pixman: Branch 'master' - 2 commits
Andrea Canciani
ranma42 at kemper.freedesktop.org
Tue Oct 12 05:47:58 PDT 2010
pixman/pixman-private.h | 9
pixman/pixman-radial-gradient.c | 454 ++++++++++++++++++++++------------------
2 files changed, 265 insertions(+), 198 deletions(-)
New commits:
commit f6ab20ca6604739b82311fc078d6ce850f43adc0
Author: Andrea Canciani <ranma42 at gmail.com>
Date: Tue Oct 12 09:52:53 2010 +0200
Add comments about errors
Explain how errors are introduced in the computation performed for
radial gradients.
diff --git a/pixman/pixman-radial-gradient.c b/pixman/pixman-radial-gradient.c
index ff7bfba..ed073ab 100644
--- a/pixman/pixman-radial-gradient.c
+++ b/pixman/pixman-radial-gradient.c
@@ -42,6 +42,10 @@ dot (pixman_fixed_48_16_t x1,
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;
}
@@ -53,6 +57,12 @@ fdot (double x1,
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;
}
@@ -66,6 +76,22 @@ radial_compute_color (double a,
pixman_gradient_walker_t *walker,
pixman_repeat_t repeat)
{
+ /*
+ * In this function error propagation can lead to bad results:
+ * - det 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 sqrtdet;
+ * if det 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 det;
if (a == 0)
@@ -246,9 +272,19 @@ radial_gradient_get_scanline_32 (pixman_image_t *image,
*/
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,
@@ -284,6 +320,9 @@ radial_gradient_get_scanline_32 (pixman_image_t *image,
else
{
/* projective */
+ /* Warning:
+ * error propagation guarantees are much looser than in the affine case
+ */
while (buffer < end)
{
if (!mask || *mask++)
@@ -371,10 +410,13 @@ pixman_image_create_radial_gradient (pixman_point_fixed_t * inner,
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)
commit 1ca715ed1e6914e9bd9f050065e827d7a9e2efc9
Author: Andrea Canciani <ranma42 at gmail.com>
Date: Sun Aug 15 09:07:33 2010 +0200
Draw radial gradients with PDF semantics
Change radial gradient computations and definition to reflect the
radial gradients in PDF specifications (see section 8.7.4.5.4,
Type 3 (Radial) Shadings of the PDF Reference Manual).
Instead of having a valid interpolation parameter value for every
point of the plane, define it only for points withing the area
covered by the family of circles generated by interpolating or
extrapolating the start and end circles.
Points outside this area are now transparent black (rgba 0 0 0 0).
Points within this area have the color assiciated with the maximum
value of the interpolation parameter in that point (if multiple
solutions exist within the range specified by the extend mode).
diff --git a/pixman/pixman-private.h b/pixman/pixman-private.h
index 3979f60..71b96c1 100644
--- a/pixman/pixman-private.h
+++ b/pixman/pixman-private.h
@@ -152,10 +152,11 @@ struct radial_gradient
circle_t c1;
circle_t c2;
- double cdx;
- double cdy;
- double dr;
- double A;
+
+ circle_t delta;
+ double a;
+ double inva;
+ double mindr;
};
struct conical_gradient
diff --git a/pixman/pixman-radial-gradient.c b/pixman/pixman-radial-gradient.c
index 08d5f14..ff7bfba 100644
--- a/pixman/pixman-radial-gradient.c
+++ b/pixman/pixman-radial-gradient.c
@@ -1,3 +1,4 @@
+/* -*- Mode: c; c-basic-offset: 4; tab-width: 8; indent-tabs-mode: t; -*- */
/*
*
* Copyright © 2000 Keith Packard, member of The XFree86 Project, Inc.
@@ -33,6 +34,74 @@
#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)
+{
+ return x1 * x2 + y1 * y2 + z1 * z2;
+}
+
+static inline double
+fdot (double x1,
+ double y1,
+ double z1,
+ double x2,
+ double y2,
+ double z2)
+{
+ 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)
+{
+ double det;
+
+ if (a == 0)
+ {
+ return _pixman_gradient_walker_pixel (walker,
+ pixman_fixed_1 / 2 * c / b);
+ }
+
+ det = fdot (b, a, 0, b, -c, 0);
+ if (det >= 0)
+ {
+ double sqrtdet, t0, t1;
+
+ sqrtdet = sqrt (det);
+ t0 = (b + sqrtdet) * inva;
+ t1 = (b - sqrtdet) * inva;
+
+ 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 void
radial_gradient_get_scanline_32 (pixman_image_t *image,
int x,
@@ -42,118 +111,85 @@ radial_gradient_get_scanline_32 (pixman_image_t *image,
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 (câ‚,râ‚) and
- * (câ‚‚,râ‚‚) that define the gradient itself. Then, for any point p, we
- * must compute the value(s) of t within [0.0, 1.0] representing the
- * circle(s) that would color the point.
- *
- * There are potentially two values of t since the point p can be
- * colored by both sides of the circle, (which happens whenever one
- * circle is not entirely contained within the other).
- *
- * If we solve for a value of t that is outside of [0.0, 1.0] then we
- * use the extend mode (NONE, REPEAT, REFLECT, or PAD) to map to a
- * value within [0.0, 1.0].
- *
- * Here is an illustration of the problem:
- *
- * pâ‚‚
- * p •
- * • ╲
- * · ╲r₂
- * p₠· ╲
- * • θ╲
- * ╲ ╌╌•
- * ╲r₠· c₂
- * θ╲ ·
- * ╌╌•
- * câ‚
- *
- * Given (câ‚,râ‚), (câ‚‚,râ‚‚) and p, we must find an angle θ such that two
- * points pâ‚ and pâ‚‚ on the two circles are collinear with p. Then, the
- * desired value of t is the ratio of the length of pâ‚p to the length
- * of pâ‚pâ‚‚.
- *
- * So, we have six unknown values: (pâ‚x, pâ‚y), (pâ‚‚x, pâ‚‚y), θ and t.
- * We can also write six equations that constrain the problem:
- *
- * Point p₠is a distance r₠from c₠at an angle of θ:
+ * (câ‚‚,râ‚‚) that define the gradient itself.
*
- * 1. pâ‚x = câ‚x + râ‚·cos θ
- * 2. pâ‚y = câ‚y + râ‚·sin θ
+ * Mathematically the gradient can be defined as the family of circles
*
- * Point p₂ is a distance r₂ from c₂ at an angle of θ:
+ * ((1-t)·c₠+ t·(c₂), (1-t)·r₠+ t·r₂)
*
- * 3. p₂x = c₂x + r2·cos θ
- * 4. p₂y = c₂y + r2·sin θ
+ * 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].
*
- * Point p lies at a fraction t along the line segment pâ‚pâ‚‚:
+ * 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 operatior composition.
*
- * 5. px = t·pâ‚‚x + (1-t)·pâ‚x
- * 6. py = t·pâ‚‚y + (1-t)·pâ‚y
+ * 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.
*
- * To solve, first subtitute 1-4 into 5 and 6:
+ * 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:
*
- * px = t·(câ‚‚x + r₂·cos θ) + (1-t)·(câ‚x + râ‚·cos θ)
- * py = t·(câ‚‚y + r₂·sin θ) + (1-t)·(câ‚y + râ‚·sin θ)
+ * length((1-t)·c₠+ t·(c₂) - p) = (1-t)·r₠+ t·r₂
+ *
+ * Let's rewrite it in a simpler way, by defining some auxiliary
+ * variables:
*
- * Then solve each for cos θ and sin θ expressed as a function of t:
+ * cd = câ‚‚ - câ‚
+ * pd = p - câ‚
+ * dr = râ‚‚ - râ‚
+ * lenght(t·cd - pd) = r₠+ t·dr
*
- * cos θ = (-(câ‚‚x - câ‚x)·t + (px - câ‚x)) / ((râ‚‚-râ‚)·t + râ‚)
- * sin θ = (-(câ‚‚y - câ‚y)·t + (py - câ‚y)) / ((râ‚‚-râ‚)·t + râ‚)
+ * which actually means
*
- * To simplify this a bit, we define new variables for several of the
- * common terms as shown below:
+ * hypot(t·cdx - pdx, t·cdy - pdy) = r₠+ t·dr
*
- * pâ‚‚
- * p •
- * • ╲
- * · ┆ ╲r₂
- * p₠· ┆ ╲
- * • pdy┆ ╲
- * ╲ ┆ •c₂
- * ╲r₠┆ · ┆
- * ╲ ·┆ ┆cdy
- * •╌╌╌╌┴╌╌╌╌╌╌╌┘
- * câ‚ pdx cdx
+ * or
*
- * cdx = (câ‚‚x - câ‚x)
- * cdy = (câ‚‚y - câ‚y)
- * dr = râ‚‚-râ‚
- * pdx = px - câ‚x
- * pdy = py - câ‚y
+ * ⎷((t·cdx - pdx)² + (t·cdy - pdy)²) = r₠+ t·dr.
*
- * Note that cdx, cdy, and dr do not depend on point p at all, so can
- * be pre-computed for the entire gradient. The simplifed equations
- * are now:
+ * If we impose (as stated earlier) that r₠+ t·dr >= 0, it becomes:
*
- * cos θ = (-cdx·t + pdx) / (dr·t + râ‚)
- * sin θ = (-cdy·t + pdy) / (dr·t + râ‚)
+ * (t·cdx - pdx)² + (t·cdy - pdy)² = (r₠+ t·dr)²
*
- * Finally, to get a single function of t and eliminate the last
- * unknown θ, we use the identity sin²θ + cos²θ = 1. First, square
- * each equation, (we knew a quadratic was coming since it must be
- * possible to obtain two solutions in some cases):
+ * where we can actually expand the squares and solve for t:
*
- * cos²θ = (cdx²t² - 2·cdx·pdx·t + pdx²) / (dr²·t² + 2·râ‚·dr·t + r₲)
- * sin²θ = (cdy²t² - 2·cdy·pdy·t + pdy²) / (dr²·t² + 2·râ‚·dr·t + r₲)
+ * t²cdx² - 2t·cdx·pdx + pdx² + t²cdy² - 2t·cdy·pdy + pdy² =
+ * = r₲ + 2·râ‚·t·dr + t²·dr²
*
- * Then add both together, set the result equal to 1, and express as a
- * standard quadratic equation in t of the form At² + Bt + C = 0
+ * (cdx² + cdy² - dr²)t² - 2(cdx·pdx + cdy·pdy + râ‚·dr)t +
+ * (pdx² + pdy² - r₲) = 0
*
- * (cdx² + cdy² - dr²)·t² - 2·(cdx·pdx + cdy·pdy + râ‚·dr)·t + (pdx² + pdy² - r₲) = 0
+ * A = cdx² + cdy² - dr²
+ * B = pdx·cdx + pdy·cdy + râ‚·dr
+ * C = pdx² + pdy² - r₲
+ * At² - 2Bt + C = 0
+ *
+ * The solutions (unless the equation degenerates because of A = 0) are:
*
- * In other words:
+ * t = (B ± ⎷(B² - A·C)) / A
*
- * A = cdx² + cdy² - dr²
- * B = -2·(pdx·cdx + pdy·cdy + râ‚·dr)
- * C = pdx² + pdy² - r₲
+ * 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).
*
- * And again, notice that A does not depend on p, so can be
- * precomputed. From here we just use the quadratic formula to solve
- * for t:
+ * Additional observations (useful for optimizations):
+ * A does not depend on p
*
- * t = (-2·B ± ⎷(B² - 4·A·C)) / 2·A
+ * 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
*/
gradient_t *gradient = (gradient_t *)image;
@@ -161,100 +197,88 @@ radial_gradient_get_scanline_32 (pixman_image_t *image,
radial_gradient_t *radial = (radial_gradient_t *)image;
uint32_t *end = buffer + width;
pixman_gradient_walker_t walker;
- pixman_bool_t affine = TRUE;
- double cx = 1.;
- double cy = 0.;
- double cz = 0.;
- double rx = x + 0.5;
- double ry = y + 0.5;
- double rz = 1.;
+ 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, source->common.repeat);
if (source->common.transform)
{
- pixman_vector_t v;
- /* 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;
-
if (!pixman_transform_point_3d (source->common.transform, &v))
return;
-
- cx = source->common.transform->matrix[0][0] / 65536.;
- cy = source->common.transform->matrix[1][0] / 65536.;
- cz = source->common.transform->matrix[2][0] / 65536.;
- rx = v.vector[0] / 65536.;
- ry = v.vector[1] / 65536.;
- rz = v.vector[2] / 65536.;
-
- affine =
- source->common.transform->matrix[2][0] == 0 &&
- v.vector[2] == pixman_fixed_1;
+ unit.vector[0] = source->common.transform->matrix[0][0];
+ unit.vector[1] = source->common.transform->matrix[1][0];
+ unit.vector[2] = source->common.transform->matrix[2][0];
+ }
+ else
+ {
+ unit.vector[0] = pixman_fixed_1;
+ unit.vector[1] = 0;
+ unit.vector[2] = 0;
}
- if (affine)
+ if (unit.vector[2] == 0 && v.vector[2] == pixman_fixed_1)
{
- /* When computing t over a scanline, we notice that some expressions
- * are constant so we can compute them just once. Given:
+ /*
+ * Given:
*
- * t = (-2·B ± ⎷(B² - 4·A·C)) / 2·A
+ * t = (B ± ⎷(B² - A·C)) / A
*
* where
*
- * A = cdx² + cdy² - dr² [precomputed as radial->A]
- * B = -2·(pdx·cdx + pdy·cdy + râ‚·dr)
+ * A = cdx² + cdy² - dr²
+ * B = pdx·cdx + pdy·cdy + râ‚·dr
* C = pdx² + pdy² - r₲
+ * det = B² - A·C
*
* Since we have an affine transformation, we know that (pdx, pdy)
* increase linearly with each pixel,
*
- * pdx = pdx₀ + n·cx,
- * pdy = pdy₀ + n·cy,
- *
- * we can then express B in terms of an linear increment along
- * the scanline:
+ * pdx = pdx₀ + n·ux,
+ * pdy = pdy₀ + n·uy,
*
- * B = B₀ + n·cB, with
- * Bâ‚€ = -2·(pdx₀·cdx + pdy₀·cdy + râ‚·dr) and
- * cB = -2·(cx·cdx + cy·cdy)
- *
- * Thus we can replace the full evaluation of B per-pixel (4 multiplies,
- * 2 additions) with a single addition.
+ * we can then express B, C and det through multiple differentiation.
*/
- double r1 = radial->c1.radius / 65536.;
- double r1sq = r1 * r1;
- double pdx = rx - radial->c1.x / 65536.;
- double pdy = ry - radial->c1.y / 65536.;
- double A = radial->A;
- double invA = -65536. / (2. * A);
- double A4 = -4. * A;
- double B = -2. * (pdx*radial->cdx + pdy*radial->cdy + r1*radial->dr);
- double cB = -2. * (cx*radial->cdx + cy*radial->cdy);
- pixman_bool_t invert = A * radial->dr < 0;
+ pixman_fixed_32_32_t b, db, c, dc, ddc;
+
+ v.vector[0] -= radial->c1.x;
+ v.vector[1] -= radial->c1.y;
+
+ 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], -radial->c1.radius,
+ v.vector[0], v.vector[1], radial->c1.radius);
+ dc = dot (2 * v.vector[0] + unit.vector[0],
+ 2 * 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++)
{
- pixman_fixed_48_16_t t;
- double det = B * B + A4 * (pdx * pdx + pdy * pdy - r1sq);
- if (det <= 0.)
- t = (pixman_fixed_48_16_t) (B * invA);
- else if (invert)
- t = (pixman_fixed_48_16_t) ((B + sqrt (det)) * invA);
- else
- t = (pixman_fixed_48_16_t) ((B - sqrt (det)) * invA);
-
- *buffer = _pixman_gradient_walker_pixel (&walker, t);
+ *buffer = radial_compute_color (radial->a, b, c,
+ radial->inva,
+ radial->delta.radius,
+ radial->mindr,
+ &walker,
+ source->common.repeat);
}
- ++buffer;
- pdx += cx;
- pdy += cy;
- B += cB;
+ b += db;
+ c += dc;
+ dc += ddc;
+ ++buffer;
}
}
else
@@ -264,50 +288,45 @@ radial_gradient_get_scanline_32 (pixman_image_t *image,
{
if (!mask || *mask++)
{
- double pdx, pdy;
- double B, C;
- double det;
- double c1x = radial->c1.x / 65536.0;
- double c1y = radial->c1.y / 65536.0;
- double r1 = radial->c1.radius / 65536.0;
- pixman_fixed_48_16_t t;
- double x, y;
-
- if (rz != 0)
- {
- x = rx / rz;
- y = ry / rz;
- }
- else
+ if (v.vector[2] != 0)
{
- x = y = 0.;
- }
+ double pdx, pdy, invv2, b, c;
- pdx = x - c1x;
- pdy = y - c1y;
+ invv2 = 1. * pixman_fixed_1 / v.vector[2];
- B = -2 * (pdx * radial->cdx +
- pdy * radial->cdy +
- r1 * radial->dr);
- C = (pdx * pdx + pdy * pdy - r1 * r1);
+ pdx = v.vector[0] * invv2 - radial->c1.x;
+ /* / pixman_fixed_1 */
- det = (B * B) - (4 * radial->A * C);
- if (det < 0.0)
- det = 0.0;
+ pdy = v.vector[1] * invv2 - radial->c1.y;
+ /* / pixman_fixed_1 */
- if (radial->A * radial->dr < 0)
- t = (pixman_fixed_48_16_t) ((-B - sqrt (det)) / (2.0 * radial->A) * 65536);
- else
- t = (pixman_fixed_48_16_t) ((-B + sqrt (det)) / (2.0 * radial->A) * 65536);
+ 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 = _pixman_gradient_walker_pixel (&walker, t);
+ *buffer = radial_compute_color (radial->a, b, c,
+ radial->inva,
+ radial->delta.radius,
+ radial->mindr,
+ &walker,
+ source->common.repeat);
+ }
+ else
+ {
+ *buffer = 0;
+ }
}
++buffer;
- rx += cx;
- ry += cy;
- rz += cz;
+ v.vector[0] += unit.vector[0];
+ v.vector[1] += unit.vector[1];
+ v.vector[2] += unit.vector[2];
}
}
}
@@ -351,12 +370,17 @@ pixman_image_create_radial_gradient (pixman_point_fixed_t * inner,
radial->c2.x = outer->x;
radial->c2.y = outer->y;
radial->c2.radius = outer_radius;
- radial->cdx = pixman_fixed_to_double (radial->c2.x - radial->c1.x);
- radial->cdy = pixman_fixed_to_double (radial->c2.y - radial->c1.y);
- radial->dr = pixman_fixed_to_double (radial->c2.radius - radial->c1.radius);
- radial->A = (radial->cdx * radial->cdx +
- radial->cdy * radial->cdy -
- radial->dr * radial->dr);
+
+ 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;
+
+ 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;
image->common.property_changed = radial_gradient_property_changed;
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