0; comp < cinfo->comps_in_scan; comp++) {
compptr = cinfo->cur_comp_info[comp];
ci = compptr->component_index;
if (diff->iMCU_row_num < last_iMCU_row)
samp_rows = compptr->v_samp_factor;
else {
/* NB: can't use last_row_height here, since may not be set! */
samp_rows = (int) (compptr->height_in_data_units % compptr->v_samp_factor);
if (samp_rows == 0) samp_rows = compptr->v_samp_factor;
else {
/* Fill dummy difference rows at the bottom edge with zeros, which
* will encode to the smallest amount of data.
*/
for (samp_row = samp_rows; samp_row < compptr->v_samp_factor;
samp_row++)
MEMZERO(diff->diff_buf[ci][samp_row],
jround_up((long) compptr->width_in_data_units,
(long) compptr->h_samp_factor) * SIZEOF(JDIFF));
}
}
samps_across = compptr->width_in_data_units;
for (samp_row = 0; samp_row < samp_rows; samp_row++) {
(*losslsc->scaler_scale) (cinfo,
input_buf[ci][samp_row],
diff->cur_row[ci], samps_across);
(*losslsc->predict_difference[ci]) (cinfo, ci,
diff->cur_row[ci],
diff->prev_row[ci],
diff->diff_buf[ci][samp_row],
samps_across);
SWAP_ROWS(diff->cur_row[ci], diff->prev_row[ci]);
}
}
}
/* Try to write the MCU-row (or remaining portion of suspended MCU-row). */
MCU_count =
(*losslsc->entropy_encode_mcus) (cinfo,
diff->diff_buf, yoffset, MCU_col_num,
cinfo->MCUs_per_row - MCU_col_num);
if (MCU_count != cinfo->MCUs_per_row - MCU_col_num) {
/* Suspension forced; update state counters and exit */
diff->MCU_vert_offset = yoffset;
diff->mcu_ctr += MCU_col_num;
return FALSE;
}
/* Completed an MCU row, but perhaps not an iMCU row */
diff->mcu_ctr = 0;
}
/* Completed the iMCU row, advance counters for next one */
diff->iMCU_row_num++;
start_iMCU_row(cinfo);
return TRUE;
}
int invert(Matrix4x4* mat, Matrix4x4* inv)
{
double wtmp[4][8];
double m0, m1, m2, m3, s;
double *r0, *r1, *r2, *r3;
r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];
r0[0] = MAT(mat,0,0);
r0[1] = MAT(mat,0,1);
r0[2] = MAT(mat,0,2);
r0[3] = MAT(mat,0,3);
r0[4] = 1.0;
r0[5] = r0[6] = r0[7] = 0.0;
r1[0] = MAT(mat,1,0);
r1[1] = MAT(mat,1,1);
r1[2] = MAT(mat,1,2);
r1[3] = MAT(mat,1,3);
r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0;
r2[0] = MAT(mat,2,0);
r2[1] = MAT(mat,2,1);
r2[2] = MAT(mat,2,2);
r2[3] = MAT(mat,2,3);
r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0;
r3[0] = MAT(mat,3,0);
r3[1] = MAT(mat,3,1);
r3[2] = MAT(mat,3,2);
r3[3] = MAT(mat,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 0;
/* 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 0;
/* 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 0;
/* 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 0;
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);
MAT(inv,0,0) = r0[4];
MAT(inv,0,1) = r0[5],
MAT(inv,0,2) = r0[6];
MAT(inv,0,3) = r0[7],
MAT(inv,1,0) = r1[4];
MAT(inv,1,1) = r1[5],
MAT(inv,1,2) = r1[6];
MAT(inv,1,3) = r1[7],
MAT(inv,2,0) = r2[4];
MAT(inv,2,1) = r2[5],
MAT(inv,2,2) = r2[6];
MAT(inv,2,3) = r2[7],
MAT(inv,3,0) = r3[4];
MAT(inv,3,1) = r3[5],
MAT(inv,3,2) = r3[6];
MAT(inv,3,3) = r3[7];
return 1;
}
// Matrix Inverse
bool Matrix::Invert()
{
#define SWAP_ROWS(a , b) { float *_tmp = a; (a)=(b); (b)=_tmp; }
#define MAT(m,r,c) ((m)[(c)*4+(r)])
float dst[16]; //destination matrix (i.e. inverse)
float wtmp[4][8];
float m0, m1, m2, m3, s;
float *r0, *r1, *r2, *r3;
r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];
r0[0] = MAT(fMatrix,0,0), r0[1] = MAT(fMatrix,0,1),
r0[2] = MAT(fMatrix,0,2), r0[3] = MAT(fMatrix,0,3),
r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0,
r1[0] = MAT(fMatrix,1,0), r1[1] = MAT(fMatrix,1,1),
r1[2] = MAT(fMatrix,1,2), r1[3] = MAT(fMatrix,1,3),
r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0,
r2[0] = MAT(fMatrix,2,0), r2[1] = MAT(fMatrix,2,1),
r2[2] = MAT(fMatrix,2,2), r2[3] = MAT(fMatrix,2,3),
r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0,
r3[0] = MAT(fMatrix,3,0), r3[1] = MAT(fMatrix,3,1),
r3[2] = MAT(fMatrix,3,2), r3[3] = MAT(fMatrix,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 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 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 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 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);
MAT(dst,0,0) = r0[4]; MAT(dst,0,1) = r0[5],
MAT(dst,0,2) = r0[6]; MAT(dst,0,3) = r0[7],
MAT(dst,1,0) = r1[4]; MAT(dst,1,1) = r1[5],
MAT(dst,1,2) = r1[6]; MAT(dst,1,3) = r1[7],
MAT(dst,2,0) = r2[4]; MAT(dst,2,1) = r2[5],
MAT(dst,2,2) = r2[6]; MAT(dst,2,3) = r2[7],
MAT(dst,3,0) = r3[4]; MAT(dst,3,1) = r3[5],
MAT(dst,3,2) = r3[6]; MAT(dst,3,3) = r3[7];
memcpy (fMatrix, dst, 64);
return true;
#undef MAT
#undef SWAP_ROWS
}
/* * Compute inverse of 4x4 transformation matrix. * Code contributed by Jacques Leroy [email protected] * Return GL_TRUE for success, GL_FALSE for failure (singular matrix) */ static GLboolean invert_matrix( const GLdouble *m, GLdouble *out ){ /* NB. OpenGL Matrices are COLUMN major. */ #define SWAP_ROWS( a, b ) { GLdouble *_tmp = a; ( a ) = ( b ); ( b ) = _tmp; } #define MAT( m,r,c ) ( m )[( c ) * 4 + ( r )] GLdouble wtmp[4][8]; GLdouble m0, m1, m2, m3, s; GLdouble *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 MAT #undef SWAP_ROWS }
/* Invert a row-major (C-style) 4x4 matrix. */
static void InvertMatrix(var *out, const var *m)
{
/* Assumes matrices are ROW major. */
#define SWAP_ROWS(a, b) { double *_tmp = a; (a)=(b); (b)=_tmp; }
#define MAT(m,r,c) (m)[(r)*4+(c)]
double wtmp[4][8];
double m0, m1, m2, m3, s;
double *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 myPivot, 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);
/* 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 myPivot, or die. */
if (fabs(r3[1])>fabs(r2[1])) SWAP_ROWS(r3, r2);
if (fabs(r2[1])>fabs(r1[1])) SWAP_ROWS(r2, r1);
/* 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 myPivot, or die. */
if (fabs(r3[2])>fabs(r2[2])) SWAP_ROWS(r3, r2);
/* 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];
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];
#undef MAT
#undef SWAP_ROWS
}
void Matrix4x4<T>::copyInverseTo(Matrix4x4<T>& inMatrix) const
{
#define SWAP_ROWS(a, b) { T* _tmp = a; (a) = (b); (b) = _tmp; }
T wtmp[4][8];
T m0;
T m1;
T m2;
T m3;
T s;
T* r0;
T* r1;
T* r2;
T* r3;
r0 = wtmp[0];
r1 = wtmp[1];
r2 = wtmp[2];
r3 = wtmp[3];
r0[0] = at(0, 0);
r0[1] = at(0, 1);
r0[2] = at(0, 2);
r0[3] = at(0, 3);
r0[4] = 1.0;
r0[5] = r0[6] = r0[7] = 0.0;
r1[0] = at(1, 0);
r1[1] = at(1, 1);
r1[2] = at(1, 2);
r1[3] = at(1, 3);
r1[5] = 1.0;
r1[4] = r1[6] = r1[7] = 0.0;
r2[0] = at(2, 0);
r2[1] = at(2, 1);
r2[2] = at(2, 2);
r2[3] = at(2, 3);
r2[6] = 1.0;
r2[4] = r2[5] = r2[7] = 0.0;
r3[0] = at(3, 0);
r3[1] = at(3, 1);
r3[2] = at(3, 2);
r3[3] = at(3, 3);
r3[7] = 1.0;
r3[4] = r3[5] = r3[6] = 0.0;
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;
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;
}
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;
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;
}
if (fabs(r3[2]) > fabs(r2[2])) SWAP_ROWS(r3, r2);
if (0.0 == r2[2]) return;
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];
if (0.0 == r3[3]) return;
s = 1.0 / r3[3];
r3[4] *= s;
r3[5] *= s;
r3[6] *= s;
r3[7] *= s;
m2 = r2[3];
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];
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];
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);
inMatrix(0, 0) = r0[4];
inMatrix(0, 1) = r0[5];
inMatrix(0, 2) = r0[6];
inMatrix(0, 3) = r0[7];
inMatrix(1, 0) = r1[4];
inMatrix(1, 1) = r1[5];
inMatrix(1, 2) = r1[6];
inMatrix(1, 3) = r1[7];
inMatrix(2, 0) = r2[4];
inMatrix(2, 1) = r2[5];
inMatrix(2, 2) = r2[6];
inMatrix(2, 3) = r2[7];
inMatrix(3, 0) = r3[4];
inMatrix(3, 1) = r3[5];
inMatrix(3, 2) = r3[6];
inMatrix(3, 3) = r3[7];
}
/** * Compute inverse of 4x4 transformation matrix. * * \param mat pointer to a GLmatrix structure. The matrix inverse will be * stored in the GLmatrix::inv attribute. * * \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix). * * \author * Code contributed by Jacques Leroy [email protected] * * Calculates the inverse matrix by performing the gaussian matrix reduction * with partial pivoting followed by back/substitution with the loops manually * unrolled. */ 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 (FABSF(r3[0])>FABSF(r2[0])) SWAP_ROWS(r3, r2); if (FABSF(r2[0])>FABSF(r1[0])) SWAP_ROWS(r2, r1); if (FABSF(r1[0])>FABSF(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 (FABSF(r3[1])>FABSF(r2[1])) SWAP_ROWS(r3, r2); if (FABSF(r2[1])>FABSF(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 (FABSF(r3[2])>FABSF(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 = 1.0F/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); 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; }
Matrix mInversed(const Matrix matrix) {
float* m = (float*)&matrix.values[0][0];
Matrix returnValue;
float* out = &returnValue.values[0][0];
/* NB. OpenGL Matrices are COLUMN major. */
#define SWAP_ROWS(a, b) { float *_tmp = a; (a)=(b); (b)=_tmp; }
#define MAT(m,r,c) (m)[(c)*4+(r)]
float wtmp[4][8];
float m0, m1, m2, m3, s;
float *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 makeMatrixZero();
/* 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 makeMatrixZero();
/* 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 makeMatrixZero();
/* 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 makeMatrixZero();
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];
#undef MAT
#undef SWAP_ROWS
return returnValue;
}