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27 #include <GLES2/gl2.h>
28 #include <wayland-server.h>
34 * Matrices are stored in column-major order, that is the array indices are:
42 weston_matrix_init(struct weston_matrix *matrix)
44 static const struct weston_matrix identity = {
45 { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 }
48 memcpy(matrix, &identity, sizeof identity);
51 /* m <- n * m, that is, m is multiplied on the LEFT. */
53 weston_matrix_multiply(struct weston_matrix *m, const struct weston_matrix *n)
55 struct weston_matrix tmp;
56 const float *row, *column;
60 for (i = 0; i < 16; i++) {
63 row = m->d + d.quot * 4;
64 column = n->d + d.rem;
65 for (j = 0; j < 4; j++)
66 tmp.d[i] += row[j] * column[j * 4];
68 memcpy(m, &tmp, sizeof tmp);
72 weston_matrix_translate(struct weston_matrix *matrix, float x, float y, float z)
74 struct weston_matrix translate = {
75 { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, x, y, z, 1 }
78 weston_matrix_multiply(matrix, &translate);
82 weston_matrix_scale(struct weston_matrix *matrix, float x, float y,float z)
84 struct weston_matrix scale = {
85 { x, 0, 0, 0, 0, y, 0, 0, 0, 0, z, 0, 0, 0, 0, 1 }
88 weston_matrix_multiply(matrix, &scale);
93 weston_matrix_transform(struct weston_matrix *matrix, struct weston_vector *v)
96 struct weston_vector t;
98 for (i = 0; i < 4; i++) {
100 for (j = 0; j < 4; j++)
101 t.f[i] += v->f[j] * matrix->d[i + j * 4];
108 swap_rows(double *a, double *b)
113 for (k = 0; k < 13; k += 4) {
121 swap_unsigned(unsigned *a, unsigned *b)
130 static inline unsigned
131 find_pivot(double *column, unsigned k)
134 for (++k; k < 4; ++k)
135 if (fabs(column[p]) < fabs(column[k]))
142 * reference: Gene H. Golub and Charles F. van Loan. Matrix computations.
143 * 3rd ed. The Johns Hopkins University Press. 1996.
144 * LU decomposition, forward and back substitution: Chapter 3.
147 MATRIX_TEST_EXPORT inline int
148 matrix_invert(double *A, unsigned *p, const struct weston_matrix *matrix)
154 for (i = 0; i < 4; ++i)
159 /* LU decomposition with partial pivoting */
160 for (k = 0; k < 4; ++k) {
161 pivot = find_pivot(&A[k * 4], k);
163 swap_unsigned(&p[k], &p[pivot]);
164 swap_rows(&A[k], &A[pivot]);
169 return -1; /* zero pivot, not invertible */
171 for (i = k + 1; i < 4; ++i) {
174 for (j = k + 1; j < 4; ++j)
175 A[i + j * 4] -= A[i + k * 4] * A[k + j * 4];
182 MATRIX_TEST_EXPORT inline void
183 inverse_transform(const double *LU, const unsigned *p, float *v)
185 /* Solve A * x = v, when we have P * A = L * U.
186 * P * A * x = P * v => L * U * x = P * v
187 * Let U * x = b, then L * b = P * v.
192 /* Forward substitution, column version, solves L * b = P * v */
193 /* The diagonal of L is all ones, and not explicitly stored. */
195 b[1] = (double)v[p[1]] - b[0] * LU[1 + 0 * 4];
196 b[2] = (double)v[p[2]] - b[0] * LU[2 + 0 * 4];
197 b[3] = (double)v[p[3]] - b[0] * LU[3 + 0 * 4];
198 b[2] -= b[1] * LU[2 + 1 * 4];
199 b[3] -= b[1] * LU[3 + 1 * 4];
200 b[3] -= b[2] * LU[3 + 2 * 4];
202 /* backward substitution, column version, solves U * y = b */
204 /* hand-unrolled, 25% faster for whole function */
205 b[3] /= LU[3 + 3 * 4];
206 b[0] -= b[3] * LU[0 + 3 * 4];
207 b[1] -= b[3] * LU[1 + 3 * 4];
208 b[2] -= b[3] * LU[2 + 3 * 4];
210 b[2] /= LU[2 + 2 * 4];
211 b[0] -= b[2] * LU[0 + 2 * 4];
212 b[1] -= b[2] * LU[1 + 2 * 4];
214 b[1] /= LU[1 + 1 * 4];
215 b[0] -= b[1] * LU[0 + 1 * 4];
217 b[0] /= LU[0 + 0 * 4];
219 for (j = 3; j > 0; --j) {
221 b[j] /= LU[j + j * 4];
222 for (k = 0; k < j; ++k)
223 b[k] -= b[j] * LU[k + j * 4];
226 b[0] /= LU[0 + 0 * 4];
230 for (j = 0; j < 4; ++j)
235 weston_matrix_invert(struct weston_matrix *inverse,
236 const struct weston_matrix *matrix)
238 double LU[16]; /* column-major */
239 unsigned perm[4]; /* permutation */
242 if (matrix_invert(LU, perm, matrix) < 0)
245 weston_matrix_init(inverse);
246 for (c = 0; c < 4; ++c)
247 inverse_transform(LU, perm, &inverse->d[c * 4]);