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/* -*- Mode: c; tab-width: 8; c-basic-offset: 4; indent-tabs-mode: t; -*- */
/* cairo - a vector graphics library with display and print output
*
* Copyright 2009 Andrea Canciani
*
* This library is free software; you can redistribute it and/or
* modify it either under the terms of the GNU Lesser General Public
* License version 2.1 as published by the Free Software Foundation
* (the "LGPL") or, at your option, under the terms of the Mozilla
* Public License Version 1.1 (the "MPL"). If you do not alter this
* notice, a recipient may use your version of this file under either
* the MPL or the LGPL.
*
* You should have received a copy of the LGPL along with this library
* in the file COPYING-LGPL-2.1; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Suite 500, Boston, MA 02110-1335, USA
* You should have received a copy of the MPL along with this library
* in the file COPYING-MPL-1.1
*
* The contents of this file are subject to the Mozilla Public License
* Version 1.1 (the "License"); you may not use this file except in
* compliance with the License. You may obtain a copy of the License at
* http://www.mozilla.org/MPL/
*
* This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
* OF ANY KIND, either express or implied. See the LGPL or the MPL for
* the specific language governing rights and limitations.
*
* The Original Code is the cairo graphics library.
*
* The Initial Developer of the Original Code is Andrea Canciani.
*
* Contributor(s):
* Andrea Canciani <ranma42@gmail.com>
*/
#include "cairoint.h"
#include "cairo-array-private.h"
#include "cairo-pattern-private.h"
/*
* Rasterizer for mesh patterns.
*
* This implementation is based on techniques derived from several
* papers (available from ACM):
*
* - Lien, Shantz and Pratt "Adaptive Forward Differencing for
* Rendering Curves and Surfaces" (discussion of the AFD technique,
* bound of 1/sqrt(2) on step length without proof)
*
* - Popescu and Rosen, "Forward rasterization" (description of
* forward rasterization, proof of the previous bound)
*
* - Klassen, "Integer Forward Differencing of Cubic Polynomials:
* Analysis and Algorithms"
*
* - Klassen, "Exact Integer Hybrid Subdivision and Forward
* Differencing of Cubics" (improving the bound on the minimum
* number of steps)
*
* - Chang, Shantz and Rocchetti, "Rendering Cubic Curves and Surfaces
* with Integer Adaptive Forward Differencing" (analysis of forward
* differencing applied to Bezier patches)
*
* Notes:
* - Poor performance expected in degenerate cases
*
* - Patches mostly outside the drawing area are drawn completely (and
* clipped), wasting time
*
* - Both previous problems are greatly reduced by splitting until a
* reasonably small size and clipping the new tiles: execution time
* is quadratic in the convex-hull diameter instead than linear to
* the painted area. Splitting the tiles doesn't change the painted
* area but (usually) reduces the bounding box area (bbox area can
* remain the same after splitting, but cannot grow)
*
* - The initial implementation used adaptive forward differencing,
* but simple forward differencing scored better in benchmarks
*
* Idea:
*
* We do a sampling over the cubic patch with step du and dv (in the
* two parameters) that guarantees that any point of our sampling will
* be at most at 1/sqrt(2) from its adjacent points. In formulae
* (assuming B is the patch):
*
* |B(u,v) - B(u+du,v)| < 1/sqrt(2)
* |B(u,v) - B(u,v+dv)| < 1/sqrt(2)
*
* This means that every pixel covered by the patch will contain at
* least one of the samples, thus forward rasterization can be
* performed. Sketch of proof (from Popescu and Rosen):
*
* Let's take the P pixel we're interested into. If we assume it to be
* square, its boundaries define 9 regions on the plane:
*
* 1|2|3
* -+-+-
* 8|P|4
* -+-+-
* 7|6|5
*
* Let's check that the pixel P will contain at least one point
* assuming that it is covered by the patch.
*
* Since the pixel is covered by the patch, its center will belong to
* (at least) one of the quads:
*
* {(B(u,v), B(u+du,v), B(u,v+dv), B(u+du,v+dv)) for u,v in [0,1]}
*
* If P doesn't contain any of the corners of the quad:
*
* - if one of the corners is in 1,3,5 or 7, other two of them have to
* be in 2,4,6 or 8, thus if the last corner is not in P, the length
* of one of the edges will be > 1/sqrt(2)
*
* - if none of the corners is in 1,3,5 or 7, all of them are in 2,4,6
* and/or 8. If they are all in different regions, they can't
* satisfy the distance constraint. If two of them are in the same
* region (let's say 2), no point is in 6 and again it is impossible
* to have the center of P in the quad respecting the distance
* constraint (both these assertions can be checked by continuity
* considering the length of the edges of a quad with the vertices
* on the edges of P)
*
* Each of the cases led to a contradiction, so P contains at least
* one of the corners of the quad.
*/
/*
* Make sure that errors are less than 1 in fixed point math if you
* change these values.
*
* The error is amplified by about steps^3/4 times.
* The rasterizer always uses a number of steps that is a power of 2.
*
* 256 is the maximum allowed number of steps (to have error < 1)
* using 8.24 for the differences.
*/
#define STEPS_MAX_V 256.0
#define STEPS_MAX_U 256.0
/*
* If the patch/curve is only partially visible, split it to a finer
* resolution to get higher chances to clip (part of) it.
*
* These values have not been computed, but simply obtained
* empirically (by benchmarking some patches). They should never be
* greater than STEPS_MAX_V (or STEPS_MAX_U), but they can be as small
* as 1 (depending on how much you want to spend time in splitting the
* patch/curve when trying to save some rasterization time).
*/
#define STEPS_CLIP_V 64.0
#define STEPS_CLIP_U 64.0
/* Utils */
static inline double
sqlen (cairo_point_double_t p0, cairo_point_double_t p1)
{
cairo_point_double_t delta;
delta.x = p0.x - p1.x;
delta.y = p0.y - p1.y;
return delta.x * delta.x + delta.y * delta.y;
}
static inline int16_t
_color_delta_to_shifted_short (int32_t from, int32_t to, int shift)
{
int32_t delta = to - from;
/* We need to round toward zero, because otherwise adding the
* delta 2^shift times can overflow */
if (delta >= 0)
return delta >> shift;
else
return -((-delta) >> shift);
}
/*
* Convert a number of steps to the equivalent shift.
*
* Input: the square of the minimum number of steps
*
* Output: the smallest integer x such that 2^x > steps
*/
static inline int
sqsteps2shift (double steps_sq)
{
int r;
frexp (MAX (1.0, steps_sq), &r);
return (r + 1) >> 1;
}
/*
* FD functions
*
* A Bezier curve is defined (with respect to a parameter t in
* [0,1]) from its nodes (x,y,z,w) like this:
*
* B(t) = x(1-t)^3 + 3yt(1-t)^2 + 3zt^2(1-t) + wt^3
*
* To efficiently evaluate a Bezier curve, the rasterizer uses forward
* differences. Given x, y, z, w (the 4 nodes of the Bezier curve), it
* is possible to convert them to forward differences form and walk
* over the curve using fd_init (), fd_down () and fd_fwd ().
*
* f[0] is always the value of the Bezier curve for "current" t.
*/
/*
* Initialize the coefficient for forward differences.
*
* Input: x,y,z,w are the 4 nodes of the Bezier curve
*
* Output: f[i] is the i-th difference of the curve
*
* f[0] is the value of the curve for t==0, i.e. f[0]==x.
*
* The initial step is 1; this means that each step increases t by 1
* (so fd_init () immediately followed by fd_fwd (f) n times makes
* f[0] be the value of the curve for t==n).
*/
static inline void
fd_init (double x, double y, double z, double w, double f[4])
{
f[0] = x;
f[1] = w - x;
f[2] = 6. * (w - 2. * z + y);
f[3] = 6. * (w - 3. * z + 3. * y - x);
}
/*
* Halve the step of the coefficients for forward differences.
*
* Input: f[i] is the i-th difference of the curve
*
* Output: f[i] is the i-th difference of the curve with half the
* original step
*
* f[0] is not affected, so the current t is not changed.
*
* The other coefficients are changed so that the step is half the
* original step. This means that doing fd_fwd (f) n times with the
* input f results in the same f[0] as doing fd_fwd (f) 2n times with
* the output f.
*/
static inline void
fd_down (double f[4])
{
f[3] *= 0.125;
f[2] = f[2] * 0.25 - f[3];
f[1] = (f[1] - f[2]) * 0.5;
}
/*
* Perform one step of forward differences along the curve.
*
* Input: f[i] is the i-th difference of the curve
*
* Output: f[i] is the i-th difference of the curve after one step
*/
static inline void
fd_fwd (double f[4])
{
f[0] += f[1];
f[1] += f[2];
f[2] += f[3];
}
/*
* Transform to integer forward differences.
*
* Input: d[n] is the n-th difference (in double precision)
*
* Output: i[n] is the n-th difference (in fixed point precision)
*
* i[0] is 9.23 fixed point, other differences are 4.28 fixed point.
*/
static inline void
fd_fixed (double d[4], int32_t i[4])
{
i[0] = _cairo_fixed_16_16_from_double (256 * 2 * d[0]);
i[1] = _cairo_fixed_16_16_from_double (256 * 16 * d[1]);
i[2] = _cairo_fixed_16_16_from_double (256 * 16 * d[2]);
i[3] = _cairo_fixed_16_16_from_double (256 * 16 * d[3]);
}
/*
* Perform one step of integer forward differences along the curve.
*
* Input: f[n] is the n-th difference
*
* Output: f[n] is the n-th difference
*
* f[0] is 9.23 fixed point, other differences are 4.28 fixed point.
*/
static inline void
fd_fixed_fwd (int32_t f[4])
{
f[0] += (f[1] >> 5) + ((f[1] >> 4) & 1);
f[1] += f[2];
f[2] += f[3];
}
/*
* Compute the minimum number of steps that guarantee that walking
* over a curve will leave no holes.
*
* Input: p[0..3] the nodes of the Bezier curve
*
* Returns: the square of the number of steps
*
* Idea:
*
* We want to make sure that at every step we move by less than
* 1/sqrt(2).
*
* The derivative of the cubic Bezier with nodes (p0, p1, p2, p3) is
* the quadratic Bezier with nodes (p1-p0, p2-p1, p3-p2) scaled by 3,
* so (since a Bezier curve is always bounded by its convex hull), we
* can say that:
*
* max(|B'(t)|) <= 3 max (|p1-p0|, |p2-p1|, |p3-p2|)
*
* We can improve this by noticing that a quadratic Bezier (a,b,c) is
* bounded by the quad (a,lerp(a,b,t),lerp(b,c,t),c) for any t, so
* (substituting the previous values, using t=0.5 and simplifying):
*
* max(|B'(t)|) <= 3 max (|p1-p0|, |p2-p0|/2, |p3-p1|/2, |p3-p2|)
*
* So, to guarantee a maximum step length of 1/sqrt(2) we must do:
*
* 3 max (|p1-p0|, |p2-p0|/2, |p3-p1|/2, |p3-p2|) sqrt(2) steps
*/
static inline double
bezier_steps_sq (cairo_point_double_t p[4])
{
double tmp = sqlen (p[0], p[1]);
tmp = MAX (tmp, sqlen (p[2], p[3]));
tmp = MAX (tmp, sqlen (p[0], p[2]) * .25);
tmp = MAX (tmp, sqlen (p[1], p[3]) * .25);
return 18.0 * tmp;
}
/*
* Split a 1D Bezier cubic using de Casteljau's algorithm.
*
* Input: x,y,z,w the nodes of the Bezier curve
*
* Output: x0,y0,z0,w0 and x1,y1,z1,w1 are respectively the nodes of
* the first half and of the second half of the curve
*
* The output control nodes have to be distinct.
*/
static inline void
split_bezier_1D (double x, double y, double z, double w,
double *x0, double *y0, double *z0, double *w0,
double *x1, double *y1, double *z1, double *w1)
{
double tmp;
*x0 = x;
*w1 = w;
tmp = 0.5 * (y + z);
*y0 = 0.5 * (x + y);
*z1 = 0.5 * (z + w);
*z0 = 0.5 * (*y0 + tmp);
*y1 = 0.5 * (tmp + *z1);
*w0 = *x1 = 0.5 * (*z0 + *y1);
}
/*
* Split a Bezier curve using de Casteljau's algorithm.
*
* Input: p[0..3] the nodes of the Bezier curve
*
* Output: fst_half[0..3] and snd_half[0..3] are respectively the
* nodes of the first and of the second half of the curve
*
* fst_half and snd_half must be different, but they can be the same as
* nodes.
*/
static void
split_bezier (cairo_point_double_t p[4],
cairo_point_double_t fst_half[4],
cairo_point_double_t snd_half[4])
{
split_bezier_1D (p[0].x, p[1].x, p[2].x, p[3].x,
&fst_half[0].x, &fst_half[1].x, &fst_half[2].x, &fst_half[3].x,
&snd_half[0].x, &snd_half[1].x, &snd_half[2].x, &snd_half[3].x);
split_bezier_1D (p[0].y, p[1].y, p[2].y, p[3].y,
&fst_half[0].y, &fst_half[1].y, &fst_half[2].y, &fst_half[3].y,
&snd_half[0].y, &snd_half[1].y, &snd_half[2].y, &snd_half[3].y);
}
typedef enum _intersection {
INSIDE = -1, /* the interval is entirely contained in the reference interval */
OUTSIDE = 0, /* the interval has no intersection with the reference interval */
PARTIAL = 1 /* the interval intersects the reference interval (but is not fully inside it) */
} intersection_t;
/*
* Check if an interval if inside another.
*
* Input: a,b are the extrema of the first interval
* c,d are the extrema of the second interval
*
* Returns: INSIDE iff [a,b) intersection [c,d) = [a,b)
* OUTSIDE iff [a,b) intersection [c,d) = {}
* PARTIAL otherwise
*
* The function assumes a < b and c < d
*
* Note: Bitwise-anding the results along each component gives the
* expected result for [a,b) x [A,B) intersection [c,d) x [C,D).
*/
static inline int
intersect_interval (double a, double b, double c, double d)
{
if (c <= a && b <= d)
return INSIDE;
else if (a >= d || b <= c)
return OUTSIDE;
else
return PARTIAL;
}
/*
* Set the color of a pixel.
*
* Input: data is the base pointer of the image
* width, height are the dimensions of the image
* stride is the stride in bytes between adjacent rows
* x, y are the coordinates of the pixel to be colored
* r,g,b,a are the color components of the color to be set
*
* Output: the (x,y) pixel in data has the (r,g,b,a) color
*
* The input color components are not premultiplied, but the data
* stored in the image is assumed to be in CAIRO_FORMAT_ARGB32 (8 bpc,
* premultiplied).
*
* If the pixel to be set is outside the image, this function does
* nothing.
*/
static inline void
draw_pixel (unsigned char *data, int width, int height, int stride,
int x, int y, uint16_t r, uint16_t g, uint16_t b, uint16_t a)
{
if (likely (0 <= x && 0 <= y && x < width && y < height)) {
uint32_t tr, tg, tb, ta;
/* Premultiply and round */
ta = a;
tr = r * ta + 0x8000;
tg = g * ta + 0x8000;
tb = b * ta + 0x8000;
tr += tr >> 16;
tg += tg >> 16;
tb += tb >> 16;
*((uint32_t*) (data + y*stride + 4*x)) = ((ta << 16) & 0xff000000) |
((tr >> 8) & 0xff0000) | ((tg >> 16) & 0xff00) | (tb >> 24);
}
}
/*
* Forward-rasterize a cubic curve using forward differences.
*
* Input: data is the base pointer of the image
* width, height are the dimensions of the image
* stride is the stride in bytes between adjacent rows
* ushift is log2(n) if n is the number of desired steps
* dxu[i], dyu[i] are the x,y forward differences of the curve
* r0,g0,b0,a0 are the color components of the start point
* r3,g3,b3,a3 are the color components of the end point
*
* Output: data will be changed to have the requested curve drawn in
* the specified colors
*
* The input color components are not premultiplied, but the data
* stored in the image is assumed to be in CAIRO_FORMAT_ARGB32 (8 bpc,
* premultiplied).
*
* The function draws n+1 pixels, that is from the point at step 0 to
* the point at step n, both included. This is the discrete equivalent
* to drawing the curve for values of the interpolation parameter in
* [0,1] (including both extremes).
*/
static inline void
rasterize_bezier_curve (unsigned char *data, int width, int height, int stride,
int ushift, double dxu[4], double dyu[4],
uint16_t r0, uint16_t g0, uint16_t b0, uint16_t a0,
uint16_t r3, uint16_t g3, uint16_t b3, uint16_t a3)
{
int32_t xu[4], yu[4];
int x0, y0, u, usteps = 1 << ushift;
uint16_t r = r0, g = g0, b = b0, a = a0;
int16_t dr = _color_delta_to_shifted_short (r0, r3, ushift);
int16_t dg = _color_delta_to_shifted_short (g0, g3, ushift);
int16_t db = _color_delta_to_shifted_short (b0, b3, ushift);
int16_t da = _color_delta_to_shifted_short (a0, a3, ushift);
fd_fixed (dxu, xu);
fd_fixed (dyu, yu);
/*
* Use (dxu[0],dyu[0]) as origin for the forward differences.
*
* This makes it possible to handle much larger coordinates (the
* ones that can be represented as cairo_fixed_t)
*/
x0 = _cairo_fixed_from_double (dxu[0]);
y0 = _cairo_fixed_from_double (dyu[0]);
xu[0] = 0;
yu[0] = 0;
for (u = 0; u <= usteps; ++u) {
/*
* This rasterizer assumes that pixels are integer aligned
* squares, so a generic (x,y) point belongs to the pixel with
* top-left coordinates (floor(x), floor(y))
*/
int x = _cairo_fixed_integer_floor (x0 + (xu[0] >> 15) + ((xu[0] >> 14) & 1));
int y = _cairo_fixed_integer_floor (y0 + (yu[0] >> 15) + ((yu[0] >> 14) & 1));
draw_pixel (data, width, height, stride, x, y, r, g, b, a);
fd_fixed_fwd (xu);
fd_fixed_fwd (yu);
r += dr;
g += dg;
b += db;
a += da;
}
}
/*
* Clip, split and rasterize a Bezier curve.
*
* Input: data is the base pointer of the image
* width, height are the dimensions of the image
* stride is the stride in bytes between adjacent rows
* p[i] is the i-th node of the Bezier curve
* c0[i] is the i-th color component at the start point
* c3[i] is the i-th color component at the end point
*
* Output: data will be changed to have the requested curve drawn in
* the specified colors
*
* The input color components are not premultiplied, but the data
* stored in the image is assumed to be in CAIRO_FORMAT_ARGB32 (8 bpc,
* premultiplied).
*
* The color components are red, green, blue and alpha, in this order.
*
* The function guarantees that it will draw the curve with a step
* small enough to never have a distance above 1/sqrt(2) between two
* consecutive points (which is needed to ensure that no hole can
* appear when using this function to rasterize a patch).
*/
static void
draw_bezier_curve (unsigned char *data, int width, int height, int stride,
cairo_point_double_t p[4], double c0[4], double c3[4])
{
double top, bottom, left, right, steps_sq;
int i, v;
top = bottom = p[0].y;
for (i = 1; i < 4; ++i) {
top = MIN (top, p[i].y);
bottom = MAX (bottom, p[i].y);
}
/* Check visibility */
v = intersect_interval (top, bottom, 0, height);
if (v == OUTSIDE)
return;
left = right = p[0].x;
for (i = 1; i < 4; ++i) {
left = MIN (left, p[i].x);
right = MAX (right, p[i].x);
}
v &= intersect_interval (left, right, 0, width);
if (v == OUTSIDE)
return;
steps_sq = bezier_steps_sq (p);
if (steps_sq >= (v == INSIDE ? STEPS_MAX_U * STEPS_MAX_U : STEPS_CLIP_U * STEPS_CLIP_U)) {
/*
* The number of steps is greater than the threshold. This
* means that either the error would become too big if we
* directly rasterized it or that we can probably save some
* time by splitting the curve and clipping part of it
*/
cairo_point_double_t first[4], second[4];
double midc[4];
split_bezier (p, first, second);
midc[0] = (c0[0] + c3[0]) * 0.5;
midc[1] = (c0[1] + c3[1]) * 0.5;
midc[2] = (c0[2] + c3[2]) * 0.5;
midc[3] = (c0[3] + c3[3]) * 0.5;
draw_bezier_curve (data, width, height, stride, first, c0, midc);
draw_bezier_curve (data, width, height, stride, second, midc, c3);
} else {
double xu[4], yu[4];
int ushift = sqsteps2shift (steps_sq), k;
fd_init (p[0].x, p[1].x, p[2].x, p[3].x, xu);
fd_init (p[0].y, p[1].y, p[2].y, p[3].y, yu);
for (k = 0; k < ushift; ++k) {
fd_down (xu);
fd_down (yu);
}
rasterize_bezier_curve (data, width, height, stride, ushift,
xu, yu,
_cairo_color_double_to_short (c0[0]),
_cairo_color_double_to_short (c0[1]),
_cairo_color_double_to_short (c0[2]),
_cairo_color_double_to_short (c0[3]),
_cairo_color_double_to_short (c3[0]),
_cairo_color_double_to_short (c3[1]),
_cairo_color_double_to_short (c3[2]),
_cairo_color_double_to_short (c3[3]));
/* Draw the end point, to make sure that we didn't leave it
* out because of rounding */
draw_pixel (data, width, height, stride,
_cairo_fixed_integer_floor (_cairo_fixed_from_double (p[3].x)),
_cairo_fixed_integer_floor (_cairo_fixed_from_double (p[3].y)),
_cairo_color_double_to_short (c3[0]),
_cairo_color_double_to_short (c3[1]),
_cairo_color_double_to_short (c3[2]),
_cairo_color_double_to_short (c3[3]));
}
}
/*
* Forward-rasterize a cubic Bezier patch using forward differences.
*
* Input: data is the base pointer of the image
* width, height are the dimensions of the image
* stride is the stride in bytes between adjacent rows
* vshift is log2(n) if n is the number of desired steps
* p[i][j], p[i][j] are the the nodes of the Bezier patch
* col[i][j] is the j-th color component of the i-th corner
*
* Output: data will be changed to have the requested patch drawn in
* the specified colors
*
* The nodes of the patch are as follows:
*
* u\v 0 - > 1
* 0 p00 p01 p02 p03
* | p10 p11 p12 p13
* v p20 p21 p22 p23
* 1 p30 p31 p32 p33
*
* i.e. u varies along the first component (rows), v varies along the
* second one (columns).
*
* The color components are red, green, blue and alpha, in this order.
* c[0..3] are the colors in p00, p30, p03, p33 respectively
*
* The input color components are not premultiplied, but the data
* stored in the image is assumed to be in CAIRO_FORMAT_ARGB32 (8 bpc,
* premultiplied).
*
* If the patch folds over itself, the part with the highest v
* parameter is considered above. If both have the same v, the one
* with the highest u parameter is above.
*
* The function draws n+1 curves, that is from the curve at step 0 to
* the curve at step n, both included. This is the discrete equivalent
* to drawing the patch for values of the interpolation parameter in
* [0,1] (including both extremes).
*/
static inline void
rasterize_bezier_patch (unsigned char *data, int width, int height, int stride, int vshift,
cairo_point_double_t p[4][4], double col[4][4])
{
double pv[4][2][4], cstart[4], cend[4], dcstart[4], dcend[4];
int v, i, k;
v = 1 << vshift;
/*
* pv[i][0] is the function (represented using forward
* differences) mapping v to the x coordinate of the i-th node of
* the Bezier curve with parameter u.
* (Likewise p[i][0] gives the y coordinate).
*
* This means that (pv[0][0][0],pv[0][1][0]),
* (pv[1][0][0],pv[1][1][0]), (pv[2][0][0],pv[2][1][0]) and
* (pv[3][0][0],pv[3][1][0]) are the nodes of the Bezier curve for
* the "current" v value (see the FD comments for more details).
*/
for (i = 0; i < 4; ++i) {
fd_init (p[i][0].x, p[i][1].x, p[i][2].x, p[i][3].x, pv[i][0]);
fd_init (p[i][0].y, p[i][1].y, p[i][2].y, p[i][3].y, pv[i][1]);
for (k = 0; k < vshift; ++k) {
fd_down (pv[i][0]);
fd_down (pv[i][1]);
}
}
for (i = 0; i < 4; ++i) {
cstart[i] = col[0][i];
cend[i] = col[1][i];
dcstart[i] = (col[2][i] - col[0][i]) / v;
dcend[i] = (col[3][i] - col[1][i]) / v;
}
v++;
while (v--) {
cairo_point_double_t nodes[4];
for (i = 0; i < 4; ++i) {
nodes[i].x = pv[i][0][0];
nodes[i].y = pv[i][1][0];
}
draw_bezier_curve (data, width, height, stride, nodes, cstart, cend);
for (i = 0; i < 4; ++i) {
fd_fwd (pv[i][0]);
fd_fwd (pv[i][1]);
cstart[i] += dcstart[i];
cend[i] += dcend[i];
}
}
}
/*
* Clip, split and rasterize a Bezier cubic patch.
*
* Input: data is the base pointer of the image
* width, height are the dimensions of the image
* stride is the stride in bytes between adjacent rows
* p[i][j], p[i][j] are the nodes of the patch
* col[i][j] is the j-th color component of the i-th corner
*
* Output: data will be changed to have the requested patch drawn in
* the specified colors
*
* The nodes of the patch are as follows:
*
* u\v 0 - > 1
* 0 p00 p01 p02 p03
* | p10 p11 p12 p13
* v p20 p21 p22 p23
* 1 p30 p31 p32 p33
*
* i.e. u varies along the first component (rows), v varies along the
* second one (columns).
*
* The color components are red, green, blue and alpha, in this order.
* c[0..3] are the colors in p00, p30, p03, p33 respectively
*
* The input color components are not premultiplied, but the data
* stored in the image is assumed to be in CAIRO_FORMAT_ARGB32 (8 bpc,
* premultiplied).
*
* If the patch folds over itself, the part with the highest v
* parameter is considered above. If both have the same v, the one
* with the highest u parameter is above.
*
* The function guarantees that it will draw the patch with a step
* small enough to never have a distance above 1/sqrt(2) between two
* adjacent points (which guarantees that no hole can appear).
*
* This function can be used to rasterize a tile of PDF type 7
* shadings (see http://www.adobe.com/devnet/pdf/pdf_reference.html).
*/
static void
draw_bezier_patch (unsigned char *data, int width, int height, int stride,
cairo_point_double_t p[4][4], double c[4][4])
{
double top, bottom, left, right, steps_sq;
int i, j, v;
top = bottom = p[0][0].y;
for (i = 0; i < 4; ++i) {
for (j= 0; j < 4; ++j) {
top = MIN (top, p[i][j].y);
bottom = MAX (bottom, p[i][j].y);
}
}
v = intersect_interval (top, bottom, 0, height);
if (v == OUTSIDE)
return;
left = right = p[0][0].x;
for (i = 0; i < 4; ++i) {
for (j= 0; j < 4; ++j) {
left = MIN (left, p[i][j].x);
right = MAX (right, p[i][j].x);
}
}
v &= intersect_interval (left, right, 0, width);
if (v == OUTSIDE)
return;
steps_sq = 0;
for (i = 0; i < 4; ++i)
steps_sq = MAX (steps_sq, bezier_steps_sq (p[i]));
if (steps_sq >= (v == INSIDE ? STEPS_MAX_V * STEPS_MAX_V : STEPS_CLIP_V * STEPS_CLIP_V)) {
/* The number of steps is greater than the threshold. This
* means that either the error would become too big if we
* directly rasterized it or that we can probably save some
* time by splitting the curve and clipping part of it. The
* patch is only split in the v direction to guarantee that
* rasterizing each part will overwrite parts with low v with
* overlapping parts with higher v. */
cairo_point_double_t first[4][4], second[4][4];
double subc[4][4];
for (i = 0; i < 4; ++i)
split_bezier (p[i], first[i], second[i]);
for (i = 0; i < 4; ++i) {
subc[0][i] = c[0][i];
subc[1][i] = c[1][i];
subc[2][i] = 0.5 * (c[0][i] + c[2][i]);
subc[3][i] = 0.5 * (c[1][i] + c[3][i]);
}
draw_bezier_patch (data, width, height, stride, first, subc);
for (i = 0; i < 4; ++i) {
subc[0][i] = subc[2][i];
subc[1][i] = subc[3][i];
subc[2][i] = c[2][i];
subc[3][i] = c[3][i];
}
draw_bezier_patch (data, width, height, stride, second, subc);
} else {
rasterize_bezier_patch (data, width, height, stride, sqsteps2shift (steps_sq), p, c);
}
}
/*
* Draw a tensor product shading pattern.
*
* Input: mesh is the mesh pattern
* data is the base pointer of the image
* width, height are the dimensions of the image
* stride is the stride in bytes between adjacent rows
*
* Output: data will be changed to have the pattern drawn on it
*
* data is assumed to be clear and its content is assumed to be in
* CAIRO_FORMAT_ARGB32 (8 bpc, premultiplied).
*
* This function can be used to rasterize a PDF type 7 shading (see
* http://www.adobe.com/devnet/pdf/pdf_reference.html).
*/
void
_cairo_mesh_pattern_rasterize (const cairo_mesh_pattern_t *mesh,
void *data,
int width,
int height,
int stride,
double x_offset,
double y_offset)
{
cairo_point_double_t nodes[4][4];
double colors[4][4];
cairo_matrix_t p2u;
unsigned int i, j, k, n;
cairo_status_t status;
const cairo_mesh_patch_t *patch;
const cairo_color_t *c;
assert (mesh->base.status == CAIRO_STATUS_SUCCESS);
assert (mesh->current_patch == NULL);
p2u = mesh->base.matrix;
status = cairo_matrix_invert (&p2u);
assert (status == CAIRO_STATUS_SUCCESS);
n = _cairo_array_num_elements (&mesh->patches);
patch = _cairo_array_index_const (&mesh->patches, 0);
for (i = 0; i < n; i++) {
for (j = 0; j < 4; j++) {
for (k = 0; k < 4; k++) {
nodes[j][k] = patch->points[j][k];
cairo_matrix_transform_point (&p2u, &nodes[j][k].x, &nodes[j][k].y);
nodes[j][k].x += x_offset;
nodes[j][k].y += y_offset;
}
}
c = &patch->colors[0];
colors[0][0] = c->red;
colors[0][1] = c->green;
colors[0][2] = c->blue;
colors[0][3] = c->alpha;
c = &patch->colors[3];
colors[1][0] = c->red;
colors[1][1] = c->green;
colors[1][2] = c->blue;
colors[1][3] = c->alpha;
c = &patch->colors[1];
colors[2][0] = c->red;
colors[2][1] = c->green;
colors[2][2] = c->blue;
colors[2][3] = c->alpha;
c = &patch->colors[2];
colors[3][0] = c->red;
colors[3][1] = c->green;
colors[3][2] = c->blue;
colors[3][3] = c->alpha;
draw_bezier_patch (data, width, height, stride, nodes, colors);
patch++;
}
}