diff options
Diffstat (limited to 'pixman/pixman/pixman-matrix.c')
-rw-r--r-- | pixman/pixman/pixman-matrix.c | 1535 |
1 files changed, 766 insertions, 769 deletions
diff --git a/pixman/pixman/pixman-matrix.c b/pixman/pixman/pixman-matrix.c index f2f67ab41..0b3ae78b3 100644 --- a/pixman/pixman/pixman-matrix.c +++ b/pixman/pixman/pixman-matrix.c @@ -1,769 +1,766 @@ -/* - * Copyright © 2008 Keith Packard - * - * Permission to use, copy, modify, distribute, and sell this software and its - * documentation for any purpose is hereby granted without fee, provided that - * the above copyright notice appear in all copies and that both that copyright - * notice and this permission notice appear in supporting documentation, and - * that the name of the copyright holders not be used in advertising or - * publicity pertaining to distribution of the software without specific, - * written prior permission. The copyright holders make no representations - * about the suitability of this software for any purpose. It is provided "as - * is" without express or implied warranty. - * - * THE COPYRIGHT HOLDERS DISCLAIM ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, - * INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS, IN NO - * EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY SPECIAL, INDIRECT OR - * CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, - * DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER - * TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE - * OF THIS SOFTWARE. - */ - -/* - * Matrix interfaces - */ - -#ifdef HAVE_CONFIG_H -#include "config.h" -#endif - -#include <math.h> -#include <string.h> -#include "pixman-private.h" - -#define F(x) pixman_int_to_fixed (x) - -PIXMAN_EXPORT void -pixman_transform_init_identity (struct pixman_transform *matrix) -{ - int i; - - memset (matrix, '\0', sizeof (struct pixman_transform)); - for (i = 0; i < 3; i++) - matrix->matrix[i][i] = F (1); -} - -typedef pixman_fixed_32_32_t pixman_fixed_34_30_t; - -PIXMAN_EXPORT pixman_bool_t -pixman_transform_point_3d (const struct pixman_transform *transform, - struct pixman_vector * vector) -{ - struct pixman_vector result; - pixman_fixed_32_32_t partial; - pixman_fixed_48_16_t v; - int i, j; - - for (j = 0; j < 3; j++) - { - v = 0; - for (i = 0; i < 3; i++) - { - partial = ((pixman_fixed_48_16_t) transform->matrix[j][i] * - (pixman_fixed_48_16_t) vector->vector[i]); - v += partial >> 16; - } - - if (v > pixman_max_fixed_48_16 || v < pixman_min_fixed_48_16) - return FALSE; - - result.vector[j] = (pixman_fixed_t) v; - } - - *vector = result; - - if (!result.vector[2]) - return FALSE; - - return TRUE; -} - -PIXMAN_EXPORT pixman_bool_t -pixman_transform_point (const struct pixman_transform *transform, - struct pixman_vector * vector) -{ - pixman_fixed_32_32_t partial; - pixman_fixed_34_30_t v[3]; - pixman_fixed_48_16_t quo; - int i, j; - - for (j = 0; j < 3; j++) - { - v[j] = 0; - - for (i = 0; i < 3; i++) - { - partial = ((pixman_fixed_32_32_t) transform->matrix[j][i] * - (pixman_fixed_32_32_t) vector->vector[i]); - v[j] += partial >> 2; - } - } - - if (!(v[2] >> 16)) - return FALSE; - - for (j = 0; j < 2; j++) - { - quo = v[j] / (v[2] >> 16); - if (quo > pixman_max_fixed_48_16 || quo < pixman_min_fixed_48_16) - return FALSE; - vector->vector[j] = (pixman_fixed_t) quo; - } - - vector->vector[2] = pixman_fixed_1; - return TRUE; -} - -PIXMAN_EXPORT pixman_bool_t -pixman_transform_multiply (struct pixman_transform * dst, - const struct pixman_transform *l, - const struct pixman_transform *r) -{ - struct pixman_transform d; - int dx, dy; - int o; - - for (dy = 0; dy < 3; dy++) - { - for (dx = 0; dx < 3; dx++) - { - pixman_fixed_48_16_t v; - pixman_fixed_32_32_t partial; - - v = 0; - for (o = 0; o < 3; o++) - { - partial = - (pixman_fixed_32_32_t) l->matrix[dy][o] * - (pixman_fixed_32_32_t) r->matrix[o][dx]; - - v += partial >> 16; - } - - if (v > pixman_max_fixed_48_16 || v < pixman_min_fixed_48_16) - return FALSE; - - d.matrix[dy][dx] = (pixman_fixed_t) v; - } - } - - *dst = d; - return TRUE; -} - -PIXMAN_EXPORT void -pixman_transform_init_scale (struct pixman_transform *t, - pixman_fixed_t sx, - pixman_fixed_t sy) -{ - memset (t, '\0', sizeof (struct pixman_transform)); - - t->matrix[0][0] = sx; - t->matrix[1][1] = sy; - t->matrix[2][2] = F (1); -} - -static pixman_fixed_t -fixed_inverse (pixman_fixed_t x) -{ - return (pixman_fixed_t) ((((pixman_fixed_48_16_t) F (1)) * F (1)) / x); -} - -PIXMAN_EXPORT pixman_bool_t -pixman_transform_scale (struct pixman_transform *forward, - struct pixman_transform *reverse, - pixman_fixed_t sx, - pixman_fixed_t sy) -{ - struct pixman_transform t; - - if (sx == 0 || sy == 0) - return FALSE; - - if (forward) - { - pixman_transform_init_scale (&t, sx, sy); - if (!pixman_transform_multiply (forward, &t, forward)) - return FALSE; - } - - if (reverse) - { - pixman_transform_init_scale (&t, fixed_inverse (sx), - fixed_inverse (sy)); - if (!pixman_transform_multiply (reverse, reverse, &t)) - return FALSE; - } - - return TRUE; -} - -PIXMAN_EXPORT void -pixman_transform_init_rotate (struct pixman_transform *t, - pixman_fixed_t c, - pixman_fixed_t s) -{ - memset (t, '\0', sizeof (struct pixman_transform)); - - t->matrix[0][0] = c; - t->matrix[0][1] = -s; - t->matrix[1][0] = s; - t->matrix[1][1] = c; - t->matrix[2][2] = F (1); -} - -PIXMAN_EXPORT pixman_bool_t -pixman_transform_rotate (struct pixman_transform *forward, - struct pixman_transform *reverse, - pixman_fixed_t c, - pixman_fixed_t s) -{ - struct pixman_transform t; - - if (forward) - { - pixman_transform_init_rotate (&t, c, s); - if (!pixman_transform_multiply (forward, &t, forward)) - return FALSE; - } - - if (reverse) - { - pixman_transform_init_rotate (&t, c, -s); - if (!pixman_transform_multiply (reverse, reverse, &t)) - return FALSE; - } - - return TRUE; -} - -PIXMAN_EXPORT void -pixman_transform_init_translate (struct pixman_transform *t, - pixman_fixed_t tx, - pixman_fixed_t ty) -{ - memset (t, '\0', sizeof (struct pixman_transform)); - - t->matrix[0][0] = F (1); - t->matrix[0][2] = tx; - t->matrix[1][1] = F (1); - t->matrix[1][2] = ty; - t->matrix[2][2] = F (1); -} - -PIXMAN_EXPORT pixman_bool_t -pixman_transform_translate (struct pixman_transform *forward, - struct pixman_transform *reverse, - pixman_fixed_t tx, - pixman_fixed_t ty) -{ - struct pixman_transform t; - - if (forward) - { - pixman_transform_init_translate (&t, tx, ty); - - if (!pixman_transform_multiply (forward, &t, forward)) - return FALSE; - } - - if (reverse) - { - pixman_transform_init_translate (&t, -tx, -ty); - - if (!pixman_transform_multiply (reverse, reverse, &t)) - return FALSE; - } - return TRUE; -} - -PIXMAN_EXPORT pixman_bool_t -pixman_transform_bounds (const struct pixman_transform *matrix, - struct pixman_box16 * b) - -{ - struct pixman_vector v[4]; - int i; - int x1, y1, x2, y2; - - v[0].vector[0] = F (b->x1); - v[0].vector[1] = F (b->y1); - v[0].vector[2] = F (1); - - v[1].vector[0] = F (b->x2); - v[1].vector[1] = F (b->y1); - v[1].vector[2] = F (1); - - v[2].vector[0] = F (b->x2); - v[2].vector[1] = F (b->y2); - v[2].vector[2] = F (1); - - v[3].vector[0] = F (b->x1); - v[3].vector[1] = F (b->y2); - v[3].vector[2] = F (1); - - for (i = 0; i < 4; i++) - { - if (!pixman_transform_point (matrix, &v[i])) - return FALSE; - - x1 = pixman_fixed_to_int (v[i].vector[0]); - y1 = pixman_fixed_to_int (v[i].vector[1]); - x2 = pixman_fixed_to_int (pixman_fixed_ceil (v[i].vector[0])); - y2 = pixman_fixed_to_int (pixman_fixed_ceil (v[i].vector[1])); - - if (i == 0) - { - b->x1 = x1; - b->y1 = y1; - b->x2 = x2; - b->y2 = y2; - } - else - { - if (x1 < b->x1) b->x1 = x1; - if (y1 < b->y1) b->y1 = y1; - if (x2 > b->x2) b->x2 = x2; - if (y2 > b->y2) b->y2 = y2; - } - } - - return TRUE; -} - -PIXMAN_EXPORT pixman_bool_t -pixman_transform_invert (struct pixman_transform * dst, - const struct pixman_transform *src) -{ - struct pixman_f_transform m, r; - - pixman_f_transform_from_pixman_transform (&m, src); - - if (!pixman_f_transform_invert (&r, &m)) - return FALSE; - - if (!pixman_transform_from_pixman_f_transform (dst, &r)) - return FALSE; - - return TRUE; -} - -static pixman_bool_t -within_epsilon (pixman_fixed_t a, - pixman_fixed_t b, - pixman_fixed_t epsilon) -{ - pixman_fixed_t t = a - b; - - if (t < 0) - t = -t; - - return t <= epsilon; -} - -#define EPSILON (pixman_fixed_t) (2) - -#define IS_SAME(a, b) (within_epsilon (a, b, EPSILON)) -#define IS_ZERO(a) (within_epsilon (a, 0, EPSILON)) -#define IS_ONE(a) (within_epsilon (a, F (1), EPSILON)) -#define IS_UNIT(a) \ - (within_epsilon (a, F (1), EPSILON) || \ - within_epsilon (a, F (-1), EPSILON) || \ - IS_ZERO (a)) -#define IS_INT(a) (IS_ZERO (pixman_fixed_frac (a))) - -PIXMAN_EXPORT pixman_bool_t -pixman_transform_is_identity (const struct pixman_transform *t) -{ - return (IS_SAME (t->matrix[0][0], t->matrix[1][1]) && - IS_SAME (t->matrix[0][0], t->matrix[2][2]) && - !IS_ZERO (t->matrix[0][0]) && - IS_ZERO (t->matrix[0][1]) && - IS_ZERO (t->matrix[0][2]) && - IS_ZERO (t->matrix[1][0]) && - IS_ZERO (t->matrix[1][2]) && - IS_ZERO (t->matrix[2][0]) && - IS_ZERO (t->matrix[2][1])); -} - -PIXMAN_EXPORT pixman_bool_t -pixman_transform_is_scale (const struct pixman_transform *t) -{ - return (!IS_ZERO (t->matrix[0][0]) && - IS_ZERO (t->matrix[0][1]) && - IS_ZERO (t->matrix[0][2]) && - - IS_ZERO (t->matrix[1][0]) && - !IS_ZERO (t->matrix[1][1]) && - IS_ZERO (t->matrix[1][2]) && - - IS_ZERO (t->matrix[2][0]) && - IS_ZERO (t->matrix[2][1]) && - !IS_ZERO (t->matrix[2][2])); -} - -PIXMAN_EXPORT pixman_bool_t -pixman_transform_is_int_translate (const struct pixman_transform *t) -{ - return (IS_ONE (t->matrix[0][0]) && - IS_ZERO (t->matrix[0][1]) && - IS_INT (t->matrix[0][2]) && - - IS_ZERO (t->matrix[1][0]) && - IS_ONE (t->matrix[1][1]) && - IS_INT (t->matrix[1][2]) && - - IS_ZERO (t->matrix[2][0]) && - IS_ZERO (t->matrix[2][1]) && - IS_ONE (t->matrix[2][2])); -} - -PIXMAN_EXPORT pixman_bool_t -pixman_transform_is_inverse (const struct pixman_transform *a, - const struct pixman_transform *b) -{ - struct pixman_transform t; - - if (!pixman_transform_multiply (&t, a, b)) - return FALSE; - - return pixman_transform_is_identity (&t); -} - -PIXMAN_EXPORT void -pixman_f_transform_from_pixman_transform (struct pixman_f_transform * ft, - const struct pixman_transform *t) -{ - int i, j; - - for (j = 0; j < 3; j++) - { - for (i = 0; i < 3; i++) - ft->m[j][i] = pixman_fixed_to_double (t->matrix[j][i]); - } -} - -PIXMAN_EXPORT pixman_bool_t -pixman_transform_from_pixman_f_transform (struct pixman_transform * t, - const struct pixman_f_transform *ft) -{ - int i, j; - - for (j = 0; j < 3; j++) - { - for (i = 0; i < 3; i++) - { - double d = ft->m[j][i]; - if (d < -32767.0 || d > 32767.0) - return FALSE; - d = d * 65536.0 + 0.5; - t->matrix[j][i] = (pixman_fixed_t) floor (d); - } - } - - return TRUE; -} - -static const int a[3] = { 3, 3, 2 }; -static const int b[3] = { 2, 1, 1 }; - -PIXMAN_EXPORT pixman_bool_t -pixman_f_transform_invert (struct pixman_f_transform * dst, - const struct pixman_f_transform *src) -{ - double det; - int i, j; - static int a[3] = { 2, 2, 1 }; - static int b[3] = { 1, 0, 0 }; - - det = 0; - for (i = 0; i < 3; i++) - { - double p; - int ai = a[i]; - int bi = b[i]; - p = src->m[i][0] * (src->m[ai][2] * src->m[bi][1] - - src->m[ai][1] * src->m[bi][2]); - if (i == 1) - p = -p; - det += p; - } - - if (det == 0) - return FALSE; - - det = 1 / det; - for (j = 0; j < 3; j++) - { - for (i = 0; i < 3; i++) - { - double p; - int ai = a[i]; - int aj = a[j]; - int bi = b[i]; - int bj = b[j]; - - p = (src->m[ai][aj] * src->m[bi][bj] - - src->m[ai][bj] * src->m[bi][aj]); - - if (((i + j) & 1) != 0) - p = -p; - - dst->m[j][i] = det * p; - } - } - - return TRUE; -} - -PIXMAN_EXPORT pixman_bool_t -pixman_f_transform_point (const struct pixman_f_transform *t, - struct pixman_f_vector * v) -{ - struct pixman_f_vector result; - int i, j; - double a; - - for (j = 0; j < 3; j++) - { - a = 0; - for (i = 0; i < 3; i++) - a += t->m[j][i] * v->v[i]; - result.v[j] = a; - } - - if (!result.v[2]) - return FALSE; - - for (j = 0; j < 2; j++) - v->v[j] = result.v[j] / result.v[2]; - - v->v[2] = 1; - - return TRUE; -} - -PIXMAN_EXPORT void -pixman_f_transform_point_3d (const struct pixman_f_transform *t, - struct pixman_f_vector * v) -{ - struct pixman_f_vector result; - int i, j; - double a; - - for (j = 0; j < 3; j++) - { - a = 0; - for (i = 0; i < 3; i++) - a += t->m[j][i] * v->v[i]; - result.v[j] = a; - } - - *v = result; -} - -PIXMAN_EXPORT void -pixman_f_transform_multiply (struct pixman_f_transform * dst, - const struct pixman_f_transform *l, - const struct pixman_f_transform *r) -{ - struct pixman_f_transform d; - int dx, dy; - int o; - - for (dy = 0; dy < 3; dy++) - { - for (dx = 0; dx < 3; dx++) - { - double v = 0; - for (o = 0; o < 3; o++) - v += l->m[dy][o] * r->m[o][dx]; - d.m[dy][dx] = v; - } - } - - *dst = d; -} - -PIXMAN_EXPORT void -pixman_f_transform_init_scale (struct pixman_f_transform *t, - double sx, - double sy) -{ - t->m[0][0] = sx; - t->m[0][1] = 0; - t->m[0][2] = 0; - t->m[1][0] = 0; - t->m[1][1] = sy; - t->m[1][2] = 0; - t->m[2][0] = 0; - t->m[2][1] = 0; - t->m[2][2] = 1; -} - -PIXMAN_EXPORT pixman_bool_t -pixman_f_transform_scale (struct pixman_f_transform *forward, - struct pixman_f_transform *reverse, - double sx, - double sy) -{ - struct pixman_f_transform t; - - if (sx == 0 || sy == 0) - return FALSE; - - if (forward) - { - pixman_f_transform_init_scale (&t, sx, sy); - pixman_f_transform_multiply (forward, &t, forward); - } - - if (reverse) - { - pixman_f_transform_init_scale (&t, 1 / sx, 1 / sy); - pixman_f_transform_multiply (reverse, reverse, &t); - } - - return TRUE; -} - -PIXMAN_EXPORT void -pixman_f_transform_init_rotate (struct pixman_f_transform *t, - double c, - double s) -{ - t->m[0][0] = c; - t->m[0][1] = -s; - t->m[0][2] = 0; - t->m[1][0] = s; - t->m[1][1] = c; - t->m[1][2] = 0; - t->m[2][0] = 0; - t->m[2][1] = 0; - t->m[2][2] = 1; -} - -PIXMAN_EXPORT pixman_bool_t -pixman_f_transform_rotate (struct pixman_f_transform *forward, - struct pixman_f_transform *reverse, - double c, - double s) -{ - struct pixman_f_transform t; - - if (forward) - { - pixman_f_transform_init_rotate (&t, c, s); - pixman_f_transform_multiply (forward, &t, forward); - } - - if (reverse) - { - pixman_f_transform_init_rotate (&t, c, -s); - pixman_f_transform_multiply (reverse, reverse, &t); - } - - return TRUE; -} - -PIXMAN_EXPORT void -pixman_f_transform_init_translate (struct pixman_f_transform *t, - double tx, - double ty) -{ - t->m[0][0] = 1; - t->m[0][1] = 0; - t->m[0][2] = tx; - t->m[1][0] = 0; - t->m[1][1] = 1; - t->m[1][2] = ty; - t->m[2][0] = 0; - t->m[2][1] = 0; - t->m[2][2] = 1; -} - -PIXMAN_EXPORT pixman_bool_t -pixman_f_transform_translate (struct pixman_f_transform *forward, - struct pixman_f_transform *reverse, - double tx, - double ty) -{ - struct pixman_f_transform t; - - if (forward) - { - pixman_f_transform_init_translate (&t, tx, ty); - pixman_f_transform_multiply (forward, &t, forward); - } - - if (reverse) - { - pixman_f_transform_init_translate (&t, -tx, -ty); - pixman_f_transform_multiply (reverse, reverse, &t); - } - - return TRUE; -} - -PIXMAN_EXPORT pixman_bool_t -pixman_f_transform_bounds (const struct pixman_f_transform *t, - struct pixman_box16 * b) -{ - struct pixman_f_vector v[4]; - int i; - int x1, y1, x2, y2; - - v[0].v[0] = b->x1; - v[0].v[1] = b->y1; - v[0].v[2] = 1; - v[1].v[0] = b->x2; - v[1].v[1] = b->y1; - v[1].v[2] = 1; - v[2].v[0] = b->x2; - v[2].v[1] = b->y2; - v[2].v[2] = 1; - v[3].v[0] = b->x1; - v[3].v[1] = b->y2; - v[3].v[2] = 1; - - for (i = 0; i < 4; i++) - { - if (!pixman_f_transform_point (t, &v[i])) - return FALSE; - - x1 = floor (v[i].v[0]); - y1 = floor (v[i].v[1]); - x2 = ceil (v[i].v[0]); - y2 = ceil (v[i].v[1]); - - if (i == 0) - { - b->x1 = x1; - b->y1 = y1; - b->x2 = x2; - b->y2 = y2; - } - else - { - if (x1 < b->x1) b->x1 = x1; - if (y1 < b->y1) b->y1 = y1; - if (x2 > b->x2) b->x2 = x2; - if (y2 > b->y2) b->y2 = y2; - } - } - - return TRUE; -} - -PIXMAN_EXPORT void -pixman_f_transform_init_identity (struct pixman_f_transform *t) -{ - int i, j; - - for (j = 0; j < 3; j++) - { - for (i = 0; i < 3; i++) - t->m[j][i] = i == j ? 1 : 0; - } -} +/*
+ * Copyright © 2008 Keith Packard
+ *
+ * Permission to use, copy, modify, distribute, and sell this software and its
+ * documentation for any purpose is hereby granted without fee, provided that
+ * the above copyright notice appear in all copies and that both that copyright
+ * notice and this permission notice appear in supporting documentation, and
+ * that the name of the copyright holders not be used in advertising or
+ * publicity pertaining to distribution of the software without specific,
+ * written prior permission. The copyright holders make no representations
+ * about the suitability of this software for any purpose. It is provided "as
+ * is" without express or implied warranty.
+ *
+ * THE COPYRIGHT HOLDERS DISCLAIM ALL WARRANTIES WITH REGARD TO THIS SOFTWARE,
+ * INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS, IN NO
+ * EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY SPECIAL, INDIRECT OR
+ * CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE,
+ * DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER
+ * TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE
+ * OF THIS SOFTWARE.
+ */
+
+/*
+ * Matrix interfaces
+ */
+
+#ifdef HAVE_CONFIG_H
+#include "config.h"
+#endif
+
+#include <math.h>
+#include <string.h>
+#include "pixman-private.h"
+
+#define F(x) pixman_int_to_fixed (x)
+
+PIXMAN_EXPORT void
+pixman_transform_init_identity (struct pixman_transform *matrix)
+{
+ int i;
+
+ memset (matrix, '\0', sizeof (struct pixman_transform));
+ for (i = 0; i < 3; i++)
+ matrix->matrix[i][i] = F (1);
+}
+
+typedef pixman_fixed_32_32_t pixman_fixed_34_30_t;
+
+PIXMAN_EXPORT pixman_bool_t
+pixman_transform_point_3d (const struct pixman_transform *transform,
+ struct pixman_vector * vector)
+{
+ struct pixman_vector result;
+ pixman_fixed_32_32_t partial;
+ pixman_fixed_48_16_t v;
+ int i, j;
+
+ for (j = 0; j < 3; j++)
+ {
+ v = 0;
+ for (i = 0; i < 3; i++)
+ {
+ partial = ((pixman_fixed_48_16_t) transform->matrix[j][i] *
+ (pixman_fixed_48_16_t) vector->vector[i]);
+ v += partial >> 16;
+ }
+
+ if (v > pixman_max_fixed_48_16 || v < pixman_min_fixed_48_16)
+ return FALSE;
+
+ result.vector[j] = (pixman_fixed_t) v;
+ }
+
+ *vector = result;
+
+ if (!result.vector[2])
+ return FALSE;
+
+ return TRUE;
+}
+
+PIXMAN_EXPORT pixman_bool_t
+pixman_transform_point (const struct pixman_transform *transform,
+ struct pixman_vector * vector)
+{
+ pixman_fixed_32_32_t partial;
+ pixman_fixed_34_30_t v[3];
+ pixman_fixed_48_16_t quo;
+ int i, j;
+
+ for (j = 0; j < 3; j++)
+ {
+ v[j] = 0;
+
+ for (i = 0; i < 3; i++)
+ {
+ partial = ((pixman_fixed_32_32_t) transform->matrix[j][i] *
+ (pixman_fixed_32_32_t) vector->vector[i]);
+ v[j] += partial >> 2;
+ }
+ }
+
+ if (!(v[2] >> 16))
+ return FALSE;
+
+ for (j = 0; j < 2; j++)
+ {
+ quo = v[j] / (v[2] >> 16);
+ if (quo > pixman_max_fixed_48_16 || quo < pixman_min_fixed_48_16)
+ return FALSE;
+ vector->vector[j] = (pixman_fixed_t) quo;
+ }
+
+ vector->vector[2] = pixman_fixed_1;
+ return TRUE;
+}
+
+PIXMAN_EXPORT pixman_bool_t
+pixman_transform_multiply (struct pixman_transform * dst,
+ const struct pixman_transform *l,
+ const struct pixman_transform *r)
+{
+ struct pixman_transform d;
+ int dx, dy;
+ int o;
+
+ for (dy = 0; dy < 3; dy++)
+ {
+ for (dx = 0; dx < 3; dx++)
+ {
+ pixman_fixed_48_16_t v;
+ pixman_fixed_32_32_t partial;
+
+ v = 0;
+ for (o = 0; o < 3; o++)
+ {
+ partial =
+ (pixman_fixed_32_32_t) l->matrix[dy][o] *
+ (pixman_fixed_32_32_t) r->matrix[o][dx];
+
+ v += partial >> 16;
+ }
+
+ if (v > pixman_max_fixed_48_16 || v < pixman_min_fixed_48_16)
+ return FALSE;
+
+ d.matrix[dy][dx] = (pixman_fixed_t) v;
+ }
+ }
+
+ *dst = d;
+ return TRUE;
+}
+
+PIXMAN_EXPORT void
+pixman_transform_init_scale (struct pixman_transform *t,
+ pixman_fixed_t sx,
+ pixman_fixed_t sy)
+{
+ memset (t, '\0', sizeof (struct pixman_transform));
+
+ t->matrix[0][0] = sx;
+ t->matrix[1][1] = sy;
+ t->matrix[2][2] = F (1);
+}
+
+static pixman_fixed_t
+fixed_inverse (pixman_fixed_t x)
+{
+ return (pixman_fixed_t) ((((pixman_fixed_48_16_t) F (1)) * F (1)) / x);
+}
+
+PIXMAN_EXPORT pixman_bool_t
+pixman_transform_scale (struct pixman_transform *forward,
+ struct pixman_transform *reverse,
+ pixman_fixed_t sx,
+ pixman_fixed_t sy)
+{
+ struct pixman_transform t;
+
+ if (sx == 0 || sy == 0)
+ return FALSE;
+
+ if (forward)
+ {
+ pixman_transform_init_scale (&t, sx, sy);
+ if (!pixman_transform_multiply (forward, &t, forward))
+ return FALSE;
+ }
+
+ if (reverse)
+ {
+ pixman_transform_init_scale (&t, fixed_inverse (sx),
+ fixed_inverse (sy));
+ if (!pixman_transform_multiply (reverse, reverse, &t))
+ return FALSE;
+ }
+
+ return TRUE;
+}
+
+PIXMAN_EXPORT void
+pixman_transform_init_rotate (struct pixman_transform *t,
+ pixman_fixed_t c,
+ pixman_fixed_t s)
+{
+ memset (t, '\0', sizeof (struct pixman_transform));
+
+ t->matrix[0][0] = c;
+ t->matrix[0][1] = -s;
+ t->matrix[1][0] = s;
+ t->matrix[1][1] = c;
+ t->matrix[2][2] = F (1);
+}
+
+PIXMAN_EXPORT pixman_bool_t
+pixman_transform_rotate (struct pixman_transform *forward,
+ struct pixman_transform *reverse,
+ pixman_fixed_t c,
+ pixman_fixed_t s)
+{
+ struct pixman_transform t;
+
+ if (forward)
+ {
+ pixman_transform_init_rotate (&t, c, s);
+ if (!pixman_transform_multiply (forward, &t, forward))
+ return FALSE;
+ }
+
+ if (reverse)
+ {
+ pixman_transform_init_rotate (&t, c, -s);
+ if (!pixman_transform_multiply (reverse, reverse, &t))
+ return FALSE;
+ }
+
+ return TRUE;
+}
+
+PIXMAN_EXPORT void
+pixman_transform_init_translate (struct pixman_transform *t,
+ pixman_fixed_t tx,
+ pixman_fixed_t ty)
+{
+ memset (t, '\0', sizeof (struct pixman_transform));
+
+ t->matrix[0][0] = F (1);
+ t->matrix[0][2] = tx;
+ t->matrix[1][1] = F (1);
+ t->matrix[1][2] = ty;
+ t->matrix[2][2] = F (1);
+}
+
+PIXMAN_EXPORT pixman_bool_t
+pixman_transform_translate (struct pixman_transform *forward,
+ struct pixman_transform *reverse,
+ pixman_fixed_t tx,
+ pixman_fixed_t ty)
+{
+ struct pixman_transform t;
+
+ if (forward)
+ {
+ pixman_transform_init_translate (&t, tx, ty);
+
+ if (!pixman_transform_multiply (forward, &t, forward))
+ return FALSE;
+ }
+
+ if (reverse)
+ {
+ pixman_transform_init_translate (&t, -tx, -ty);
+
+ if (!pixman_transform_multiply (reverse, reverse, &t))
+ return FALSE;
+ }
+ return TRUE;
+}
+
+PIXMAN_EXPORT pixman_bool_t
+pixman_transform_bounds (const struct pixman_transform *matrix,
+ struct pixman_box16 * b)
+
+{
+ struct pixman_vector v[4];
+ int i;
+ int x1, y1, x2, y2;
+
+ v[0].vector[0] = F (b->x1);
+ v[0].vector[1] = F (b->y1);
+ v[0].vector[2] = F (1);
+
+ v[1].vector[0] = F (b->x2);
+ v[1].vector[1] = F (b->y1);
+ v[1].vector[2] = F (1);
+
+ v[2].vector[0] = F (b->x2);
+ v[2].vector[1] = F (b->y2);
+ v[2].vector[2] = F (1);
+
+ v[3].vector[0] = F (b->x1);
+ v[3].vector[1] = F (b->y2);
+ v[3].vector[2] = F (1);
+
+ for (i = 0; i < 4; i++)
+ {
+ if (!pixman_transform_point (matrix, &v[i]))
+ return FALSE;
+
+ x1 = pixman_fixed_to_int (v[i].vector[0]);
+ y1 = pixman_fixed_to_int (v[i].vector[1]);
+ x2 = pixman_fixed_to_int (pixman_fixed_ceil (v[i].vector[0]));
+ y2 = pixman_fixed_to_int (pixman_fixed_ceil (v[i].vector[1]));
+
+ if (i == 0)
+ {
+ b->x1 = x1;
+ b->y1 = y1;
+ b->x2 = x2;
+ b->y2 = y2;
+ }
+ else
+ {
+ if (x1 < b->x1) b->x1 = x1;
+ if (y1 < b->y1) b->y1 = y1;
+ if (x2 > b->x2) b->x2 = x2;
+ if (y2 > b->y2) b->y2 = y2;
+ }
+ }
+
+ return TRUE;
+}
+
+PIXMAN_EXPORT pixman_bool_t
+pixman_transform_invert (struct pixman_transform * dst,
+ const struct pixman_transform *src)
+{
+ struct pixman_f_transform m, r;
+
+ pixman_f_transform_from_pixman_transform (&m, src);
+
+ if (!pixman_f_transform_invert (&r, &m))
+ return FALSE;
+
+ if (!pixman_transform_from_pixman_f_transform (dst, &r))
+ return FALSE;
+
+ return TRUE;
+}
+
+static pixman_bool_t
+within_epsilon (pixman_fixed_t a,
+ pixman_fixed_t b,
+ pixman_fixed_t epsilon)
+{
+ pixman_fixed_t t = a - b;
+
+ if (t < 0)
+ t = -t;
+
+ return t <= epsilon;
+}
+
+#define EPSILON (pixman_fixed_t) (2)
+
+#define IS_SAME(a, b) (within_epsilon (a, b, EPSILON))
+#define IS_ZERO(a) (within_epsilon (a, 0, EPSILON))
+#define IS_ONE(a) (within_epsilon (a, F (1), EPSILON))
+#define IS_UNIT(a) \
+ (within_epsilon (a, F (1), EPSILON) || \
+ within_epsilon (a, F (-1), EPSILON) || \
+ IS_ZERO (a))
+#define IS_INT(a) (IS_ZERO (pixman_fixed_frac (a)))
+
+PIXMAN_EXPORT pixman_bool_t
+pixman_transform_is_identity (const struct pixman_transform *t)
+{
+ return (IS_SAME (t->matrix[0][0], t->matrix[1][1]) &&
+ IS_SAME (t->matrix[0][0], t->matrix[2][2]) &&
+ !IS_ZERO (t->matrix[0][0]) &&
+ IS_ZERO (t->matrix[0][1]) &&
+ IS_ZERO (t->matrix[0][2]) &&
+ IS_ZERO (t->matrix[1][0]) &&
+ IS_ZERO (t->matrix[1][2]) &&
+ IS_ZERO (t->matrix[2][0]) &&
+ IS_ZERO (t->matrix[2][1]));
+}
+
+PIXMAN_EXPORT pixman_bool_t
+pixman_transform_is_scale (const struct pixman_transform *t)
+{
+ return (!IS_ZERO (t->matrix[0][0]) &&
+ IS_ZERO (t->matrix[0][1]) &&
+ IS_ZERO (t->matrix[0][2]) &&
+
+ IS_ZERO (t->matrix[1][0]) &&
+ !IS_ZERO (t->matrix[1][1]) &&
+ IS_ZERO (t->matrix[1][2]) &&
+
+ IS_ZERO (t->matrix[2][0]) &&
+ IS_ZERO (t->matrix[2][1]) &&
+ !IS_ZERO (t->matrix[2][2]));
+}
+
+PIXMAN_EXPORT pixman_bool_t
+pixman_transform_is_int_translate (const struct pixman_transform *t)
+{
+ return (IS_ONE (t->matrix[0][0]) &&
+ IS_ZERO (t->matrix[0][1]) &&
+ IS_INT (t->matrix[0][2]) &&
+
+ IS_ZERO (t->matrix[1][0]) &&
+ IS_ONE (t->matrix[1][1]) &&
+ IS_INT (t->matrix[1][2]) &&
+
+ IS_ZERO (t->matrix[2][0]) &&
+ IS_ZERO (t->matrix[2][1]) &&
+ IS_ONE (t->matrix[2][2]));
+}
+
+PIXMAN_EXPORT pixman_bool_t
+pixman_transform_is_inverse (const struct pixman_transform *a,
+ const struct pixman_transform *b)
+{
+ struct pixman_transform t;
+
+ if (!pixman_transform_multiply (&t, a, b))
+ return FALSE;
+
+ return pixman_transform_is_identity (&t);
+}
+
+PIXMAN_EXPORT void
+pixman_f_transform_from_pixman_transform (struct pixman_f_transform * ft,
+ const struct pixman_transform *t)
+{
+ int i, j;
+
+ for (j = 0; j < 3; j++)
+ {
+ for (i = 0; i < 3; i++)
+ ft->m[j][i] = pixman_fixed_to_double (t->matrix[j][i]);
+ }
+}
+
+PIXMAN_EXPORT pixman_bool_t
+pixman_transform_from_pixman_f_transform (struct pixman_transform * t,
+ const struct pixman_f_transform *ft)
+{
+ int i, j;
+
+ for (j = 0; j < 3; j++)
+ {
+ for (i = 0; i < 3; i++)
+ {
+ double d = ft->m[j][i];
+ if (d < -32767.0 || d > 32767.0)
+ return FALSE;
+ d = d * 65536.0 + 0.5;
+ t->matrix[j][i] = (pixman_fixed_t) floor (d);
+ }
+ }
+
+ return TRUE;
+}
+
+PIXMAN_EXPORT pixman_bool_t
+pixman_f_transform_invert (struct pixman_f_transform * dst,
+ const struct pixman_f_transform *src)
+{
+ double det;
+ int i, j;
+ static int a[3] = { 2, 2, 1 };
+ static int b[3] = { 1, 0, 0 };
+
+ det = 0;
+ for (i = 0; i < 3; i++)
+ {
+ double p;
+ int ai = a[i];
+ int bi = b[i];
+ p = src->m[i][0] * (src->m[ai][2] * src->m[bi][1] -
+ src->m[ai][1] * src->m[bi][2]);
+ if (i == 1)
+ p = -p;
+ det += p;
+ }
+
+ if (det == 0)
+ return FALSE;
+
+ det = 1 / det;
+ for (j = 0; j < 3; j++)
+ {
+ for (i = 0; i < 3; i++)
+ {
+ double p;
+ int ai = a[i];
+ int aj = a[j];
+ int bi = b[i];
+ int bj = b[j];
+
+ p = (src->m[ai][aj] * src->m[bi][bj] -
+ src->m[ai][bj] * src->m[bi][aj]);
+
+ if (((i + j) & 1) != 0)
+ p = -p;
+
+ dst->m[j][i] = det * p;
+ }
+ }
+
+ return TRUE;
+}
+
+PIXMAN_EXPORT pixman_bool_t
+pixman_f_transform_point (const struct pixman_f_transform *t,
+ struct pixman_f_vector * v)
+{
+ struct pixman_f_vector result;
+ int i, j;
+ double a;
+
+ for (j = 0; j < 3; j++)
+ {
+ a = 0;
+ for (i = 0; i < 3; i++)
+ a += t->m[j][i] * v->v[i];
+ result.v[j] = a;
+ }
+
+ if (!result.v[2])
+ return FALSE;
+
+ for (j = 0; j < 2; j++)
+ v->v[j] = result.v[j] / result.v[2];
+
+ v->v[2] = 1;
+
+ return TRUE;
+}
+
+PIXMAN_EXPORT void
+pixman_f_transform_point_3d (const struct pixman_f_transform *t,
+ struct pixman_f_vector * v)
+{
+ struct pixman_f_vector result;
+ int i, j;
+ double a;
+
+ for (j = 0; j < 3; j++)
+ {
+ a = 0;
+ for (i = 0; i < 3; i++)
+ a += t->m[j][i] * v->v[i];
+ result.v[j] = a;
+ }
+
+ *v = result;
+}
+
+PIXMAN_EXPORT void
+pixman_f_transform_multiply (struct pixman_f_transform * dst,
+ const struct pixman_f_transform *l,
+ const struct pixman_f_transform *r)
+{
+ struct pixman_f_transform d;
+ int dx, dy;
+ int o;
+
+ for (dy = 0; dy < 3; dy++)
+ {
+ for (dx = 0; dx < 3; dx++)
+ {
+ double v = 0;
+ for (o = 0; o < 3; o++)
+ v += l->m[dy][o] * r->m[o][dx];
+ d.m[dy][dx] = v;
+ }
+ }
+
+ *dst = d;
+}
+
+PIXMAN_EXPORT void
+pixman_f_transform_init_scale (struct pixman_f_transform *t,
+ double sx,
+ double sy)
+{
+ t->m[0][0] = sx;
+ t->m[0][1] = 0;
+ t->m[0][2] = 0;
+ t->m[1][0] = 0;
+ t->m[1][1] = sy;
+ t->m[1][2] = 0;
+ t->m[2][0] = 0;
+ t->m[2][1] = 0;
+ t->m[2][2] = 1;
+}
+
+PIXMAN_EXPORT pixman_bool_t
+pixman_f_transform_scale (struct pixman_f_transform *forward,
+ struct pixman_f_transform *reverse,
+ double sx,
+ double sy)
+{
+ struct pixman_f_transform t;
+
+ if (sx == 0 || sy == 0)
+ return FALSE;
+
+ if (forward)
+ {
+ pixman_f_transform_init_scale (&t, sx, sy);
+ pixman_f_transform_multiply (forward, &t, forward);
+ }
+
+ if (reverse)
+ {
+ pixman_f_transform_init_scale (&t, 1 / sx, 1 / sy);
+ pixman_f_transform_multiply (reverse, reverse, &t);
+ }
+
+ return TRUE;
+}
+
+PIXMAN_EXPORT void
+pixman_f_transform_init_rotate (struct pixman_f_transform *t,
+ double c,
+ double s)
+{
+ t->m[0][0] = c;
+ t->m[0][1] = -s;
+ t->m[0][2] = 0;
+ t->m[1][0] = s;
+ t->m[1][1] = c;
+ t->m[1][2] = 0;
+ t->m[2][0] = 0;
+ t->m[2][1] = 0;
+ t->m[2][2] = 1;
+}
+
+PIXMAN_EXPORT pixman_bool_t
+pixman_f_transform_rotate (struct pixman_f_transform *forward,
+ struct pixman_f_transform *reverse,
+ double c,
+ double s)
+{
+ struct pixman_f_transform t;
+
+ if (forward)
+ {
+ pixman_f_transform_init_rotate (&t, c, s);
+ pixman_f_transform_multiply (forward, &t, forward);
+ }
+
+ if (reverse)
+ {
+ pixman_f_transform_init_rotate (&t, c, -s);
+ pixman_f_transform_multiply (reverse, reverse, &t);
+ }
+
+ return TRUE;
+}
+
+PIXMAN_EXPORT void
+pixman_f_transform_init_translate (struct pixman_f_transform *t,
+ double tx,
+ double ty)
+{
+ t->m[0][0] = 1;
+ t->m[0][1] = 0;
+ t->m[0][2] = tx;
+ t->m[1][0] = 0;
+ t->m[1][1] = 1;
+ t->m[1][2] = ty;
+ t->m[2][0] = 0;
+ t->m[2][1] = 0;
+ t->m[2][2] = 1;
+}
+
+PIXMAN_EXPORT pixman_bool_t
+pixman_f_transform_translate (struct pixman_f_transform *forward,
+ struct pixman_f_transform *reverse,
+ double tx,
+ double ty)
+{
+ struct pixman_f_transform t;
+
+ if (forward)
+ {
+ pixman_f_transform_init_translate (&t, tx, ty);
+ pixman_f_transform_multiply (forward, &t, forward);
+ }
+
+ if (reverse)
+ {
+ pixman_f_transform_init_translate (&t, -tx, -ty);
+ pixman_f_transform_multiply (reverse, reverse, &t);
+ }
+
+ return TRUE;
+}
+
+PIXMAN_EXPORT pixman_bool_t
+pixman_f_transform_bounds (const struct pixman_f_transform *t,
+ struct pixman_box16 * b)
+{
+ struct pixman_f_vector v[4];
+ int i;
+ int x1, y1, x2, y2;
+
+ v[0].v[0] = b->x1;
+ v[0].v[1] = b->y1;
+ v[0].v[2] = 1;
+ v[1].v[0] = b->x2;
+ v[1].v[1] = b->y1;
+ v[1].v[2] = 1;
+ v[2].v[0] = b->x2;
+ v[2].v[1] = b->y2;
+ v[2].v[2] = 1;
+ v[3].v[0] = b->x1;
+ v[3].v[1] = b->y2;
+ v[3].v[2] = 1;
+
+ for (i = 0; i < 4; i++)
+ {
+ if (!pixman_f_transform_point (t, &v[i]))
+ return FALSE;
+
+ x1 = floor (v[i].v[0]);
+ y1 = floor (v[i].v[1]);
+ x2 = ceil (v[i].v[0]);
+ y2 = ceil (v[i].v[1]);
+
+ if (i == 0)
+ {
+ b->x1 = x1;
+ b->y1 = y1;
+ b->x2 = x2;
+ b->y2 = y2;
+ }
+ else
+ {
+ if (x1 < b->x1) b->x1 = x1;
+ if (y1 < b->y1) b->y1 = y1;
+ if (x2 > b->x2) b->x2 = x2;
+ if (y2 > b->y2) b->y2 = y2;
+ }
+ }
+
+ return TRUE;
+}
+
+PIXMAN_EXPORT void
+pixman_f_transform_init_identity (struct pixman_f_transform *t)
+{
+ int i, j;
+
+ for (j = 0; j < 3; j++)
+ {
+ for (i = 0; i < 3; i++)
+ t->m[j][i] = i == j ? 1 : 0;
+ }
+}
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