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273 lines
6.3 KiB
273 lines
6.3 KiB
/*
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* Copyright © 2011 Intel Corporation
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* Copyright © 2012 Collabora, Ltd.
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*
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* Permission to use, copy, modify, distribute, and sell this software and
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* its documentation for any purpose is hereby granted without fee, provided
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* that the above copyright notice appear in all copies and that both that
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* copyright notice and this permission notice appear in supporting
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* documentation, and that the name of the copyright holders not be used in
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* advertising or publicity pertaining to distribution of the software
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* without specific, written prior permission. The copyright holders make
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* no representations about the suitability of this software for any
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* purpose. It is provided "as is" without express or implied warranty.
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*
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* THE COPYRIGHT HOLDERS DISCLAIM ALL WARRANTIES WITH REGARD TO THIS
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* SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
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* FITNESS, IN NO EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY
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* SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER
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* RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF
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* CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
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* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
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*/
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#include "config.h"
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#include <float.h>
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#include <string.h>
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#include <stdlib.h>
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#include <math.h>
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#ifdef IN_WESTON
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#include <wayland-server.h>
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#else
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#define WL_EXPORT
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#endif
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#include "matrix.h"
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/*
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* Matrices are stored in column-major order, that is the array indices are:
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* 0 4 8 12
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* 1 5 9 13
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* 2 6 10 14
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* 3 7 11 15
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*/
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WL_EXPORT void
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weston_matrix_init(struct weston_matrix *matrix)
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{
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static const struct weston_matrix identity = {
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.d = { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 },
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.type = 0,
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};
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memcpy(matrix, &identity, sizeof identity);
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}
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/* m <- n * m, that is, m is multiplied on the LEFT. */
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WL_EXPORT void
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weston_matrix_multiply(struct weston_matrix *m, const struct weston_matrix *n)
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{
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struct weston_matrix tmp;
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const float *row, *column;
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div_t d;
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int i, j;
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for (i = 0; i < 16; i++) {
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tmp.d[i] = 0;
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d = div(i, 4);
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row = m->d + d.quot * 4;
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column = n->d + d.rem;
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for (j = 0; j < 4; j++)
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tmp.d[i] += row[j] * column[j * 4];
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}
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tmp.type = m->type | n->type;
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memcpy(m, &tmp, sizeof tmp);
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}
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WL_EXPORT void
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weston_matrix_translate(struct weston_matrix *matrix, float x, float y, float z)
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{
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struct weston_matrix translate = {
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.d = { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, x, y, z, 1 },
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.type = WESTON_MATRIX_TRANSFORM_TRANSLATE,
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};
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weston_matrix_multiply(matrix, &translate);
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}
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WL_EXPORT void
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weston_matrix_scale(struct weston_matrix *matrix, float x, float y,float z)
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{
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struct weston_matrix scale = {
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.d = { x, 0, 0, 0, 0, y, 0, 0, 0, 0, z, 0, 0, 0, 0, 1 },
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.type = WESTON_MATRIX_TRANSFORM_SCALE,
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};
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weston_matrix_multiply(matrix, &scale);
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}
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WL_EXPORT void
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weston_matrix_rotate_xy(struct weston_matrix *matrix, float cos, float sin)
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{
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struct weston_matrix translate = {
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.d = { cos, sin, 0, 0, -sin, cos, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 },
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.type = WESTON_MATRIX_TRANSFORM_ROTATE,
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};
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weston_matrix_multiply(matrix, &translate);
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}
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/* v <- m * v */
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WL_EXPORT void
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weston_matrix_transform(struct weston_matrix *matrix, struct weston_vector *v)
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{
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int i, j;
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struct weston_vector t;
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for (i = 0; i < 4; i++) {
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t.f[i] = 0;
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for (j = 0; j < 4; j++)
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t.f[i] += v->f[j] * matrix->d[i + j * 4];
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}
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*v = t;
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}
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static inline void
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swap_rows(double *a, double *b)
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{
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unsigned k;
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double tmp;
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for (k = 0; k < 13; k += 4) {
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tmp = a[k];
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a[k] = b[k];
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b[k] = tmp;
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}
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}
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static inline void
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swap_unsigned(unsigned *a, unsigned *b)
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{
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unsigned tmp;
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tmp = *a;
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*a = *b;
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*b = tmp;
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}
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static inline unsigned
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find_pivot(double *column, unsigned k)
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{
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unsigned p = k;
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for (++k; k < 4; ++k)
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if (fabs(column[p]) < fabs(column[k]))
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p = k;
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return p;
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}
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/*
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* reference: Gene H. Golub and Charles F. van Loan. Matrix computations.
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* 3rd ed. The Johns Hopkins University Press. 1996.
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* LU decomposition, forward and back substitution: Chapter 3.
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*/
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MATRIX_TEST_EXPORT inline int
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matrix_invert(double *A, unsigned *p, const struct weston_matrix *matrix)
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{
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unsigned i, j, k;
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unsigned pivot;
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double pv;
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for (i = 0; i < 4; ++i)
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p[i] = i;
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for (i = 16; i--; )
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A[i] = matrix->d[i];
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/* LU decomposition with partial pivoting */
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for (k = 0; k < 4; ++k) {
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pivot = find_pivot(&A[k * 4], k);
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if (pivot != k) {
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swap_unsigned(&p[k], &p[pivot]);
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swap_rows(&A[k], &A[pivot]);
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}
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pv = A[k * 4 + k];
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if (fabs(pv) < 1e-9)
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return -1; /* zero pivot, not invertible */
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for (i = k + 1; i < 4; ++i) {
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A[i + k * 4] /= pv;
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for (j = k + 1; j < 4; ++j)
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A[i + j * 4] -= A[i + k * 4] * A[k + j * 4];
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}
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}
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return 0;
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}
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MATRIX_TEST_EXPORT inline void
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inverse_transform(const double *LU, const unsigned *p, float *v)
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{
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/* Solve A * x = v, when we have P * A = L * U.
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* P * A * x = P * v => L * U * x = P * v
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* Let U * x = b, then L * b = P * v.
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*/
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double b[4];
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unsigned j;
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/* Forward substitution, column version, solves L * b = P * v */
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/* The diagonal of L is all ones, and not explicitly stored. */
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b[0] = v[p[0]];
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b[1] = (double)v[p[1]] - b[0] * LU[1 + 0 * 4];
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b[2] = (double)v[p[2]] - b[0] * LU[2 + 0 * 4];
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b[3] = (double)v[p[3]] - b[0] * LU[3 + 0 * 4];
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b[2] -= b[1] * LU[2 + 1 * 4];
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b[3] -= b[1] * LU[3 + 1 * 4];
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b[3] -= b[2] * LU[3 + 2 * 4];
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/* backward substitution, column version, solves U * y = b */
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#if 1
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/* hand-unrolled, 25% faster for whole function */
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b[3] /= LU[3 + 3 * 4];
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b[0] -= b[3] * LU[0 + 3 * 4];
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b[1] -= b[3] * LU[1 + 3 * 4];
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b[2] -= b[3] * LU[2 + 3 * 4];
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b[2] /= LU[2 + 2 * 4];
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b[0] -= b[2] * LU[0 + 2 * 4];
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b[1] -= b[2] * LU[1 + 2 * 4];
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b[1] /= LU[1 + 1 * 4];
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b[0] -= b[1] * LU[0 + 1 * 4];
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b[0] /= LU[0 + 0 * 4];
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#else
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for (j = 3; j > 0; --j) {
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unsigned k;
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b[j] /= LU[j + j * 4];
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for (k = 0; k < j; ++k)
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b[k] -= b[j] * LU[k + j * 4];
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}
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b[0] /= LU[0 + 0 * 4];
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#endif
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/* the result */
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for (j = 0; j < 4; ++j)
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v[j] = b[j];
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}
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WL_EXPORT int
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weston_matrix_invert(struct weston_matrix *inverse,
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const struct weston_matrix *matrix)
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{
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double LU[16]; /* column-major */
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unsigned perm[4]; /* permutation */
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unsigned c;
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if (matrix_invert(LU, perm, matrix) < 0)
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return -1;
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weston_matrix_init(inverse);
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for (c = 0; c < 4; ++c)
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inverse_transform(LU, perm, &inverse->d[c * 4]);
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inverse->type = matrix->type;
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return 0;
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}
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