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Diffstat (limited to 'pixman/pixman/pixman-matrix.c')
| -rw-r--r-- | pixman/pixman/pixman-matrix.c | 768 |
1 files changed, 768 insertions, 0 deletions
diff --git a/pixman/pixman/pixman-matrix.c b/pixman/pixman/pixman-matrix.c new file mode 100644 index 000000000..abdfa0525 --- /dev/null +++ b/pixman/pixman/pixman-matrix.c @@ -0,0 +1,768 @@ +/* + * 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; + + pixman_transform_multiply (&t, a, b); + + 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; + } +} |