/* libs/graphics/sgl/SkEdge.cpp ** ** Copyright 2006, The Android Open Source Project ** ** Licensed under the Apache License, Version 2.0 (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.apache.org/licenses/LICENSE-2.0 ** ** Unless required by applicable law or agreed to in writing, software ** distributed under the License is distributed on an "AS IS" BASIS, ** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. ** See the License for the specific language governing permissions and ** limitations under the License. */ #include "SkEdge.h" #include "SkFDot6.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). */ ///////////////////////////////////////////////////////////////////////// int SkEdge::setLine(const SkPoint& p0, const SkPoint& p1, const SkIRect* clip, int shift) { SkFDot6 x0, y0, x1, y1; { #ifdef SK_SCALAR_IS_FLOAT 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); #else shift = 10 - shift; x0 = p0.fX >> shift; y0 = p0.fY >> shift; x1 = p1.fX >> shift; y1 = p1.fY >> shift; #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 (NULL != clip && (top >= clip->fBottom || bot <= clip->fTop)) { return 0; } SkFixed slope = SkFDot6Div(x1 - x0, y1 - y0); fX = SkFDot6ToFixed(x0 + SkFixedMul(slope, (32 - y0) & 63)); // + 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); fX = SkFDot6ToFixed(x0 + SkFixedMul(slope, (32 - y0) & 63)); // + 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) { // 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 5 should give us 1/2 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 dist = (dist + (1 << 4)) >> 5; // each subdivision (shift value) cuts this dist (error) by 1/4 return (32 - SkCLZ(dist)) >> 1; } int SkQuadraticEdge::setQuadratic(const SkPoint pts[3], int shift) { SkFDot6 x0, y0, x1, y1, x2, y2; { #ifdef SK_SCALAR_IS_FLOAT 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); #else shift = 10 - shift; x0 = pts[0].fX >> shift; y0 = pts[0].fY >> shift; x1 = pts[1].fX >> shift; y1 = pts[1].fY >> shift; x2 = pts[2].fX >> shift; y2 = pts[2].fY >> shift; #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 = ((x1 << 1) - x0 - x2) >> 2; SkFDot6 dy = ((y1 << 1) - y0 - y2) >> 2; shift = diff_to_shift(dx, dy); 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); fCurveShift = SkToU8(shift); //fCubicDShift only set for cubics fCurveCount = SkToS8(1 << shift); SkFixed A = SkFDot6ToFixed(x0 - x1 - x1 + x2); SkFixed B = SkFDot6ToFixed(x1 - x0 + x1 - x0); fQx = SkFDot6ToFixed(x0); fQDx = B + (A >> shift); // biased by shift fQDDx = A >> (shift - 1); // biased by shift A = SkFDot6ToFixed(y0 - y1 - y1 + y2); B = SkFDot6ToFixed(y1 - y0 + y1 - y0); fQy = SkFDot6ToFixed(y0); fQDy = B + (A >> shift); // biased by shift fQDDy = A >> (shift - 1); // biased by shift fQLastX = SkFDot6ToFixed(x2); fQLastY = SkFDot6ToFixed(y2); 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 = SkToS16(count); return success; } ///////////////////////////////////////////////////////////////////////// static inline int SkFDot6UpShift(SkFDot6 x, int upShift) { SkASSERT((x << upShift >> upShift) == x); return 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) { SkFDot6 oneThird = ((a << 3) - ((b << 4) - b) + 6*c + d) * 19 >> 9; SkFDot6 twoThird = (a + 6*b - ((c << 4) - c) + (d << 3)) * 19 >> 9; return SkMax32(SkAbs32(oneThird), SkAbs32(twoThird)); } int SkCubicEdge::setCubic(const SkPoint pts[4], const SkIRect* clip, int shift) { SkFDot6 x0, y0, x1, y1, x2, y2, x3, y3; { #ifdef SK_SCALAR_IS_FLOAT 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); #else shift = 10 - shift; x0 = pts[0].fX >> shift; y0 = pts[0].fY >> shift; x1 = pts[1].fX >> shift; y1 = pts[1].fY >> shift; x2 = pts[2].fX >> shift; y2 = pts[2].fY >> shift; x3 = pts[3].fX >> shift; y3 = pts[3].fY >> shift; #endif } int winding = 1; if (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 (top == bot) return 0; // are we completely above or below the clip? if (clip && (top >= clip->fBottom || bot <= clip->fTop)) 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(-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); if (clip) { do { for (;!this->updateCubic();) ; } while (!this->intersectsClip(*clip)); this->chopLineWithClip(*clip); return 1; } 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; } success = this->updateLine(oldx, oldy, newx, newy); oldx = newx; oldy = newy; } while (count < 0 && !success); fCx = newx; fCy = newy; fCurveCount = SkToS16(count); return success; }