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- /*
- * 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 "src/core/SkEdge.h"
- #include "include/private/SkTo.h"
- #include "src/core/SkFDot6.h"
- #include "src/core/SkMathPriv.h"
- #include <utility>
- /*
- 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) {
- using std::swap;
- swap(x0, x1);
- swap(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.
- dist = (dist + (1 << 4)) >> (3 + shiftAA);
- // 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)
- {
- using std::swap;
- swap(x0, x2);
- swap(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)
- {
- using std::swap;
- swap(x0, x3);
- swap(x1, x2);
- swap(y0, y3);
- swap(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;
- }
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