From f31bfda34abaf5fdd3c31497b476b11f23f728f3 Mon Sep 17 00:00:00 2001 From: Jason Ekstrand Date: Mon, 22 Jun 2020 15:13:29 -0500 Subject: [PATCH] util: Move the 4x4 matrix inverse function to u_math Reviewed-by: Bas Nieuwenhuizen Part-of: --- src/mesa/math/m_matrix.c | 117 +----------------------- src/util/u_math.c | 186 +++++++++++++++++++++++++++++++++++++++ src/util/u_math.h | 2 + 3 files changed, 189 insertions(+), 116 deletions(-) diff --git a/src/mesa/math/m_matrix.c b/src/mesa/math/m_matrix.c index 46f379b1f61..62303bc4e7f 100644 --- a/src/mesa/math/m_matrix.c +++ b/src/mesa/math/m_matrix.c @@ -333,13 +333,6 @@ _math_matrix_print( const GLmatrix *m ) /** \name Matrix inversion */ /*@{*/ -/** - * Swaps the values of two floating point variables. - * - * Used by invert_matrix_general() to swap the row pointers. - */ -#define SWAP_ROWS(a, b) { GLfloat *_tmp = a; (a)=(b); (b)=_tmp; } - /** * Compute inverse of 4x4 transformation matrix. * @@ -357,116 +350,8 @@ _math_matrix_print( const GLmatrix *m ) */ 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 (0.0F == 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 != 0.0F) { r1[4] -= m1 * s; r2[4] -= m2 * s; r3[4] -= m3 * s; } - s = r0[5]; - if (s != 0.0F) { r1[5] -= m1 * s; r2[5] -= m2 * s; r3[5] -= m3 * s; } - s = r0[6]; - if (s != 0.0F) { r1[6] -= m1 * s; r2[6] -= m2 * s; r3[6] -= m3 * s; } - s = r0[7]; - if (s != 0.0F) { 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 (0.0F == 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 (0.0F != 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 (fabsf(r3[2])>fabsf(r2[2])) SWAP_ROWS(r3, r2); - if (0.0F == 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 (0.0F == 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; + return util_invert_mat4x4(mat->inv, mat->m); } -#undef SWAP_ROWS /** * Compute inverse of a general 3d transformation matrix. diff --git a/src/util/u_math.c b/src/util/u_math.c index 278a93736bc..7913285a15b 100644 --- a/src/util/u_math.c +++ b/src/util/u_math.c @@ -123,3 +123,189 @@ util_fpstate_set(unsigned mxcsr) } #endif } + +/** + * Compute inverse of 4x4 matrix. + * + * \return false if the source matrix is singular. + * + * \author + * Code contributed by Jacques Leroy jle@star.be + * + * Calculates the inverse matrix by performing the gaussian matrix reduction + * with partial pivoting followed by back/substitution with the loops manually + * unrolled. + */ +bool +util_invert_mat4x4(float *out, const float *m) +{ + float wtmp[4][8]; + float m0, m1, m2, m3, s; + float *r0, *r1, *r2, *r3; + +#define MAT(m, r, c) (m)[(c)*4 + (r)] +#define SWAP_ROWS(a, b) \ + { \ + float *_tmp = a; \ + (a) = (b); \ + (b) = _tmp; \ + } + + 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 (0.0F == 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 != 0.0F) { + r1[4] -= m1 * s; + r2[4] -= m2 * s; + r3[4] -= m3 * s; + } + s = r0[5]; + if (s != 0.0F) { + r1[5] -= m1 * s; + r2[5] -= m2 * s; + r3[5] -= m3 * s; + } + s = r0[6]; + if (s != 0.0F) { + r1[6] -= m1 * s; + r2[6] -= m2 * s; + r3[6] -= m3 * s; + } + s = r0[7]; + if (s != 0.0F) { + 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 (0.0F == 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 (fabsf(r3[2]) > fabsf(r2[2])) + SWAP_ROWS(r3, 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); + + 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 true; +} diff --git a/src/util/u_math.h b/src/util/u_math.h index becae90714c..0223ecb9965 100644 --- a/src/util/u_math.h +++ b/src/util/u_math.h @@ -778,6 +778,8 @@ util_is_vbo_upload_ratio_too_large(unsigned draw_vertex_count, return upload_vertex_count > draw_vertex_count * 16; } +bool util_invert_mat4x4(float *out, const float *m); + #ifdef __cplusplus } #endif