/* * Copyright © 2011 Intel Corporation * Copyright © 2012 Collabora, Ltd. * * Permission is hereby granted, free of charge, to any person obtaining * a copy of this software and associated documentation files (the * "Software"), to deal in the Software without restriction, including * without limitation the rights to use, copy, modify, merge, publish, * distribute, sublicense, and/or sell copies of the Software, and to * permit persons to whom the Software is furnished to do so, subject to * the following conditions: * * The above copyright notice and this permission notice (including the * next paragraph) shall be included in all copies or substantial * portions of the Software. * * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE * SOFTWARE. */ #include "config.h" #include #include #include #include #include #include #include /* * Matrices are stored in column-major order, that is the array indices are: * 0 4 8 12 * 1 5 9 13 * 2 6 10 14 * 3 7 11 15 */ WL_EXPORT void weston_matrix_init(struct weston_matrix *matrix) { static const struct weston_matrix identity = { .d = { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 }, .type = 0, }; memcpy(matrix, &identity, sizeof identity); } /* m <- n * m, that is, m is multiplied on the LEFT. */ WL_EXPORT void weston_matrix_multiply(struct weston_matrix *m, const struct weston_matrix *n) { struct weston_matrix tmp; const float *row, *column; div_t d; int i, j; for (i = 0; i < 16; i++) { tmp.d[i] = 0; d = div(i, 4); row = m->d + d.quot * 4; column = n->d + d.rem; for (j = 0; j < 4; j++) tmp.d[i] += row[j] * column[j * 4]; } tmp.type = m->type | n->type; memcpy(m, &tmp, sizeof tmp); } WL_EXPORT void weston_matrix_translate(struct weston_matrix *matrix, float x, float y, float z) { struct weston_matrix translate = { .d = { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, x, y, z, 1 }, .type = WESTON_MATRIX_TRANSFORM_TRANSLATE, }; weston_matrix_multiply(matrix, &translate); } WL_EXPORT void weston_matrix_scale(struct weston_matrix *matrix, float x, float y,float z) { struct weston_matrix scale = { .d = { x, 0, 0, 0, 0, y, 0, 0, 0, 0, z, 0, 0, 0, 0, 1 }, .type = WESTON_MATRIX_TRANSFORM_SCALE, }; weston_matrix_multiply(matrix, &scale); } WL_EXPORT void weston_matrix_rotate_xy(struct weston_matrix *matrix, float cos, float sin) { struct weston_matrix translate = { .d = { cos, sin, 0, 0, -sin, cos, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 }, .type = WESTON_MATRIX_TRANSFORM_ROTATE, }; weston_matrix_multiply(matrix, &translate); } /* v <- m * v */ WL_EXPORT void weston_matrix_transform(const struct weston_matrix *matrix, struct weston_vector *v) { int i, j; struct weston_vector t; for (i = 0; i < 4; i++) { t.f[i] = 0; for (j = 0; j < 4; j++) t.f[i] += v->f[j] * matrix->d[i + j * 4]; } *v = t; } static inline void swap_rows(double *a, double *b) { unsigned k; double tmp; for (k = 0; k < 13; k += 4) { tmp = a[k]; a[k] = b[k]; b[k] = tmp; } } static inline void swap_unsigned(unsigned *a, unsigned *b) { unsigned tmp; tmp = *a; *a = *b; *b = tmp; } static inline unsigned find_pivot(double *column, unsigned k) { unsigned p = k; for (++k; k < 4; ++k) if (fabs(column[p]) < fabs(column[k])) p = k; return p; } /* * reference: Gene H. Golub and Charles F. van Loan. Matrix computations. * 3rd ed. The Johns Hopkins University Press. 1996. * LU decomposition, forward and back substitution: Chapter 3. */ static int matrix_invert(double *A, unsigned *p, const struct weston_matrix *matrix) { unsigned i, j, k; unsigned pivot; double pv; for (i = 0; i < 4; ++i) p[i] = i; for (i = 16; i--; ) A[i] = matrix->d[i]; /* LU decomposition with partial pivoting */ for (k = 0; k < 4; ++k) { pivot = find_pivot(&A[k * 4], k); if (pivot != k) { swap_unsigned(&p[k], &p[pivot]); swap_rows(&A[k], &A[pivot]); } pv = A[k * 4 + k]; if (fabs(pv) < 1e-9) return -1; /* zero pivot, not invertible */ for (i = k + 1; i < 4; ++i) { A[i + k * 4] /= pv; for (j = k + 1; j < 4; ++j) A[i + j * 4] -= A[i + k * 4] * A[k + j * 4]; } } return 0; } static void inverse_transform(const double *LU, const unsigned *p, float *v) { /* Solve A * x = v, when we have P * A = L * U. * P * A * x = P * v => L * U * x = P * v * Let U * x = b, then L * b = P * v. */ double b[4]; unsigned j; /* Forward substitution, column version, solves L * b = P * v */ /* The diagonal of L is all ones, and not explicitly stored. */ b[0] = v[p[0]]; b[1] = (double)v[p[1]] - b[0] * LU[1 + 0 * 4]; b[2] = (double)v[p[2]] - b[0] * LU[2 + 0 * 4]; b[3] = (double)v[p[3]] - b[0] * LU[3 + 0 * 4]; b[2] -= b[1] * LU[2 + 1 * 4]; b[3] -= b[1] * LU[3 + 1 * 4]; b[3] -= b[2] * LU[3 + 2 * 4]; /* backward substitution, column version, solves U * y = b */ #if 1 /* hand-unrolled, 25% faster for whole function */ b[3] /= LU[3 + 3 * 4]; b[0] -= b[3] * LU[0 + 3 * 4]; b[1] -= b[3] * LU[1 + 3 * 4]; b[2] -= b[3] * LU[2 + 3 * 4]; b[2] /= LU[2 + 2 * 4]; b[0] -= b[2] * LU[0 + 2 * 4]; b[1] -= b[2] * LU[1 + 2 * 4]; b[1] /= LU[1 + 1 * 4]; b[0] -= b[1] * LU[0 + 1 * 4]; b[0] /= LU[0 + 0 * 4]; #else for (j = 3; j > 0; --j) { unsigned k; b[j] /= LU[j + j * 4]; for (k = 0; k < j; ++k) b[k] -= b[j] * LU[k + j * 4]; } b[0] /= LU[0 + 0 * 4]; #endif /* the result */ for (j = 0; j < 4; ++j) v[j] = b[j]; } WL_EXPORT int weston_matrix_invert(struct weston_matrix *inverse, const struct weston_matrix *matrix) { double LU[16]; /* column-major */ unsigned perm[4]; /* permutation */ unsigned c; if (matrix_invert(LU, perm, matrix) < 0) return -1; weston_matrix_init(inverse); for (c = 0; c < 4; ++c) inverse_transform(LU, perm, &inverse->d[c * 4]); inverse->type = matrix->type; return 0; } static bool near_zero(float a) { if (fabs(a) > 0.00001) return false; return true; } static float get_el(const struct weston_matrix *matrix, int row, int col) { assert(row >= 0 && row <= 3); assert(col >= 0 && col <= 3); return matrix->d[col * 4 + row]; } static bool near_zero_at(const struct weston_matrix *matrix, int row, int col) { return near_zero(get_el(matrix, row, col)); } static bool near_one_at(const struct weston_matrix *matrix, int row, int col) { return near_zero(get_el(matrix, row, col) - 1.0); } static bool near_pm_one_at(const struct weston_matrix *matrix, int row, int col) { return near_zero(fabs(get_el(matrix, row, col)) - 1.0); } static bool near_int_at(const struct weston_matrix *matrix, int row, int col) { float el = get_el(matrix, row, col); return near_zero(roundf(el) - el); } /* Lazy decompose the matrix to figure out whether its operations will * cause an image to look ugly without some kind of filtering. * * while this is a 3D transformation matrix, we only concern ourselves * with 2D for this test. We do use some small rounding to try to catch * sequences of operations that lead back to a matrix that doesn't * require filters. * * We assume the matrix won't be used to transform a vector with w != 1.0 * * Filtering will be necessary when: * a non-integral translation is applied * non-affine (perspective) translation is in use * any scaling (other than -1) is in use * a rotation that isn't a multiple of 90 degrees about Z is present */ WL_EXPORT bool weston_matrix_needs_filtering(const struct weston_matrix *matrix) { /* check for non-integral X/Y translation - ignore Z */ if (!near_int_at(matrix, 0, 3) || !near_int_at(matrix, 1, 3)) return true; /* Any transform matrix that matches this will be non-affine. */ if (!near_zero_at(matrix, 3, 0) || !near_zero_at(matrix, 3, 1) || !near_zero_at(matrix, 3, 2) || !near_pm_one_at(matrix, 3, 3)) return true; /* Check for anything that could come from a rotation that isn't * around the Z axis: * [ ? ? 0 ? ] * [ ? ? 0 ? ] * [ 0 0 ±1 ? ] * [ ? ? ? 1 ] * It's not clear that we'd realistically see a -1 in [2][2], but * it wouldn't require filtering if we did, so allow it. */ if (!near_zero_at(matrix, 0, 2) || !near_zero_at(matrix, 1, 2) || !near_zero_at(matrix, 2, 0) || !near_zero_at(matrix, 2, 1) || !near_pm_one_at(matrix, 2, 2)) return true; /* We've culled the low hanging fruit, now let's match the only * matrices left we don't have to filter, before defaulting to * filtering. * * These are a combination of testing rotation and scaling at once: */ if (near_pm_one_at(matrix, 0, 0)) { /* This could be a multiple of 90 degree rotation about Z, * possibly with a flip, if the matrix is of the form: * [ ±1 0 0 ? ] * [ 0 ±1 0 ? ] * [ 0 0 1 ? ] * [ 0 0 0 1 ] * Forcing ±1 excludes non-unity scale. */ if (near_zero_at(matrix, 1, 0) && near_zero_at(matrix, 0, 1) && near_pm_one_at(matrix, 1, 1)) return false; } if (near_zero_at(matrix, 0, 0)) { /* This could be a multiple of 90 degree rotation about Z, * possibly with a flip, if the matrix is of the form: * [ 0 ±1 0 ? ] * [ ±1 0 0 ? ] * [ 0 0 1 ? ] * [ 0 0 0 1 ] * Forcing ±1 excludes non-unity scale. */ if (near_zero_at(matrix, 1, 1) && near_pm_one_at(matrix, 1, 0) && near_pm_one_at(matrix, 0, 1)) return false; } /* The matrix wasn't "simple" enough to classify with dumb * heuristics, so recommend filtering */ return true; } /** Examine a matrix to see if it applies a standard output transform. * * \param mat matrix to examine * \param[out] transform the transform, if applicable * \return true if a standard transform is present * Note that the check only considers rotations and flips. * If any other scale or translation is present, those may have to * be dealt with by the caller in some way. */ WL_EXPORT bool weston_matrix_to_transform(const struct weston_matrix *mat, enum wl_output_transform *transform) { /* As a first pass we can eliminate any matrix that doesn't have * zeroes in these positions: * [ ? ? 0 ? ] * [ ? ? 0 ? ] * [ 0 0 ? ? ] * [ 0 0 0 ? ] * As they will be non-affine, or rotations about axes * other than Z. */ if (!near_zero_at(mat, 2, 0) || !near_zero_at(mat, 3, 0) || !near_zero_at(mat, 2, 1) || !near_zero_at(mat, 3, 1) || !near_zero_at(mat, 0, 2) || !near_zero_at(mat, 1, 2) || !near_zero_at(mat, 3, 2)) return false; /* Enforce the form: * [ ? ? 0 ? ] * [ ? ? 0 ? ] * [ 0 0 ? ? ] * [ 0 0 0 1 ] * While we could scale all the elements by a constant to make * 3,3 == 1, we choose to be lazy and not bother. A matrix * that doesn't fit this form seems likely to be too complicated * to pass the other checks. */ if (!near_one_at(mat, 3, 3)) return false; if (near_zero_at(mat, 0, 0)) { if (!near_zero_at(mat, 1, 1)) return false; /* We now have a matrix like: * [ 0 A 0 ? ] * [ B 0 0 ? ] * [ 0 0 ? ? ] * [ 0 0 0 1 ] * When transforming a vector with a matrix of this form, the X * and Y coordinates are effectively exchanged, so we have a * 90 or 270 degree rotation (not 0 or 180), and could have * a flip depending on the signs of A and B. * * We don't require A and B to have the same absolute value, * so there may be independent scales in the X or Y dimensions. */ if (get_el(mat, 0, 1) > 0) { /* A is positive */ if (get_el(mat, 1, 0) > 0) *transform = WL_OUTPUT_TRANSFORM_FLIPPED_90; else *transform = WL_OUTPUT_TRANSFORM_90; } else { /* A is negative */ if (get_el(mat, 1, 0) > 0) *transform = WL_OUTPUT_TRANSFORM_270; else *transform = WL_OUTPUT_TRANSFORM_FLIPPED_270; } } else if (near_zero_at(mat, 1, 0)) { if (!near_zero_at(mat, 0, 1)) return false; /* We now have a matrix like: * [ A 0 0 ? ] * [ 0 B 0 ? ] * [ 0 0 ? ? ] * [ 0 0 0 1 ] * This case won't exchange the X and Y inputs, so the * transform is 0 or 180 degrees. We could have a flip * depending on the signs of A and B. * * We don't require A and B to have the same absolute value, * so there may be independent scales in the X or Y dimensions. */ if (get_el(mat, 0, 0) > 0) { /* A is positive */ if (get_el(mat, 1, 1) > 0) *transform = WL_OUTPUT_TRANSFORM_NORMAL; else *transform = WL_OUTPUT_TRANSFORM_FLIPPED_180; } else { /* A is negative */ if (get_el(mat, 1, 1) > 0) *transform = WL_OUTPUT_TRANSFORM_FLIPPED; else *transform = WL_OUTPUT_TRANSFORM_180; } } else { return false; } return true; }