Gradient fixes
* Port fix for bug 7685 from pixman. Patch by Carl Worth * Add projective version of radial gradient code. * Make sure that all Pict*Gradient types have PictGradient as prefix, since code in various places relies on that.
This commit is contained in:
Soren Sandmann Pedersen
parent
38d14e8589
commit
84838268b3
203
fb/fbcompose.c
203
fb/fbcompose.c
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@ -3148,13 +3148,128 @@ static void fbFetchSourcePict(PicturePtr pict, int x, int y, int width, CARD32 *
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}
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}
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} else {
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/*
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* In the radial gradient problem we are given two circles (c₁,r₁) and
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* (c₂,r₂) that define the gradient itself. Then, for any point p, we
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* must compute the value(s) of t within [0.0, 1.0] representing the
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* circle(s) that would color the point.
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*
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* There are potentially two values of t since the point p can be
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* colored by both sides of the circle, (which happens whenever one
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* circle is not entirely contained within the other).
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*
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* If we solve for a value of t that is outside of [0.0, 1.0] then we
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* use the extend mode (NONE, REPEAT, REFLECT, or PAD) to map to a
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* value within [0.0, 1.0].
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*
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* Here is an illustration of the problem:
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*
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* p₂
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* p •
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* • ╲
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* · ╲r₂
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* p₁ · ╲
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* • θ╲
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* ╲ ╌╌•
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* ╲r₁ · c₂
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* θ╲ ·
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* ╌╌•
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* c₁
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*
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* Given (c₁,r₁), (c₂,r₂) and p, we must find an angle θ such that two
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* points p₁ and p₂ on the two circles are collinear with p. Then, the
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* desired value of t is the ratio of the length of p₁p to the length
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* of p₁p₂.
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*
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* So, we have six unknown values: (p₁x, p₁y), (p₂x, p₂y), θ and t.
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* We can also write six equations that constrain the problem:
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*
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* Point p₁ is a distance r₁ from c₁ at an angle of θ:
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*
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* 1. p₁x = c₁x + r₁·cos θ
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* 2. p₁y = c₁y + r₁·sin θ
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*
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* Point p₂ is a distance r₂ from c₂ at an angle of θ:
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*
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* 3. p₂x = c₂x + r2·cos θ
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* 4. p₂y = c₂y + r2·sin θ
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*
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* Point p lies at a fraction t along the line segment p₁p₂:
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*
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* 5. px = t·p₂x + (1-t)·p₁x
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* 6. py = t·p₂y + (1-t)·p₁y
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*
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* To solve, first subtitute 1-4 into 5 and 6:
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*
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* px = t·(c₂x + r₂·cos θ) + (1-t)·(c₁x + r₁·cos θ)
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* py = t·(c₂y + r₂·sin θ) + (1-t)·(c₁y + r₁·sin θ)
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*
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* Then solve each for cos θ and sin θ expressed as a function of t:
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*
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* cos θ = (-(c₂x - c₁x)·t + (px - c₁x)) / ((r₂-r₁)·t + r₁)
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* sin θ = (-(c₂y - c₁y)·t + (py - c₁y)) / ((r₂-r₁)·t + r₁)
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*
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* To simplify this a bit, we define new variables for several of the
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* common terms as shown below:
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*
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* p₂
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* p •
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* • ╲
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* · ┆ ╲r₂
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* p₁ · ┆ ╲
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* • pdy┆ ╲
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* ╲ ┆ •c₂
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* ╲r₁ ┆ · ┆
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* ╲ ·┆ ┆cdy
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* •╌╌╌╌┴╌╌╌╌╌╌╌┘
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* c₁ pdx cdx
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*
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* cdx = (c₂x - c₁x)
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* cdy = (c₂y - c₁y)
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* dr = r₂-r₁
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* pdx = px - c₁x
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* pdy = py - c₁y
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*
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* Note that cdx, cdy, and dr do not depend on point p at all, so can
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* be pre-computed for the entire gradient. The simplifed equations
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* are now:
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*
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* cos θ = (-cdx·t + pdx) / (dr·t + r₁)
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* sin θ = (-cdy·t + pdy) / (dr·t + r₁)
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*
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* Finally, to get a single function of t and eliminate the last
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* unknown θ, we use the identity sin²θ + cos²θ = 1. First, square
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* each equation, (we knew a quadratic was coming since it must be
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* possible to obtain two solutions in some cases):
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*
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* cos²θ = (cdx²t² - 2·cdx·pdx·t + pdx²) / (dr²·t² + 2·r₁·dr·t + r₁²)
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* sin²θ = (cdy²t² - 2·cdy·pdy·t + pdy²) / (dr²·t² + 2·r₁·dr·t + r₁²)
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*
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* Then add both together, set the result equal to 1, and express as a
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* standard quadratic equation in t of the form At² + Bt + C = 0
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*
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* (cdx² + cdy² - dr²)·t² - 2·(cdx·pdx + cdy·pdy + r₁·dr)·t + (pdx² + pdy² - r₁²) = 0
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*
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* In other words:
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*
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* A = cdx² + cdy² - dr²
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* B = -2·(pdx·cdx + pdy·cdy + r₁·dr)
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* C = pdx² + pdy² - r₁²
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*
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* And again, notice that A does not depend on p, so can be
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* precomputed. From here we just use the quadratic formula to solve
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* for t:
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*
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* t = (-2·B ± ⎷(B² - 4·A·C)) / 2·A
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*/
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/* radial or conical */
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Bool affine = TRUE;
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double cx = 1.;
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double cy = 0.;
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double cz = 0.;
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double rx = x;
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double ry = y;
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double rx = x + 0.5;
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double ry = y + 0.5;
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double rz = 1.;
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if (pict->transform) {
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@ -3176,25 +3291,38 @@ static void fbFetchSourcePict(PicturePtr pict, int x, int y, int width, CARD32 *
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}
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if (pGradient->type == SourcePictTypeRadial) {
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PictRadialGradient *radial;
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radial = &pGradient->radial;
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if (affine) {
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rx -= pGradient->radial.fx;
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ry -= pGradient->radial.fy;
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while (buffer < end) {
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double b, c, det, s;
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if (!mask || *mask++ & maskBits)
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{
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xFixed_48_16 t;
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double pdx, pdy;
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double B, C;
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double det;
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double c1x = radial->c1.x / 65536.0;
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double c1y = radial->c1.y / 65536.0;
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double r1 = radial->c1.radius / 65536.0;
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xFixed_48_16 t;
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pdx = rx - c1x;
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pdy = ry - c1y;
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B = -2 * ( pdx * radial->cdx
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+ pdy * radial->cdy
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+ r1 * radial->dr);
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C = (pdx * pdx + pdy * pdy - r1 * r1);
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det = (B * B) - (4 * radial->A * C);
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if (det < 0.0)
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det = 0.0;
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if (radial->A < 0)
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t = (xFixed_48_16) ((- B - sqrt(det)) / (2.0 * radial->A) * 65536);
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else
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t = (xFixed_48_16) ((- B + sqrt(det)) / (2.0 * radial->A) * 65536);
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b = 2*(rx*pGradient->radial.dx + ry*pGradient->radial.dy);
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c = -(rx*rx + ry*ry);
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det = (b * b) - (4 * pGradient->radial.a * c);
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s = (-b + sqrt(det))/(2. * pGradient->radial.a);
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t = (xFixed_48_16)((s*pGradient->radial.m + pGradient->radial.b)*65536);
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WRITE(buffer, _gradient_walker_pixel (&walker, t));
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WRITE(buffer, _gradient_walker_pixel (&walker, t));
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}
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++buffer;
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@ -3202,35 +3330,50 @@ static void fbFetchSourcePict(PicturePtr pict, int x, int y, int width, CARD32 *
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ry += cy;
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}
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} else {
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/* projective */
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while (buffer < end) {
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double x, y;
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double b, c, det, s;
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if (!mask || *mask++ & maskBits)
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{
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xFixed_48_16 t;
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double pdx, pdy;
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double B, C;
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double det;
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double c1x = radial->c1.x / 65536.0;
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double c1y = radial->c1.y / 65536.0;
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double r1 = radial->c1.radius / 65536.0;
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xFixed_48_16 t;
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double x, y;
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if (rz != 0) {
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x = rx/rz;
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y = ry/rz;
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} else {
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x = y = 0.;
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}
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x -= pGradient->radial.fx;
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y -= pGradient->radial.fy;
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b = 2*(x*pGradient->radial.dx + y*pGradient->radial.dy);
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c = -(x*x + y*y);
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det = (b * b) - (4 * pGradient->radial.a * c);
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s = (-b + sqrt(det))/(2. * pGradient->radial.a);
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t = (xFixed_48_16)((s*pGradient->radial.m + pGradient->radial.b)*65536);
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WRITE(buffer, _gradient_walker_pixel (&walker, t));
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pdx = x - c1x;
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pdy = y - c1y;
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B = -2 * ( pdx * radial->cdx
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+ pdy * radial->cdy
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+ r1 * radial->dr);
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C = (pdx * pdx + pdy * pdy - r1 * r1);
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det = (B * B) - (4 * radial->A * C);
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if (det < 0.0)
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det = 0.0;
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if (radial->A < 0)
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t = (xFixed_48_16) ((- B - sqrt(det)) / (2.0 * radial->A) * 65536);
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else
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t = (xFixed_48_16) ((- B + sqrt(det)) / (2.0 * radial->A) * 65536);
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WRITE(buffer, _gradient_walker_pixel (&walker, t));
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}
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++buffer;
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rx += cx;
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ry += cy;
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rz += cz;
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rz += cz;
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}
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}
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} else /* SourcePictTypeConical */ {
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@ -1051,6 +1051,7 @@ CreateRadialGradientPicture (Picture pid, xPointFixed *inner, xPointFixed *outer
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radial = &pPicture->pSourcePict->radial;
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radial->type = SourcePictTypeRadial;
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#if 0
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{
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double x = (double)innerRadius / (double)outerRadius;
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radial->dx = (outer->x - inner->x);
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@ -1066,7 +1067,20 @@ CreateRadialGradientPicture (Picture pid, xPointFixed *inner, xPointFixed *outer
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x = outerRadius/65536.;
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radial->a = x*x - radial->dx*radial->dx - radial->dy*radial->dy;
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}
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#endif
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radial->c1.x = inner->x;
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radial->c1.y = inner->y;
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radial->c1.radius = innerRadius;
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radial->c2.x = outer->x;
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radial->c2.y = outer->y;
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radial->c2.radius = outerRadius;
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radial->cdx = (radial->c2.x - radial->c1.x) / 65536.;
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radial->cdy = (radial->c2.y - radial->c1.y) / 65536.;
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radial->dr = (radial->c2.radius - radial->c1.radius) / 65536.;
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radial->A = ( radial->cdx * radial->cdx
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+ radial->cdy * radial->cdy
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- radial->dr * radial->dr);
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initGradient(pPicture->pSourcePict, nStops, stops, colors, error);
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if (*error) {
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xfree(pPicture);
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@ -105,17 +105,26 @@ typedef struct _PictLinearGradient {
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xPointFixed p2;
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} PictLinearGradient, *PictLinearGradientPtr;
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typedef struct _PictCircle {
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xFixed x;
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xFixed y;
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xFixed radius;
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} PictCircle, *PictCirclePtr;
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typedef struct _PictRadialGradient {
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unsigned int type;
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unsigned int class;
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int nstops;
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PictGradientStopPtr stops;
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double fx;
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double fy;
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double dx;
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double dy;
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double a;
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double m;
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double b;
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int stopRange;
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CARD32 *colorTable;
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int colorTableSize;
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PictCircle c1;
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PictCircle c2;
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double cdx;
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double cdy;
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double dr;
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double A;
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} PictRadialGradient, *PictRadialGradientPtr;
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typedef struct _PictConicalGradient {
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