/*
* Copyright 2006 The Android Open Source Project
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "SkEdge.h"
#include "SkFDot6.h"
#include "SkMathPriv.h"
/*
In setLine, setQuadratic, setCubic, the first thing we do is to convert
the points into FDot6. This is modulated by the shift parameter, which
will either be 0, or something like 2 for antialiasing.
In the float case, we want to turn the float into .6 by saying pt * 64,
or pt * 256 for antialiasing. This is implemented as 1 << (shift + 6).
In the fixed case, we want to turn the fixed into .6 by saying pt >> 10,
or pt >> 8 for antialiasing. This is implemented as pt >> (10 - shift).
*/
static inline SkFixed SkFDot6ToFixedDiv2(SkFDot6 value) {
// we want to return SkFDot6ToFixed(value >> 1), but we don't want to throw
// away data in value, so just perform a modify up-shift
return SkLeftShift(value, 16 - 6 - 1);
}
/////////////////////////////////////////////////////////////////////////
int SkEdge::setLine(const SkPoint& p0, const SkPoint& p1, const SkIRect* clip,
int shift) {
SkFDot6 x0, y0, x1, y1;
{
#ifdef SK_RASTERIZE_EVEN_ROUNDING
x0 = SkScalarRoundToFDot6(p0.fX, shift);
y0 = SkScalarRoundToFDot6(p0.fY, shift);
x1 = SkScalarRoundToFDot6(p1.fX, shift);
y1 = SkScalarRoundToFDot6(p1.fY, shift);
#else
float scale = float(1 << (shift + 6));
x0 = int(p0.fX * scale);
y0 = int(p0.fY * scale);
x1 = int(p1.fX * scale);
y1 = int(p1.fY * scale);
#endif
}
int winding = 1;
if (y0 > y1) {
SkTSwap(x0, x1);
SkTSwap(y0, y1);
winding = -1;
}
int top = SkFDot6Round(y0);
int bot = SkFDot6Round(y1);
// are we a zero-height line?
if (top == bot) {
return 0;
}
// are we completely above or below the clip?
if (clip && (top >= clip->fBottom || bot <= clip->fTop)) {
return 0;
}
SkFixed slope = SkFDot6Div(x1 - x0, y1 - y0);
const SkFDot6 dy = SkEdge_Compute_DY(top, y0);
fX = SkFDot6ToFixed(x0 + SkFixedMul(slope, dy)); // + SK_Fixed1/2
fDX = slope;
fFirstY = top;
fLastY = bot - 1;
fCurveCount = 0;
fWinding = SkToS8(winding);
fCurveShift = 0;
if (clip) {
this->chopLineWithClip(*clip);
}
return 1;
}
// called from a curve subclass
int SkEdge::updateLine(SkFixed x0, SkFixed y0, SkFixed x1, SkFixed y1)
{
SkASSERT(fWinding == 1 || fWinding == -1);
SkASSERT(fCurveCount != 0);
// SkASSERT(fCurveShift != 0);
y0 >>= 10;
y1 >>= 10;
SkASSERT(y0 <= y1);
int top = SkFDot6Round(y0);
int bot = SkFDot6Round(y1);
// SkASSERT(top >= fFirstY);
// are we a zero-height line?
if (top == bot)
return 0;
x0 >>= 10;
x1 >>= 10;
SkFixed slope = SkFDot6Div(x1 - x0, y1 - y0);
const SkFDot6 dy = SkEdge_Compute_DY(top, y0);
fX = SkFDot6ToFixed(x0 + SkFixedMul(slope, dy)); // + SK_Fixed1/2
fDX = slope;
fFirstY = top;
fLastY = bot - 1;
return 1;
}
void SkEdge::chopLineWithClip(const SkIRect& clip)
{
int top = fFirstY;
SkASSERT(top < clip.fBottom);
// clip the line to the top
if (top < clip.fTop)
{
SkASSERT(fLastY >= clip.fTop);
fX += fDX * (clip.fTop - top);
fFirstY = clip.fTop;
}
}
///////////////////////////////////////////////////////////////////////////////
/* We store 1<<shift in a (signed) byte, so its maximum value is 1<<6 == 64.
Note that this limits the number of lines we use to approximate a curve.
If we need to increase this, we need to store fCurveCount in something
larger than int8_t.
*/
#define MAX_COEFF_SHIFT 6
static inline SkFDot6 cheap_distance(SkFDot6 dx, SkFDot6 dy)
{
dx = SkAbs32(dx);
dy = SkAbs32(dy);
// return max + min/2
if (dx > dy)
dx += dy >> 1;
else
dx = dy + (dx >> 1);
return dx;
}
static inline int diff_to_shift(SkFDot6 dx, SkFDot6 dy, int shiftAA = 2)
{
// cheap calc of distance from center of p0-p2 to the center of the curve
SkFDot6 dist = cheap_distance(dx, dy);
// shift down dist (it is currently in dot6)
// down by 3 should give us 1/8 pixel accuracy (assuming our dist is accurate...)
// this is chosen by heuristic: make it as big as possible (to minimize segments)
// ... but small enough so that our curves still look smooth
// When shift > 0, we're using AA and everything is scaled up so we can
// lower the accuracy.
#ifdef SK_SUPPORT_LEGACY_QUAD_SHIFT
dist = (dist + (1 << 4)) >> 5;
#else
dist = (dist + (1 << 4)) >> (3 + shiftAA);
#endif
// each subdivision (shift value) cuts this dist (error) by 1/4
return (32 - SkCLZ(dist)) >> 1;
}
bool SkQuadraticEdge::setQuadraticWithoutUpdate(const SkPoint pts[3], int shift) {
SkFDot6 x0, y0, x1, y1, x2, y2;
{
#ifdef SK_RASTERIZE_EVEN_ROUNDING
x0 = SkScalarRoundToFDot6(pts[0].fX, shift);
y0 = SkScalarRoundToFDot6(pts[0].fY, shift);
x1 = SkScalarRoundToFDot6(pts[1].fX, shift);
y1 = SkScalarRoundToFDot6(pts[1].fY, shift);
x2 = SkScalarRoundToFDot6(pts[2].fX, shift);
y2 = SkScalarRoundToFDot6(pts[2].fY, shift);
#else
float scale = float(1 << (shift + 6));
x0 = int(pts[0].fX * scale);
y0 = int(pts[0].fY * scale);
x1 = int(pts[1].fX * scale);
y1 = int(pts[1].fY * scale);
x2 = int(pts[2].fX * scale);
y2 = int(pts[2].fY * scale);
#endif
}
int winding = 1;
if (y0 > y2)
{
SkTSwap(x0, x2);
SkTSwap(y0, y2);
winding = -1;
}
SkASSERT(y0 <= y1 && y1 <= y2);
int top = SkFDot6Round(y0);
int bot = SkFDot6Round(y2);
// are we a zero-height quad (line)?
if (top == bot)
return 0;
// compute number of steps needed (1 << shift)
{
SkFDot6 dx = (SkLeftShift(x1, 1) - x0 - x2) >> 2;
SkFDot6 dy = (SkLeftShift(y1, 1) - y0 - y2) >> 2;
// This is a little confusing:
// before this line, shift is the scale up factor for AA;
// after this line, shift is the fCurveShift.
shift = diff_to_shift(dx, dy, shift);
SkASSERT(shift >= 0);
}
// need at least 1 subdivision for our bias trick
if (shift == 0) {
shift = 1;
} else if (shift > MAX_COEFF_SHIFT) {
shift = MAX_COEFF_SHIFT;
}
fWinding = SkToS8(winding);
//fCubicDShift only set for cubics
fCurveCount = SkToS8(1 << shift);
/*
* We want to reformulate into polynomial form, to make it clear how we
* should forward-difference.
*
* p0 (1 - t)^2 + p1 t(1 - t) + p2 t^2 ==> At^2 + Bt + C
*
* A = p0 - 2p1 + p2
* B = 2(p1 - p0)
* C = p0
*
* Our caller must have constrained our inputs (p0..p2) to all fit into
* 16.16. However, as seen above, we sometimes compute values that can be
* larger (e.g. B = 2*(p1 - p0)). To guard against overflow, we will store
* A and B at 1/2 of their actual value, and just apply a 2x scale during
* application in updateQuadratic(). Hence we store (shift - 1) in
* fCurveShift.
*/
fCurveShift = SkToU8(shift - 1);
SkFixed A = SkFDot6ToFixedDiv2(x0 - x1 - x1 + x2); // 1/2 the real value
SkFixed B = SkFDot6ToFixed(x1 - x0); // 1/2 the real value
fQx = SkFDot6ToFixed(x0);
fQDx = B + (A >> shift); // biased by shift
fQDDx = A >> (shift - 1); // biased by shift
A = SkFDot6ToFixedDiv2(y0 - y1 - y1 + y2); // 1/2 the real value
B = SkFDot6ToFixed(y1 - y0); // 1/2 the real value
fQy = SkFDot6ToFixed(y0);
fQDy = B + (A >> shift); // biased by shift
fQDDy = A >> (shift - 1); // biased by shift
fQLastX = SkFDot6ToFixed(x2);
fQLastY = SkFDot6ToFixed(y2);
return true;
}
int SkQuadraticEdge::setQuadratic(const SkPoint pts[3], int shift) {
if (!setQuadraticWithoutUpdate(pts, shift)) {
return 0;
}
return this->updateQuadratic();
}
int SkQuadraticEdge::updateQuadratic()
{
int success;
int count = fCurveCount;
SkFixed oldx = fQx;
SkFixed oldy = fQy;
SkFixed dx = fQDx;
SkFixed dy = fQDy;
SkFixed newx, newy;
int shift = fCurveShift;
SkASSERT(count > 0);
do {
if (--count > 0)
{
newx = oldx + (dx >> shift);
dx += fQDDx;
newy = oldy + (dy >> shift);
dy += fQDDy;
}
else // last segment
{
newx = fQLastX;
newy = fQLastY;
}
success = this->updateLine(oldx, oldy, newx, newy);
oldx = newx;
oldy = newy;
} while (count > 0 && !success);
fQx = newx;
fQy = newy;
fQDx = dx;
fQDy = dy;
fCurveCount = SkToS8(count);
return success;
}
/////////////////////////////////////////////////////////////////////////
static inline int SkFDot6UpShift(SkFDot6 x, int upShift) {
SkASSERT((SkLeftShift(x, upShift) >> upShift) == x);
return SkLeftShift(x, upShift);
}
/* f(1/3) = (8a + 12b + 6c + d) / 27
f(2/3) = (a + 6b + 12c + 8d) / 27
f(1/3)-b = (8a - 15b + 6c + d) / 27
f(2/3)-c = (a + 6b - 15c + 8d) / 27
use 16/512 to approximate 1/27
*/
static SkFDot6 cubic_delta_from_line(SkFDot6 a, SkFDot6 b, SkFDot6 c, SkFDot6 d)
{
// since our parameters may be negative, we don't use << to avoid ASAN warnings
SkFDot6 oneThird = (a*8 - b*15 + 6*c + d) * 19 >> 9;
SkFDot6 twoThird = (a + 6*b - c*15 + d*8) * 19 >> 9;
return SkMax32(SkAbs32(oneThird), SkAbs32(twoThird));
}
bool SkCubicEdge::setCubicWithoutUpdate(const SkPoint pts[4], int shift, bool sortY) {
SkFDot6 x0, y0, x1, y1, x2, y2, x3, y3;
{
#ifdef SK_RASTERIZE_EVEN_ROUNDING
x0 = SkScalarRoundToFDot6(pts[0].fX, shift);
y0 = SkScalarRoundToFDot6(pts[0].fY, shift);
x1 = SkScalarRoundToFDot6(pts[1].fX, shift);
y1 = SkScalarRoundToFDot6(pts[1].fY, shift);
x2 = SkScalarRoundToFDot6(pts[2].fX, shift);
y2 = SkScalarRoundToFDot6(pts[2].fY, shift);
x3 = SkScalarRoundToFDot6(pts[3].fX, shift);
y3 = SkScalarRoundToFDot6(pts[3].fY, shift);
#else
float scale = float(1 << (shift + 6));
x0 = int(pts[0].fX * scale);
y0 = int(pts[0].fY * scale);
x1 = int(pts[1].fX * scale);
y1 = int(pts[1].fY * scale);
x2 = int(pts[2].fX * scale);
y2 = int(pts[2].fY * scale);
x3 = int(pts[3].fX * scale);
y3 = int(pts[3].fY * scale);
#endif
}
int winding = 1;
if (sortY && y0 > y3)
{
SkTSwap(x0, x3);
SkTSwap(x1, x2);
SkTSwap(y0, y3);
SkTSwap(y1, y2);
winding = -1;
}
int top = SkFDot6Round(y0);
int bot = SkFDot6Round(y3);
// are we a zero-height cubic (line)?
if (sortY && top == bot)
return 0;
// compute number of steps needed (1 << shift)
{
// Can't use (center of curve - center of baseline), since center-of-curve
// need not be the max delta from the baseline (it could even be coincident)
// so we try just looking at the two off-curve points
SkFDot6 dx = cubic_delta_from_line(x0, x1, x2, x3);
SkFDot6 dy = cubic_delta_from_line(y0, y1, y2, y3);
// add 1 (by observation)
shift = diff_to_shift(dx, dy) + 1;
}
// need at least 1 subdivision for our bias trick
SkASSERT(shift > 0);
if (shift > MAX_COEFF_SHIFT) {
shift = MAX_COEFF_SHIFT;
}
/* Since our in coming data is initially shifted down by 10 (or 8 in
antialias). That means the most we can shift up is 8. However, we
compute coefficients with a 3*, so the safest upshift is really 6
*/
int upShift = 6; // largest safe value
int downShift = shift + upShift - 10;
if (downShift < 0) {
downShift = 0;
upShift = 10 - shift;
}
fWinding = SkToS8(winding);
fCurveCount = SkToS8(SkLeftShift(-1, shift));
fCurveShift = SkToU8(shift);
fCubicDShift = SkToU8(downShift);
SkFixed B = SkFDot6UpShift(3 * (x1 - x0), upShift);
SkFixed C = SkFDot6UpShift(3 * (x0 - x1 - x1 + x2), upShift);
SkFixed D = SkFDot6UpShift(x3 + 3 * (x1 - x2) - x0, upShift);
fCx = SkFDot6ToFixed(x0);
fCDx = B + (C >> shift) + (D >> 2*shift); // biased by shift
fCDDx = 2*C + (3*D >> (shift - 1)); // biased by 2*shift
fCDDDx = 3*D >> (shift - 1); // biased by 2*shift
B = SkFDot6UpShift(3 * (y1 - y0), upShift);
C = SkFDot6UpShift(3 * (y0 - y1 - y1 + y2), upShift);
D = SkFDot6UpShift(y3 + 3 * (y1 - y2) - y0, upShift);
fCy = SkFDot6ToFixed(y0);
fCDy = B + (C >> shift) + (D >> 2*shift); // biased by shift
fCDDy = 2*C + (3*D >> (shift - 1)); // biased by 2*shift
fCDDDy = 3*D >> (shift - 1); // biased by 2*shift
fCLastX = SkFDot6ToFixed(x3);
fCLastY = SkFDot6ToFixed(y3);
return true;
}
int SkCubicEdge::setCubic(const SkPoint pts[4], int shift) {
if (!this->setCubicWithoutUpdate(pts, shift)) {
return 0;
}
return this->updateCubic();
}
int SkCubicEdge::updateCubic()
{
int success;
int count = fCurveCount;
SkFixed oldx = fCx;
SkFixed oldy = fCy;
SkFixed newx, newy;
const int ddshift = fCurveShift;
const int dshift = fCubicDShift;
SkASSERT(count < 0);
do {
if (++count < 0)
{
newx = oldx + (fCDx >> dshift);
fCDx += fCDDx >> ddshift;
fCDDx += fCDDDx;
newy = oldy + (fCDy >> dshift);
fCDy += fCDDy >> ddshift;
fCDDy += fCDDDy;
}
else // last segment
{
// SkDebugf("LastX err=%d, LastY err=%d\n", (oldx + (fCDx >> shift) - fLastX), (oldy + (fCDy >> shift) - fLastY));
newx = fCLastX;
newy = fCLastY;
}
// we want to say SkASSERT(oldy <= newy), but our finite fixedpoint
// doesn't always achieve that, so we have to explicitly pin it here.
if (newy < oldy) {
newy = oldy;
}
success = this->updateLine(oldx, oldy, newx, newy);
oldx = newx;
oldy = newy;
} while (count < 0 && !success);
fCx = newx;
fCy = newy;
fCurveCount = SkToS8(count);
return success;
}