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