1074 lines
28 KiB
C
1074 lines
28 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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static force_inline int
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count_leading_zeros (uint32_t x)
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{
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#ifdef __GNUC__
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return __builtin_clz (x);
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#else
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int n = 0;
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while (x)
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{
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n++;
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x >>= 1;
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}
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return 32 - n;
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#endif
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}
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/*
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* Large signed/unsigned integer division with rounding for the platforms with
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* only 64-bit integer data type supported (no 128-bit data type).
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*
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* Arguments:
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* hi, lo - high and low 64-bit parts of the dividend
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* div - 48-bit divisor
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*
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* Returns: lowest 64 bits of the result as a return value and highest 64
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* bits of the result to "result_hi" pointer
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*/
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/* grade-school unsigned division (128-bit by 48-bit) with rounding to nearest */
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static force_inline uint64_t
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rounded_udiv_128_by_48 (uint64_t hi,
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uint64_t lo,
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uint64_t div,
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uint64_t *result_hi)
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{
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uint64_t tmp, remainder, result_lo;
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assert(div < ((uint64_t)1 << 48));
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remainder = hi % div;
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*result_hi = hi / div;
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tmp = (remainder << 16) + (lo >> 48);
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result_lo = tmp / div;
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remainder = tmp % div;
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tmp = (remainder << 16) + ((lo >> 32) & 0xFFFF);
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result_lo = (result_lo << 16) + (tmp / div);
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remainder = tmp % div;
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tmp = (remainder << 16) + ((lo >> 16) & 0xFFFF);
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result_lo = (result_lo << 16) + (tmp / div);
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remainder = tmp % div;
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tmp = (remainder << 16) + (lo & 0xFFFF);
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result_lo = (result_lo << 16) + (tmp / div);
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remainder = tmp % div;
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/* round to nearest */
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if (remainder * 2 >= div && ++result_lo == 0)
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*result_hi += 1;
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return result_lo;
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}
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/* signed division (128-bit by 49-bit) with rounding to nearest */
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static inline int64_t
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rounded_sdiv_128_by_49 (int64_t hi,
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uint64_t lo,
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int64_t div,
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int64_t *signed_result_hi)
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{
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uint64_t result_lo, result_hi;
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int sign = 0;
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if (div < 0)
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{
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div = -div;
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sign ^= 1;
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}
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if (hi < 0)
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{
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if (lo != 0)
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hi++;
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hi = -hi;
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lo = -lo;
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sign ^= 1;
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}
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result_lo = rounded_udiv_128_by_48 (hi, lo, div, &result_hi);
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if (sign)
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{
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if (result_lo != 0)
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result_hi++;
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result_hi = -result_hi;
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result_lo = -result_lo;
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}
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if (signed_result_hi)
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{
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*signed_result_hi = result_hi;
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}
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return result_lo;
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}
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/*
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* Multiply 64.16 fixed point value by (2^scalebits) and convert
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* to 128-bit integer.
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*/
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static force_inline void
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fixed_64_16_to_int128 (int64_t hi,
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int64_t lo,
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int64_t *rhi,
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int64_t *rlo,
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int scalebits)
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{
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/* separate integer and fractional parts */
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hi += lo >> 16;
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lo &= 0xFFFF;
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if (scalebits <= 0)
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{
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*rlo = hi >> (-scalebits);
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*rhi = *rlo >> 63;
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}
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else
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{
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*rhi = hi >> (64 - scalebits);
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*rlo = (uint64_t)hi << scalebits;
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if (scalebits < 16)
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*rlo += lo >> (16 - scalebits);
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else
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*rlo += lo << (scalebits - 16);
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}
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}
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/*
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* Convert 112.16 fixed point value to 48.16 with clamping for the out
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* of range values.
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*/
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static force_inline pixman_fixed_48_16_t
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fixed_112_16_to_fixed_48_16 (int64_t hi, int64_t lo, pixman_bool_t *clampflag)
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{
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if ((lo >> 63) != hi)
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{
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*clampflag = TRUE;
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return hi >= 0 ? INT64_MAX : INT64_MIN;
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}
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else
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{
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return lo;
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}
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}
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/*
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* Transform a point with 31.16 fixed point coordinates from the destination
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* space to a point with 48.16 fixed point coordinates in the source space.
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* No overflows are possible for affine transformations and the results are
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* accurate including the least significant bit. Projective transformations
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* may overflow, in this case the results are just clamped to return maximum
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* or minimum 48.16 values (so that the caller can at least handle the NONE
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* and PAD repeats correctly) and the return value is FALSE to indicate that
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* such clamping has happened.
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*/
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PIXMAN_EXPORT pixman_bool_t
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pixman_transform_point_31_16 (const pixman_transform_t *t,
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const pixman_vector_48_16_t *v,
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pixman_vector_48_16_t *result)
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{
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pixman_bool_t clampflag = FALSE;
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int i;
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int64_t tmp[3][2], divint;
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uint16_t divfrac;
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/* input vector values must have no more than 31 bits (including sign)
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* in the integer part */
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assert (v->v[0] < ((pixman_fixed_48_16_t)1 << (30 + 16)));
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assert (v->v[0] >= -((pixman_fixed_48_16_t)1 << (30 + 16)));
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assert (v->v[1] < ((pixman_fixed_48_16_t)1 << (30 + 16)));
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assert (v->v[1] >= -((pixman_fixed_48_16_t)1 << (30 + 16)));
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assert (v->v[2] < ((pixman_fixed_48_16_t)1 << (30 + 16)));
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assert (v->v[2] >= -((pixman_fixed_48_16_t)1 << (30 + 16)));
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for (i = 0; i < 3; i++)
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{
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tmp[i][0] = (int64_t)t->matrix[i][0] * (v->v[0] >> 16);
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tmp[i][1] = (int64_t)t->matrix[i][0] * (v->v[0] & 0xFFFF);
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tmp[i][0] += (int64_t)t->matrix[i][1] * (v->v[1] >> 16);
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tmp[i][1] += (int64_t)t->matrix[i][1] * (v->v[1] & 0xFFFF);
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tmp[i][0] += (int64_t)t->matrix[i][2] * (v->v[2] >> 16);
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tmp[i][1] += (int64_t)t->matrix[i][2] * (v->v[2] & 0xFFFF);
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}
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/*
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* separate 64-bit integer and 16-bit fractional parts for the divisor,
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* which is also scaled by 65536 after fixed point multiplication.
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*/
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divint = tmp[2][0] + (tmp[2][1] >> 16);
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divfrac = tmp[2][1] & 0xFFFF;
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if (divint == pixman_fixed_1 && divfrac == 0)
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{
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/*
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* this is a simple affine transformation
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*/
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result->v[0] = tmp[0][0] + ((tmp[0][1] + 0x8000) >> 16);
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result->v[1] = tmp[1][0] + ((tmp[1][1] + 0x8000) >> 16);
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result->v[2] = pixman_fixed_1;
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}
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else if (divint == 0 && divfrac == 0)
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{
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/*
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* handle zero divisor (if the values are non-zero, set the
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* results to maximum positive or minimum negative)
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*/
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clampflag = TRUE;
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result->v[0] = tmp[0][0] + ((tmp[0][1] + 0x8000) >> 16);
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result->v[1] = tmp[1][0] + ((tmp[1][1] + 0x8000) >> 16);
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if (result->v[0] > 0)
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result->v[0] = INT64_MAX;
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else if (result->v[0] < 0)
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result->v[0] = INT64_MIN;
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if (result->v[1] > 0)
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result->v[1] = INT64_MAX;
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else if (result->v[1] < 0)
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result->v[1] = INT64_MIN;
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}
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else
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{
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/*
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* projective transformation, analyze the top 32 bits of the divisor
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*/
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int32_t hi32divbits = divint >> 32;
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if (hi32divbits < 0)
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hi32divbits = ~hi32divbits;
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if (hi32divbits == 0)
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{
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/* the divisor is small, we can actually keep all the bits */
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int64_t hi, rhi, lo, rlo;
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int64_t div = (divint << 16) + divfrac;
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fixed_64_16_to_int128 (tmp[0][0], tmp[0][1], &hi, &lo, 32);
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rlo = rounded_sdiv_128_by_49 (hi, lo, div, &rhi);
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result->v[0] = fixed_112_16_to_fixed_48_16 (rhi, rlo, &clampflag);
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fixed_64_16_to_int128 (tmp[1][0], tmp[1][1], &hi, &lo, 32);
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rlo = rounded_sdiv_128_by_49 (hi, lo, div, &rhi);
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result->v[1] = fixed_112_16_to_fixed_48_16 (rhi, rlo, &clampflag);
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}
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else
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{
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/* the divisor needs to be reduced to 48 bits */
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int64_t hi, rhi, lo, rlo, div;
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int shift = 32 - count_leading_zeros (hi32divbits);
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fixed_64_16_to_int128 (divint, divfrac, &hi, &div, 16 - shift);
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fixed_64_16_to_int128 (tmp[0][0], tmp[0][1], &hi, &lo, 32 - shift);
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rlo = rounded_sdiv_128_by_49 (hi, lo, div, &rhi);
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result->v[0] = fixed_112_16_to_fixed_48_16 (rhi, rlo, &clampflag);
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fixed_64_16_to_int128 (tmp[1][0], tmp[1][1], &hi, &lo, 32 - shift);
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rlo = rounded_sdiv_128_by_49 (hi, lo, div, &rhi);
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result->v[1] = fixed_112_16_to_fixed_48_16 (rhi, rlo, &clampflag);
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}
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}
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result->v[2] = pixman_fixed_1;
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return !clampflag;
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}
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PIXMAN_EXPORT void
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pixman_transform_point_31_16_affine (const pixman_transform_t *t,
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const pixman_vector_48_16_t *v,
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pixman_vector_48_16_t *result)
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{
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int64_t hi0, lo0, hi1, lo1;
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/* input vector values must have no more than 31 bits (including sign)
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* in the integer part */
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assert (v->v[0] < ((pixman_fixed_48_16_t)1 << (30 + 16)));
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assert (v->v[0] >= -((pixman_fixed_48_16_t)1 << (30 + 16)));
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assert (v->v[1] < ((pixman_fixed_48_16_t)1 << (30 + 16)));
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assert (v->v[1] >= -((pixman_fixed_48_16_t)1 << (30 + 16)));
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hi0 = (int64_t)t->matrix[0][0] * (v->v[0] >> 16);
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lo0 = (int64_t)t->matrix[0][0] * (v->v[0] & 0xFFFF);
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hi0 += (int64_t)t->matrix[0][1] * (v->v[1] >> 16);
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lo0 += (int64_t)t->matrix[0][1] * (v->v[1] & 0xFFFF);
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hi0 += (int64_t)t->matrix[0][2];
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hi1 = (int64_t)t->matrix[1][0] * (v->v[0] >> 16);
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lo1 = (int64_t)t->matrix[1][0] * (v->v[0] & 0xFFFF);
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hi1 += (int64_t)t->matrix[1][1] * (v->v[1] >> 16);
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lo1 += (int64_t)t->matrix[1][1] * (v->v[1] & 0xFFFF);
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hi1 += (int64_t)t->matrix[1][2];
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result->v[0] = hi0 + ((lo0 + 0x8000) >> 16);
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result->v[1] = hi1 + ((lo1 + 0x8000) >> 16);
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result->v[2] = pixman_fixed_1;
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}
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PIXMAN_EXPORT void
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pixman_transform_point_31_16_3d (const pixman_transform_t *t,
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const pixman_vector_48_16_t *v,
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pixman_vector_48_16_t *result)
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{
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int i;
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int64_t tmp[3][2];
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/* input vector values must have no more than 31 bits (including sign)
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* in the integer part */
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assert (v->v[0] < ((pixman_fixed_48_16_t)1 << (30 + 16)));
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assert (v->v[0] >= -((pixman_fixed_48_16_t)1 << (30 + 16)));
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assert (v->v[1] < ((pixman_fixed_48_16_t)1 << (30 + 16)));
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assert (v->v[1] >= -((pixman_fixed_48_16_t)1 << (30 + 16)));
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assert (v->v[2] < ((pixman_fixed_48_16_t)1 << (30 + 16)));
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assert (v->v[2] >= -((pixman_fixed_48_16_t)1 << (30 + 16)));
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for (i = 0; i < 3; i++)
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{
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tmp[i][0] = (int64_t)t->matrix[i][0] * (v->v[0] >> 16);
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tmp[i][1] = (int64_t)t->matrix[i][0] * (v->v[0] & 0xFFFF);
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tmp[i][0] += (int64_t)t->matrix[i][1] * (v->v[1] >> 16);
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tmp[i][1] += (int64_t)t->matrix[i][1] * (v->v[1] & 0xFFFF);
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tmp[i][0] += (int64_t)t->matrix[i][2] * (v->v[2] >> 16);
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tmp[i][1] += (int64_t)t->matrix[i][2] * (v->v[2] & 0xFFFF);
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}
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result->v[0] = tmp[0][0] + ((tmp[0][1] + 0x8000) >> 16);
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result->v[1] = tmp[1][0] + ((tmp[1][1] + 0x8000) >> 16);
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result->v[2] = tmp[2][0] + ((tmp[2][1] + 0x8000) >> 16);
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}
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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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pixman_vector_48_16_t tmp;
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tmp.v[0] = vector->vector[0];
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tmp.v[1] = vector->vector[1];
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tmp.v[2] = vector->vector[2];
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pixman_transform_point_31_16_3d (transform, &tmp, &tmp);
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vector->vector[0] = tmp.v[0];
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vector->vector[1] = tmp.v[1];
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vector->vector[2] = tmp.v[2];
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return vector->vector[0] == tmp.v[0] &&
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vector->vector[1] == tmp.v[1] &&
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vector->vector[2] == tmp.v[2];
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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_vector_48_16_t tmp;
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tmp.v[0] = vector->vector[0];
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tmp.v[1] = vector->vector[1];
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tmp.v[2] = vector->vector[2];
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if (!pixman_transform_point_31_16 (transform, &tmp, &tmp))
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return FALSE;
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vector->vector[0] = tmp.v[0];
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vector->vector[1] = tmp.v[1];
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vector->vector[2] = tmp.v[2];
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return vector->vector[0] == tmp.v[0] &&
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vector->vector[1] == tmp.v[1] &&
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vector->vector[2] == tmp.v[2];
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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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|
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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 + 0x8000) >> 16;
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}
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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
|
|
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;
|
|
|
|
pixman_f_transform_from_pixman_transform (&m, src);
|
|
|
|
if (!pixman_f_transform_invert (&m, &m))
|
|
return FALSE;
|
|
|
|
if (!pixman_transform_from_pixman_f_transform (dst, &m))
|
|
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)
|
|
{
|
|
static const int a[3] = { 2, 2, 1 };
|
|
static const int b[3] = { 1, 0, 0 };
|
|
pixman_f_transform_t d;
|
|
double det;
|
|
int i, j;
|
|
|
|
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;
|
|
|
|
d.m[j][i] = det * p;
|
|
}
|
|
}
|
|
|
|
*dst = d;
|
|
|
|
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);
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pixman_f_transform_multiply (forward, &t, forward);
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}
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|
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if (reverse)
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{
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|
pixman_f_transform_init_translate (&t, -tx, -ty);
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pixman_f_transform_multiply (reverse, reverse, &t);
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}
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|
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return TRUE;
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|
}
|
|
|
|
PIXMAN_EXPORT pixman_bool_t
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|
pixman_f_transform_bounds (const struct pixman_f_transform *t,
|
|
struct pixman_box16 * b)
|
|
{
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|
struct pixman_f_vector v[4];
|
|
int i;
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|
int x1, y1, x2, y2;
|
|
|
|
v[0].v[0] = b->x1;
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|
v[0].v[1] = b->y1;
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|
v[0].v[2] = 1;
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|
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;
|
|
}
|
|
}
|