SVGArcConverter.cpp (5294B)
1 /* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*- */ 2 /* vim: set ts=8 sts=2 et sw=2 tw=80: */ 3 /* This Source Code Form is subject to the terms of the Mozilla Public 4 * License, v. 2.0. If a copy of the MPL was not distributed with this 5 * file, You can obtain one at http://mozilla.org/MPL/2.0/. */ 6 7 #include "SVGArcConverter.h" 8 9 using namespace mozilla::gfx; 10 11 namespace mozilla { 12 13 //----------------------------------------------------------------------- 14 15 static double CalcVectorAngle(double ux, double uy, double vx, double vy) { 16 double ta = atan2(uy, ux); 17 double tb = atan2(vy, vx); 18 if (tb >= ta) return tb - ta; 19 return 2 * M_PI - (ta - tb); 20 } 21 22 SVGArcConverter::SVGArcConverter(const Point& from, const Point& to, 23 const Point& radii, double angle, 24 bool largeArcFlag, bool sweepFlag) { 25 MOZ_ASSERT(radii.x != 0.0f && radii.y != 0.0f, "Bad radii"); 26 27 const double radPerDeg = M_PI / 180.0; 28 mTo = to; 29 30 if (from == to) { 31 mNumSegs = 0; 32 return; 33 } 34 35 // Convert to center parameterization as shown in 36 // http://www.w3.org/TR/SVG/implnote.html 37 mRx = fabs(radii.x); 38 mRy = fabs(radii.y); 39 40 mSinPhi = sin(angle * radPerDeg); 41 mCosPhi = cos(angle * radPerDeg); 42 43 double x1dash = 44 mCosPhi * (from.x - to.x) / 2.0 + mSinPhi * (from.y - to.y) / 2.0; 45 double y1dash = 46 -mSinPhi * (from.x - to.x) / 2.0 + mCosPhi * (from.y - to.y) / 2.0; 47 48 double root; 49 double numerator = mRx * mRx * mRy * mRy - mRx * mRx * y1dash * y1dash - 50 mRy * mRy * x1dash * x1dash; 51 52 if (numerator < 0.0) { 53 // If mRx , mRy and are such that there is no solution (basically, 54 // the ellipse is not big enough to reach from 'from' to 'to' 55 // then the ellipse is scaled up uniformly until there is 56 // exactly one solution (until the ellipse is just big enough). 57 58 // -> find factor s, such that numerator' with mRx'=s*mRx and 59 // mRy'=s*mRy becomes 0 : 60 double s = sqrt(1.0 - numerator / (mRx * mRx * mRy * mRy)); 61 62 mRx *= s; 63 mRy *= s; 64 root = 0.0; 65 66 } else { 67 root = (largeArcFlag == sweepFlag ? -1.0 : 1.0) * 68 sqrt(numerator / 69 (mRx * mRx * y1dash * y1dash + mRy * mRy * x1dash * x1dash)); 70 } 71 72 double cxdash = root * mRx * y1dash / mRy; 73 double cydash = -root * mRy * x1dash / mRx; 74 75 mC.x = mCosPhi * cxdash - mSinPhi * cydash + (from.x + to.x) / 2.0; 76 mC.y = mSinPhi * cxdash + mCosPhi * cydash + (from.y + to.y) / 2.0; 77 mTheta = CalcVectorAngle(1.0, 0.0, (x1dash - cxdash) / mRx, 78 (y1dash - cydash) / mRy); 79 double dtheta = 80 CalcVectorAngle((x1dash - cxdash) / mRx, (y1dash - cydash) / mRy, 81 (-x1dash - cxdash) / mRx, (-y1dash - cydash) / mRy); 82 if (!sweepFlag && dtheta > 0) 83 dtheta -= 2.0 * M_PI; 84 else if (sweepFlag && dtheta < 0) 85 dtheta += 2.0 * M_PI; 86 87 // Convert into cubic bezier segments <= 90deg 88 mNumSegs = static_cast<int>(ceil(fabs(dtheta / (M_PI / 2.0)))); 89 mDelta = dtheta / mNumSegs; 90 mT = 8.0 / 3.0 * sin(mDelta / 4.0) * sin(mDelta / 4.0) / sin(mDelta / 2.0); 91 92 mFrom = from; 93 94 if (fabs(dtheta) < 1e-8) { 95 // If the angle dtheta is extremely small, then the resulting portion of the 96 // arc is indistinguishable from a line. 97 // In this situation we are likely dealing with quantities that are large or 98 // small enough (depending on what inputs caused the dtheta to end up this 99 // way) to hit floating point precision issues, so it is safer to special 100 // case this. The threshold may need some adjustments. For reference, skia 101 // handles this case the same way: 102 // https://searchfox.org/firefox-main/rev/d0ff31da7cb418d2d86b0d83fecd7114395e5d46/gfx/skia/skia/src/core/SkPath.cpp#1323 103 mFallBackToSingleLine = true; 104 mNumSegs = 1; 105 } 106 } 107 108 bool SVGArcConverter::GetNextSegment(Point* cp1, Point* cp2, Point* to) { 109 if (mSegIndex == mNumSegs) { 110 return false; 111 } 112 113 if (mFallBackToSingleLine) { 114 Point ctrl = (mFrom + mTo) * 0.5; 115 *cp1 = ctrl; 116 *cp2 = ctrl; 117 *to = mTo; 118 mSegIndex = 1; 119 mFallBackToSingleLine = false; 120 return true; 121 } 122 123 double cosTheta1 = cos(mTheta); 124 double sinTheta1 = sin(mTheta); 125 double theta2 = mTheta + mDelta; 126 double cosTheta2 = cos(theta2); 127 double sinTheta2 = sin(theta2); 128 129 if (mSegIndex + 1 == mNumSegs) { 130 // Always set the last segment's `to` endpoint to the exact end of the 131 // arc. This prevents precision issues from "leaking" into the next path 132 // element. 133 *to = mTo; 134 } else { 135 // a) calculate endpoint of the segment: 136 to->x = mCosPhi * mRx * cosTheta2 - mSinPhi * mRy * sinTheta2 + mC.x; 137 to->y = mSinPhi * mRx * cosTheta2 + mCosPhi * mRy * sinTheta2 + mC.y; 138 } 139 140 // b) calculate gradients at start/end points of segment: 141 cp1->x = 142 mFrom.x + mT * (-mCosPhi * mRx * sinTheta1 - mSinPhi * mRy * cosTheta1); 143 cp1->y = 144 mFrom.y + mT * (-mSinPhi * mRx * sinTheta1 + mCosPhi * mRy * cosTheta1); 145 146 cp2->x = to->x + mT * (mCosPhi * mRx * sinTheta2 + mSinPhi * mRy * cosTheta2); 147 cp2->y = to->y + mT * (mSinPhi * mRx * sinTheta2 - mCosPhi * mRy * cosTheta2); 148 149 // do next segment 150 mTheta = theta2; 151 mFrom = *to; 152 ++mSegIndex; 153 154 return true; 155 } 156 157 } // namespace mozilla