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Diffstat (limited to 'src/pixman/pixman/pixman-radial-gradient.c')
| -rw-r--r-- | src/pixman/pixman/pixman-radial-gradient.c | 471 |
1 files changed, 471 insertions, 0 deletions
diff --git a/src/pixman/pixman/pixman-radial-gradient.c b/src/pixman/pixman/pixman-radial-gradient.c new file mode 100644 index 0000000..6a21796 --- /dev/null +++ b/src/pixman/pixman/pixman-radial-gradient.c @@ -0,0 +1,471 @@ +/* -*- Mode: c; c-basic-offset: 4; tab-width: 8; indent-tabs-mode: t; -*- */ +/* + * + * Copyright © 2000 Keith Packard, member of The XFree86 Project, Inc. + * Copyright © 2000 SuSE, Inc. + * 2005 Lars Knoll & Zack Rusin, Trolltech + * Copyright © 2007 Red Hat, Inc. + * + * + * 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 Keith Packard not be used in + * advertising or publicity pertaining to distribution of the software without + * specific, written prior permission. Keith Packard makes 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. + */ + +#ifdef HAVE_CONFIG_H +#include <config.h> +#endif +#include <stdlib.h> +#include <math.h> +#include "pixman-private.h" + +static inline pixman_fixed_32_32_t +dot (pixman_fixed_48_16_t x1, + pixman_fixed_48_16_t y1, + pixman_fixed_48_16_t z1, + pixman_fixed_48_16_t x2, + pixman_fixed_48_16_t y2, + pixman_fixed_48_16_t z2) +{ + /* + * Exact computation, assuming that the input values can + * be represented as pixman_fixed_16_16_t + */ + return x1 * x2 + y1 * y2 + z1 * z2; +} + +static inline double +fdot (double x1, + double y1, + double z1, + double x2, + double y2, + double z2) +{ + /* + * Error can be unbound in some special cases. + * Using clever dot product algorithms (for example compensated + * dot product) would improve this but make the code much less + * obvious + */ + return x1 * x2 + y1 * y2 + z1 * z2; +} + +static uint32_t +radial_compute_color (double a, + double b, + double c, + double inva, + double dr, + double mindr, + pixman_gradient_walker_t *walker, + pixman_repeat_t repeat) +{ + /* + * In this function error propagation can lead to bad results: + * - discr can have an unbound error (if b*b-a*c is very small), + * potentially making it the opposite sign of what it should have been + * (thus clearing a pixel that would have been colored or vice-versa) + * or propagating the error to sqrtdiscr; + * if discr has the wrong sign or b is very small, this can lead to bad + * results + * + * - the algorithm used to compute the solutions of the quadratic + * equation is not numerically stable (but saves one division compared + * to the numerically stable one); + * this can be a problem if a*c is much smaller than b*b + * + * - the above problems are worse if a is small (as inva becomes bigger) + */ + double discr; + + if (a == 0) + { + double t; + + if (b == 0) + return 0; + + t = pixman_fixed_1 / 2 * c / b; + if (repeat == PIXMAN_REPEAT_NONE) + { + if (0 <= t && t <= pixman_fixed_1) + return _pixman_gradient_walker_pixel (walker, t); + } + else + { + if (t * dr >= mindr) + return _pixman_gradient_walker_pixel (walker, t); + } + + return 0; + } + + discr = fdot (b, a, 0, b, -c, 0); + if (discr >= 0) + { + double sqrtdiscr, t0, t1; + + sqrtdiscr = sqrt (discr); + t0 = (b + sqrtdiscr) * inva; + t1 = (b - sqrtdiscr) * inva; + + /* + * The root that must be used is the biggest one that belongs + * to the valid range ([0,1] for PIXMAN_REPEAT_NONE, any + * solution that results in a positive radius otherwise). + * + * If a > 0, t0 is the biggest solution, so if it is valid, it + * is the correct result. + * + * If a < 0, only one of the solutions can be valid, so the + * order in which they are tested is not important. + */ + if (repeat == PIXMAN_REPEAT_NONE) + { + if (0 <= t0 && t0 <= pixman_fixed_1) + return _pixman_gradient_walker_pixel (walker, t0); + else if (0 <= t1 && t1 <= pixman_fixed_1) + return _pixman_gradient_walker_pixel (walker, t1); + } + else + { + if (t0 * dr >= mindr) + return _pixman_gradient_walker_pixel (walker, t0); + else if (t1 * dr >= mindr) + return _pixman_gradient_walker_pixel (walker, t1); + } + } + + return 0; +} + +static uint32_t * +radial_get_scanline_narrow (pixman_iter_t *iter, const uint32_t *mask) +{ + /* + * Implementation of radial gradients following the PDF specification. + * See section 8.7.4.5.4 Type 3 (Radial) Shadings of the PDF Reference + * Manual (PDF 32000-1:2008 at the time of this writing). + * + * In the radial gradient problem we are given two circles (c₁,r₁) and + * (c₂,r₂) that define the gradient itself. + * + * Mathematically the gradient can be defined as the family of circles + * + * ((1-t)·c₁ + t·(c₂), (1-t)·r₁ + t·r₂) + * + * excluding those circles whose radius would be < 0. When a point + * belongs to more than one circle, the one with a bigger t is the only + * one that contributes to its color. When a point does not belong + * to any of the circles, it is transparent black, i.e. RGBA (0, 0, 0, 0). + * Further limitations on the range of values for t are imposed when + * the gradient is not repeated, namely t must belong to [0,1]. + * + * The graphical result is the same as drawing the valid (radius > 0) + * circles with increasing t in [-inf, +inf] (or in [0,1] if the gradient + * is not repeated) using SOURCE operator composition. + * + * It looks like a cone pointing towards the viewer if the ending circle + * is smaller than the starting one, a cone pointing inside the page if + * the starting circle is the smaller one and like a cylinder if they + * have the same radius. + * + * What we actually do is, given the point whose color we are interested + * in, compute the t values for that point, solving for t in: + * + * length((1-t)·c₁ + t·(c₂) - p) = (1-t)·r₁ + t·r₂ + * + * Let's rewrite it in a simpler way, by defining some auxiliary + * variables: + * + * cd = c₂ - c₁ + * pd = p - c₁ + * dr = r₂ - r₁ + * length(t·cd - pd) = r₁ + t·dr + * + * which actually means + * + * hypot(t·cdx - pdx, t·cdy - pdy) = r₁ + t·dr + * + * or + * + * ⎷((t·cdx - pdx)² + (t·cdy - pdy)²) = r₁ + t·dr. + * + * If we impose (as stated earlier) that r₁ + t·dr >= 0, it becomes: + * + * (t·cdx - pdx)² + (t·cdy - pdy)² = (r₁ + t·dr)² + * + * where we can actually expand the squares and solve for t: + * + * t²cdx² - 2t·cdx·pdx + pdx² + t²cdy² - 2t·cdy·pdy + pdy² = + * = r₁² + 2·r₁·t·dr + t²·dr² + * + * (cdx² + cdy² - dr²)t² - 2(cdx·pdx + cdy·pdy + r₁·dr)t + + * (pdx² + pdy² - r₁²) = 0 + * + * A = cdx² + cdy² - dr² + * B = pdx·cdx + pdy·cdy + r₁·dr + * C = pdx² + pdy² - r₁² + * At² - 2Bt + C = 0 + * + * The solutions (unless the equation degenerates because of A = 0) are: + * + * t = (B ± ⎷(B² - A·C)) / A + * + * The solution we are going to prefer is the bigger one, unless the + * radius associated to it is negative (or it falls outside the valid t + * range). + * + * Additional observations (useful for optimizations): + * A does not depend on p + * + * A < 0 <=> one of the two circles completely contains the other one + * <=> for every p, the radiuses associated with the two t solutions + * have opposite sign + */ + pixman_image_t *image = iter->image; + int x = iter->x; + int y = iter->y; + int width = iter->width; + uint32_t *buffer = iter->buffer; + + gradient_t *gradient = (gradient_t *)image; + radial_gradient_t *radial = (radial_gradient_t *)image; + uint32_t *end = buffer + width; + pixman_gradient_walker_t walker; + pixman_vector_t v, unit; + + /* reference point is the center of the pixel */ + v.vector[0] = pixman_int_to_fixed (x) + pixman_fixed_1 / 2; + v.vector[1] = pixman_int_to_fixed (y) + pixman_fixed_1 / 2; + v.vector[2] = pixman_fixed_1; + + _pixman_gradient_walker_init (&walker, gradient, image->common.repeat); + + if (image->common.transform) + { + if (!pixman_transform_point_3d (image->common.transform, &v)) + return iter->buffer; + + unit.vector[0] = image->common.transform->matrix[0][0]; + unit.vector[1] = image->common.transform->matrix[1][0]; + unit.vector[2] = image->common.transform->matrix[2][0]; + } + else + { + unit.vector[0] = pixman_fixed_1; + unit.vector[1] = 0; + unit.vector[2] = 0; + } + + if (unit.vector[2] == 0 && v.vector[2] == pixman_fixed_1) + { + /* + * Given: + * + * t = (B ± ⎷(B² - A·C)) / A + * + * where + * + * A = cdx² + cdy² - dr² + * B = pdx·cdx + pdy·cdy + r₁·dr + * C = pdx² + pdy² - r₁² + * det = B² - A·C + * + * Since we have an affine transformation, we know that (pdx, pdy) + * increase linearly with each pixel, + * + * pdx = pdx₀ + n·ux, + * pdy = pdy₀ + n·uy, + * + * we can then express B, C and det through multiple differentiation. + */ + pixman_fixed_32_32_t b, db, c, dc, ddc; + + /* warning: this computation may overflow */ + v.vector[0] -= radial->c1.x; + v.vector[1] -= radial->c1.y; + + /* + * B and C are computed and updated exactly. + * If fdot was used instead of dot, in the worst case it would + * lose 11 bits of precision in each of the multiplication and + * summing up would zero out all the bit that were preserved, + * thus making the result 0 instead of the correct one. + * This would mean a worst case of unbound relative error or + * about 2^10 absolute error + */ + b = dot (v.vector[0], v.vector[1], radial->c1.radius, + radial->delta.x, radial->delta.y, radial->delta.radius); + db = dot (unit.vector[0], unit.vector[1], 0, + radial->delta.x, radial->delta.y, 0); + + c = dot (v.vector[0], v.vector[1], + -((pixman_fixed_48_16_t) radial->c1.radius), + v.vector[0], v.vector[1], radial->c1.radius); + dc = dot (2 * (pixman_fixed_48_16_t) v.vector[0] + unit.vector[0], + 2 * (pixman_fixed_48_16_t) v.vector[1] + unit.vector[1], + 0, + unit.vector[0], unit.vector[1], 0); + ddc = 2 * dot (unit.vector[0], unit.vector[1], 0, + unit.vector[0], unit.vector[1], 0); + + while (buffer < end) + { + if (!mask || *mask++) + { + *buffer = radial_compute_color (radial->a, b, c, + radial->inva, + radial->delta.radius, + radial->mindr, + &walker, + image->common.repeat); + } + + b += db; + c += dc; + dc += ddc; + ++buffer; + } + } + else + { + /* projective */ + /* Warning: + * error propagation guarantees are much looser than in the affine case + */ + while (buffer < end) + { + if (!mask || *mask++) + { + if (v.vector[2] != 0) + { + double pdx, pdy, invv2, b, c; + + invv2 = 1. * pixman_fixed_1 / v.vector[2]; + + pdx = v.vector[0] * invv2 - radial->c1.x; + /* / pixman_fixed_1 */ + + pdy = v.vector[1] * invv2 - radial->c1.y; + /* / pixman_fixed_1 */ + + b = fdot (pdx, pdy, radial->c1.radius, + radial->delta.x, radial->delta.y, + radial->delta.radius); + /* / pixman_fixed_1 / pixman_fixed_1 */ + + c = fdot (pdx, pdy, -radial->c1.radius, + pdx, pdy, radial->c1.radius); + /* / pixman_fixed_1 / pixman_fixed_1 */ + + *buffer = radial_compute_color (radial->a, b, c, + radial->inva, + radial->delta.radius, + radial->mindr, + &walker, + image->common.repeat); + } + else + { + *buffer = 0; + } + } + + ++buffer; + + v.vector[0] += unit.vector[0]; + v.vector[1] += unit.vector[1]; + v.vector[2] += unit.vector[2]; + } + } + + iter->y++; + return iter->buffer; +} + +static uint32_t * +radial_get_scanline_wide (pixman_iter_t *iter, const uint32_t *mask) +{ + uint32_t *buffer = radial_get_scanline_narrow (iter, NULL); + + pixman_expand_to_float ( + (argb_t *)buffer, buffer, PIXMAN_a8r8g8b8, iter->width); + + return buffer; +} + +void +_pixman_radial_gradient_iter_init (pixman_image_t *image, pixman_iter_t *iter) +{ + if (iter->iter_flags & ITER_NARROW) + iter->get_scanline = radial_get_scanline_narrow; + else + iter->get_scanline = radial_get_scanline_wide; +} + +PIXMAN_EXPORT pixman_image_t * +pixman_image_create_radial_gradient (const pixman_point_fixed_t * inner, + const pixman_point_fixed_t * outer, + pixman_fixed_t inner_radius, + pixman_fixed_t outer_radius, + const pixman_gradient_stop_t *stops, + int n_stops) +{ + pixman_image_t *image; + radial_gradient_t *radial; + + image = _pixman_image_allocate (); + + if (!image) + return NULL; + + radial = &image->radial; + + if (!_pixman_init_gradient (&radial->common, stops, n_stops)) + { + free (image); + return NULL; + } + + image->type = RADIAL; + + radial->c1.x = inner->x; + radial->c1.y = inner->y; + radial->c1.radius = inner_radius; + radial->c2.x = outer->x; + radial->c2.y = outer->y; + radial->c2.radius = outer_radius; + + /* warning: this computations may overflow */ + radial->delta.x = radial->c2.x - radial->c1.x; + radial->delta.y = radial->c2.y - radial->c1.y; + radial->delta.radius = radial->c2.radius - radial->c1.radius; + + /* computed exactly, then cast to double -> every bit of the double + representation is correct (53 bits) */ + radial->a = dot (radial->delta.x, radial->delta.y, -radial->delta.radius, + radial->delta.x, radial->delta.y, radial->delta.radius); + if (radial->a != 0) + radial->inva = 1. * pixman_fixed_1 / radial->a; + + radial->mindr = -1. * pixman_fixed_1 * radial->c1.radius; + + return image; +} |
