583 lines
14 KiB
C
583 lines
14 KiB
C
/*
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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 is hereby granted, free of charge, to any person obtaining
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* a copy of this software and associated documentation files (the
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* "Software"), to deal in the Software without restriction, including
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* without limitation the rights to use, copy, modify, merge, publish,
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* distribute, sublicense, and/or sell copies of the Software, and to
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* permit persons to whom the Software is furnished to do so, subject to
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* the following conditions:
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*
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* The above copyright notice and this permission notice (including the
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* next paragraph) shall be included in all copies or substantial
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* portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
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* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
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* BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
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* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
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* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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* SOFTWARE.
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*/
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#include "config.h"
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#include <assert.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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#include <wayland-server.h>
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#include <libweston/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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int i, j, k;
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for (i = 0; i < 4; i++) {
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row = m->d + i * 4;
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for (j = 0; j < 4; j++) {
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tmp.d[4 * i + j] = 0;
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column = n->d + j;
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for (k = 0; k < 4; k++)
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tmp.d[4 * i + j] += row[k] * column[k * 4];
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}
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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(const struct weston_matrix *matrix,
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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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WL_EXPORT struct weston_coord
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weston_matrix_transform_coord(const struct weston_matrix *matrix,
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struct weston_coord c)
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{
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struct weston_coord out;
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struct weston_vector t = { { c.x, c.y, 0.0, 1.0 } };
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weston_matrix_transform(matrix, &t);
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assert(fabsf(t.f[3]) > 1e-6);
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out.x = t.f[0] / t.f[3];
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out.y = t.f[1] / t.f[3];
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return out;
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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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static 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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static 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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static bool
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near_zero(float a)
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{
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if (fabs(a) > 0.00001)
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return false;
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return true;
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}
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static float
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get_el(const struct weston_matrix *matrix, int row, int col)
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{
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assert(row >= 0 && row <= 3);
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assert(col >= 0 && col <= 3);
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return matrix->d[col * 4 + row];
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}
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static bool
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near_zero_at(const struct weston_matrix *matrix, int row, int col)
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{
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return near_zero(get_el(matrix, row, col));
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}
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static bool
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near_one_at(const struct weston_matrix *matrix, int row, int col)
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{
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return near_zero(get_el(matrix, row, col) - 1.0);
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}
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static bool
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near_pm_one_at(const struct weston_matrix *matrix, int row, int col)
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{
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return near_zero(fabs(get_el(matrix, row, col)) - 1.0);
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}
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static bool
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near_int_at(const struct weston_matrix *matrix, int row, int col)
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{
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float el = get_el(matrix, row, col);
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return near_zero(roundf(el) - el);
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}
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/* Lazy decompose the matrix to figure out whether its operations will
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* cause an image to look ugly without some kind of filtering.
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*
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* while this is a 3D transformation matrix, we only concern ourselves
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* with 2D for this test. We do use some small rounding to try to catch
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* sequences of operations that lead back to a matrix that doesn't
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* require filters.
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*
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* We assume the matrix won't be used to transform a vector with w != 1.0
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*
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* Filtering will be necessary when:
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* a non-integral translation is applied
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* non-affine (perspective) translation is in use
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* any scaling (other than -1) is in use
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* a rotation that isn't a multiple of 90 degrees about Z is present
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*/
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WL_EXPORT bool
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weston_matrix_needs_filtering(const struct weston_matrix *matrix)
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{
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/* check for non-integral X/Y translation - ignore Z */
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if (!near_int_at(matrix, 0, 3) ||
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!near_int_at(matrix, 1, 3))
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return true;
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/* Any transform matrix that matches this will be non-affine. */
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if (!near_zero_at(matrix, 3, 0) ||
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!near_zero_at(matrix, 3, 1) ||
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!near_zero_at(matrix, 3, 2) ||
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!near_pm_one_at(matrix, 3, 3))
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return true;
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/* Check for anything that could come from a rotation that isn't
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* around the Z axis:
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* [ ? ? 0 ? ]
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* [ ? ? 0 ? ]
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* [ 0 0 ±1 ? ]
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* [ ? ? ? 1 ]
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* It's not clear that we'd realistically see a -1 in [2][2], but
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* it wouldn't require filtering if we did, so allow it.
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*/
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if (!near_zero_at(matrix, 0, 2) ||
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!near_zero_at(matrix, 1, 2) ||
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!near_zero_at(matrix, 2, 0) ||
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!near_zero_at(matrix, 2, 1) ||
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!near_pm_one_at(matrix, 2, 2))
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return true;
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/* We've culled the low hanging fruit, now let's match the only
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* matrices left we don't have to filter, before defaulting to
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* filtering.
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*
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* These are a combination of testing rotation and scaling at once: */
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if (near_pm_one_at(matrix, 0, 0)) {
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/* This could be a multiple of 90 degree rotation about Z,
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* possibly with a flip, if the matrix is of the form:
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* [ ±1 0 0 ? ]
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* [ 0 ±1 0 ? ]
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* [ 0 0 1 ? ]
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* [ 0 0 0 1 ]
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* Forcing ±1 excludes non-unity scale.
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*/
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if (near_zero_at(matrix, 1, 0) &&
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near_zero_at(matrix, 0, 1) &&
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near_pm_one_at(matrix, 1, 1))
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return false;
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}
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if (near_zero_at(matrix, 0, 0)) {
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/* This could be a multiple of 90 degree rotation about Z,
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* possibly with a flip, if the matrix is of the form:
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* [ 0 ±1 0 ? ]
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* [ ±1 0 0 ? ]
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* [ 0 0 1 ? ]
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* [ 0 0 0 1 ]
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* Forcing ±1 excludes non-unity scale.
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*/
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if (near_zero_at(matrix, 1, 1) &&
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near_pm_one_at(matrix, 1, 0) &&
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near_pm_one_at(matrix, 0, 1))
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return false;
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}
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/* The matrix wasn't "simple" enough to classify with dumb
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* heuristics, so recommend filtering */
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return true;
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}
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/** Examine a matrix to see if it applies a standard output transform.
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*
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* \param mat matrix to examine
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* \param[out] transform the transform, if applicable
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* \return true if a standard transform is present
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* Note that the check only considers rotations and flips.
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* If any other scale or translation is present, those may have to
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* be dealt with by the caller in some way.
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*/
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WL_EXPORT bool
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weston_matrix_to_transform(const struct weston_matrix *mat,
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enum wl_output_transform *transform)
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{
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/* As a first pass we can eliminate any matrix that doesn't have
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* zeroes in these positions:
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* [ ? ? 0 ? ]
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* [ ? ? 0 ? ]
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* [ 0 0 ? ? ]
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* [ 0 0 0 ? ]
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* As they will be non-affine, or rotations about axes
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* other than Z.
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*/
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if (!near_zero_at(mat, 2, 0) ||
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!near_zero_at(mat, 3, 0) ||
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!near_zero_at(mat, 2, 1) ||
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!near_zero_at(mat, 3, 1) ||
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!near_zero_at(mat, 0, 2) ||
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!near_zero_at(mat, 1, 2) ||
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!near_zero_at(mat, 3, 2))
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return false;
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/* Enforce the form:
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* [ ? ? 0 ? ]
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* [ ? ? 0 ? ]
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* [ 0 0 ? ? ]
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* [ 0 0 0 1 ]
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* While we could scale all the elements by a constant to make
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* 3,3 == 1, we choose to be lazy and not bother. A matrix
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* that doesn't fit this form seems likely to be too complicated
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* to pass the other checks.
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*/
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if (!near_one_at(mat, 3, 3))
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return false;
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if (near_zero_at(mat, 0, 0)) {
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if (!near_zero_at(mat, 1, 1))
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return false;
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/* We now have a matrix like:
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* [ 0 A 0 ? ]
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* [ B 0 0 ? ]
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* [ 0 0 ? ? ]
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* [ 0 0 0 1 ]
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* When transforming a vector with a matrix of this form, the X
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* and Y coordinates are effectively exchanged, so we have a
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* 90 or 270 degree rotation (not 0 or 180), and could have
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* a flip depending on the signs of A and B.
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*
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* We don't require A and B to have the same absolute value,
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* so there may be independent scales in the X or Y dimensions.
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*/
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if (get_el(mat, 0, 1) > 0) {
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/* A is positive */
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if (get_el(mat, 1, 0) > 0)
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*transform = WL_OUTPUT_TRANSFORM_FLIPPED_90;
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else
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*transform = WL_OUTPUT_TRANSFORM_90;
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} else {
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/* A is negative */
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if (get_el(mat, 1, 0) > 0)
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*transform = WL_OUTPUT_TRANSFORM_270;
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else
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*transform = WL_OUTPUT_TRANSFORM_FLIPPED_270;
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}
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} else if (near_zero_at(mat, 1, 0)) {
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if (!near_zero_at(mat, 0, 1))
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return false;
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/* We now have a matrix like:
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* [ A 0 0 ? ]
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* [ 0 B 0 ? ]
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* [ 0 0 ? ? ]
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* [ 0 0 0 1 ]
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* This case won't exchange the X and Y inputs, so the
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* transform is 0 or 180 degrees. We could have a flip
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* depending on the signs of A and B.
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*
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* We don't require A and B to have the same absolute value,
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* so there may be independent scales in the X or Y dimensions.
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*/
|
|
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;
|
|
}
|
|
|
|
WL_EXPORT void
|
|
weston_matrix_init_transform(struct weston_matrix *matrix,
|
|
enum wl_output_transform transform,
|
|
int x, int y, int width, int height,
|
|
int scale)
|
|
{
|
|
weston_matrix_init(matrix);
|
|
|
|
weston_matrix_translate(matrix, -x, -y, 0);
|
|
|
|
switch (transform) {
|
|
case WL_OUTPUT_TRANSFORM_FLIPPED:
|
|
case WL_OUTPUT_TRANSFORM_FLIPPED_90:
|
|
case WL_OUTPUT_TRANSFORM_FLIPPED_180:
|
|
case WL_OUTPUT_TRANSFORM_FLIPPED_270:
|
|
weston_matrix_scale(matrix, -1, 1, 1);
|
|
weston_matrix_translate(matrix, width, 0, 0);
|
|
break;
|
|
default:
|
|
break;
|
|
}
|
|
|
|
switch (transform) {
|
|
default:
|
|
case WL_OUTPUT_TRANSFORM_NORMAL:
|
|
case WL_OUTPUT_TRANSFORM_FLIPPED:
|
|
break;
|
|
case WL_OUTPUT_TRANSFORM_90:
|
|
case WL_OUTPUT_TRANSFORM_FLIPPED_90:
|
|
weston_matrix_rotate_xy(matrix, 0, -1);
|
|
weston_matrix_translate(matrix, 0, width, 0);
|
|
break;
|
|
case WL_OUTPUT_TRANSFORM_180:
|
|
case WL_OUTPUT_TRANSFORM_FLIPPED_180:
|
|
weston_matrix_rotate_xy(matrix, -1, 0);
|
|
weston_matrix_translate(matrix,
|
|
width, height, 0);
|
|
break;
|
|
case WL_OUTPUT_TRANSFORM_270:
|
|
case WL_OUTPUT_TRANSFORM_FLIPPED_270:
|
|
weston_matrix_rotate_xy(matrix, 0, 1);
|
|
weston_matrix_translate(matrix, height, 0, 0);
|
|
break;
|
|
}
|
|
|
|
weston_matrix_scale(matrix, scale, scale, 1);
|
|
}
|