The Tor Browser: gfx/2d/Path.cpp@b8a032363ba2 (annotated)

gfx/2d/Path.cpp@b8a032363ba2 (annotated)

gfx/2d/Path.cpp

Thu, 22 Jan 2015 13:21:57 +0100

author: Michael Schloh von Bennewitz <michael@schloh.com>
date: Thu, 22 Jan 2015 13:21:57 +0100
branch: TOR_BUG_9701
changeset 15: b8a032363ba2
permissions: -rw-r--r--

Incorporate requested changes from Mozilla in review:
https://bugzilla.mozilla.org/show_bug.cgi?id=1123480#c6

 /* -*- Mode: C++; tab-width: 20; indent-tabs-mode: nil; c-basic-offset: 2 -*-
  * This Source Code Form is subject to the terms of the Mozilla Public
  * License, v. 2.0. If a copy of the MPL was not distributed with this
  * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
 #include "2D.h"
 #include "PathAnalysis.h"
 #include "PathHelpers.h"
 namespace mozilla {
 namespace gfx {
 static float CubicRoot(float aValue) {
   if (aValue < 0.0) {
     return -CubicRoot(-aValue);
   }
   else {
     return powf(aValue, 1.0f / 3.0f);
   }
 }
 struct BezierControlPoints
 {
   BezierControlPoints() {}
   BezierControlPoints(const Point &aCP1, const Point &aCP2,
                       const Point &aCP3, const Point &aCP4)
     : mCP1(aCP1), mCP2(aCP2), mCP3(aCP3), mCP4(aCP4)
   {
   }
   Point mCP1, mCP2, mCP3, mCP4;
 };
 void
 FlattenBezier(const BezierControlPoints &aPoints,
               PathSink *aSink, Float aTolerance);
 Path::Path()
 {
 }
 Path::~Path()
 {
 }
 Float
 Path::ComputeLength()
 {
   EnsureFlattenedPath();
   return mFlattenedPath->ComputeLength();
 }
 Point
 Path::ComputePointAtLength(Float aLength, Point* aTangent)
 {
   EnsureFlattenedPath();
   return mFlattenedPath->ComputePointAtLength(aLength, aTangent);
 }
 void
 Path::EnsureFlattenedPath()
 {
   if (!mFlattenedPath) {
     mFlattenedPath = new FlattenedPath();
     StreamToSink(mFlattenedPath);
   }
 }
 // This is the maximum deviation we allow (with an additional ~20% margin of
 // error) of the approximation from the actual Bezier curve.
 const Float kFlatteningTolerance = 0.0001f;
 void
 FlattenedPath::MoveTo(const Point &aPoint)
 {
   MOZ_ASSERT(!mCalculatedLength);
   FlatPathOp op;
   op.mType = FlatPathOp::OP_MOVETO;
   op.mPoint = aPoint;
   mPathOps.push_back(op);
   mLastMove = aPoint;
 }
 void
 FlattenedPath::LineTo(const Point &aPoint)
 {
   MOZ_ASSERT(!mCalculatedLength);
   FlatPathOp op;
   op.mType = FlatPathOp::OP_LINETO;
   op.mPoint = aPoint;
   mPathOps.push_back(op);
 }
 void
 FlattenedPath::BezierTo(const Point &aCP1,
                         const Point &aCP2,
                         const Point &aCP3)
 {
   MOZ_ASSERT(!mCalculatedLength);
   FlattenBezier(BezierControlPoints(CurrentPoint(), aCP1, aCP2, aCP3), this, kFlatteningTolerance);
 }
 void
 FlattenedPath::QuadraticBezierTo(const Point &aCP1,
                                  const Point &aCP2)
 {
   MOZ_ASSERT(!mCalculatedLength);
   // We need to elevate the degree of this quadratic B�zier to cubic, so we're
   // going to add an intermediate control point, and recompute control point 1.
   // The first and last control points remain the same.
   // This formula can be found on http://fontforge.sourceforge.net/bezier.html
   Point CP0 = CurrentPoint();
   Point CP1 = (CP0 + aCP1 * 2.0) / 3.0;
   Point CP2 = (aCP2 + aCP1 * 2.0) / 3.0;
   Point CP3 = aCP2;
   BezierTo(CP1, CP2, CP3);
 }
 void
 FlattenedPath::Close()
 {
   MOZ_ASSERT(!mCalculatedLength);
   LineTo(mLastMove);
 }
 void
 FlattenedPath::Arc(const Point &aOrigin, float aRadius, float aStartAngle,
                    float aEndAngle, bool aAntiClockwise)
 {
   ArcToBezier(this, aOrigin, Size(aRadius, aRadius), aStartAngle, aEndAngle, aAntiClockwise);
 }
 Float
 FlattenedPath::ComputeLength()
 {
   if (!mCalculatedLength) {
     Point currentPoint;
     for (uint32_t i = 0; i < mPathOps.size(); i++) {
       if (mPathOps[i].mType == FlatPathOp::OP_MOVETO) {
         currentPoint = mPathOps[i].mPoint;
       } else {
         mCachedLength += Distance(currentPoint, mPathOps[i].mPoint);
         currentPoint = mPathOps[i].mPoint;
       }
     }
     mCalculatedLength =  true;
   }
   return mCachedLength;
 }
 Point
 FlattenedPath::ComputePointAtLength(Float aLength, Point *aTangent)
 {
   // We track the last point that -wasn't- in the same place as the current
   // point so if we pass the edge of the path with a bunch of zero length
   // paths we still get the correct tangent vector.
   Point lastPointSinceMove;
   Point currentPoint;
   for (uint32_t i = 0; i < mPathOps.size(); i++) {
     if (mPathOps[i].mType == FlatPathOp::OP_MOVETO) {
       if (Distance(currentPoint, mPathOps[i].mPoint)) {
         lastPointSinceMove = currentPoint;
       }
       currentPoint = mPathOps[i].mPoint;
     } else {
       Float segmentLength = Distance(currentPoint, mPathOps[i].mPoint);
       if (segmentLength) {
         lastPointSinceMove = currentPoint;
         if (segmentLength > aLength) {
           Point currentVector = mPathOps[i].mPoint - currentPoint;
           Point tangent = currentVector / segmentLength;
           if (aTangent) {
             *aTangent = tangent;
           }
           return currentPoint + tangent * aLength;
         }
       }
       aLength -= segmentLength;
       currentPoint = mPathOps[i].mPoint;
     }
   }
   Point currentVector = currentPoint - lastPointSinceMove;
   if (aTangent) {
     if (hypotf(currentVector.x, currentVector.y)) {
       *aTangent = currentVector / hypotf(currentVector.x, currentVector.y);
     } else {
       *aTangent = Point();
     }
   }
   return currentPoint;
 }
 // This function explicitly permits aControlPoints to refer to the same object
 // as either of the other arguments.
 static void
 SplitBezier(const BezierControlPoints &aControlPoints,
             BezierControlPoints *aFirstSegmentControlPoints,
             BezierControlPoints *aSecondSegmentControlPoints,
             Float t)
 {
   MOZ_ASSERT(aSecondSegmentControlPoints);
   *aSecondSegmentControlPoints = aControlPoints;
   Point cp1a = aControlPoints.mCP1 + (aControlPoints.mCP2 - aControlPoints.mCP1) * t;
   Point cp2a = aControlPoints.mCP2 + (aControlPoints.mCP3 - aControlPoints.mCP2) * t;
   Point cp1aa = cp1a + (cp2a - cp1a) * t;
   Point cp3a = aControlPoints.mCP3 + (aControlPoints.mCP4 - aControlPoints.mCP3) * t;
   Point cp2aa = cp2a + (cp3a - cp2a) * t;
   Point cp1aaa = cp1aa + (cp2aa - cp1aa) * t;
   aSecondSegmentControlPoints->mCP4 = aControlPoints.mCP4;
   if(aFirstSegmentControlPoints) {
     aFirstSegmentControlPoints->mCP1 = aControlPoints.mCP1;
     aFirstSegmentControlPoints->mCP2 = cp1a;
     aFirstSegmentControlPoints->mCP3 = cp1aa;
     aFirstSegmentControlPoints->mCP4 = cp1aaa;
   }
   aSecondSegmentControlPoints->mCP1 = cp1aaa;
   aSecondSegmentControlPoints->mCP2 = cp2aa;
   aSecondSegmentControlPoints->mCP3 = cp3a;
 }
 static void
 FlattenBezierCurveSegment(const BezierControlPoints &aControlPoints,
                           PathSink *aSink,
                           Float aTolerance)
 {
   /* The algorithm implemented here is based on:
    * http://cis.usouthal.edu/~hain/general/Publications/Bezier/Bezier%20Offset%20Curves.pdf
    *
    * The basic premise is that for a small t the third order term in the
    * equation of a cubic bezier curve is insignificantly small. This can
    * then be approximated by a quadratic equation for which the maximum
    * difference from a linear approximation can be much more easily determined.
    */
   BezierControlPoints currentCP = aControlPoints;
   Float t = 0;
   while (t < 1.0f) {
     Point cp21 = currentCP.mCP2 - currentCP.mCP3;
     Point cp31 = currentCP.mCP3 - currentCP.mCP1;
     Float s3 = (cp31.x * cp21.y - cp31.y * cp21.x) / hypotf(cp21.x, cp21.y);
     t = 2 * Float(sqrt(aTolerance / (3. * abs(s3))));
     if (t >= 1.0f) {
       aSink->LineTo(aControlPoints.mCP4);
       break;
     }
     Point prevCP2, prevCP3, nextCP1, nextCP2, nextCP3;
     SplitBezier(currentCP, nullptr, &currentCP, t);
     aSink->LineTo(currentCP.mCP1);
   }
 }
 static inline void
 FindInflectionApproximationRange(BezierControlPoints aControlPoints,
                                  Float *aMin, Float *aMax, Float aT,
                                  Float aTolerance)
 {
     SplitBezier(aControlPoints, nullptr, &aControlPoints, aT);
     Point cp21 = aControlPoints.mCP2 - aControlPoints.mCP1;
     Point cp41 = aControlPoints.mCP4 - aControlPoints.mCP1;
     if (cp21.x == 0 && cp21.y == 0) {
       // In this case s3 becomes lim[n->0] (cp41.x * n) / n - (cp41.y * n) / n = cp41.x - cp41.y.
       // Use the absolute value so that Min and Max will correspond with the
       // minimum and maximum of the range.
       *aMin = aT - CubicRoot(abs(aTolerance / (cp41.x - cp41.y)));
       *aMax = aT + CubicRoot(abs(aTolerance / (cp41.x - cp41.y)));
       return;
     }
     Float s3 = (cp41.x * cp21.y - cp41.y * cp21.x) / hypotf(cp21.x, cp21.y);
     if (s3 == 0) {
       // This means within the precision we have it can be approximated
       // infinitely by a linear segment. Deal with this by specifying the
       // approximation range as extending beyond the entire curve.
       *aMin = -1.0f;
       *aMax = 2.0f;
       return;
     }
     Float tf = CubicRoot(abs(aTolerance / s3));
     *aMin = aT - tf * (1 - aT);
     *aMax = aT + tf * (1 - aT);
 }
 /* Find the inflection points of a bezier curve. Will return false if the
  * curve is degenerate in such a way that it is best approximated by a straight
  * line.
  *
  * The below algorithm was written by Jeff Muizelaar <jmuizelaar@mozilla.com>, explanation follows:
  *
  * The lower inflection point is returned in aT1, the higher one in aT2. In the
  * case of a single inflection point this will be in aT1.
  *
  * The method is inspired by the algorithm in "analysis of in?ection points for planar cubic bezier curve"
  *
  * Here are some differences between this algorithm and versions discussed elsewhere in the literature:
  *
  * zhang et. al compute a0, d0 and e0 incrementally using the follow formula:
  *
  * Point a0 = CP2 - CP1
  * Point a1 = CP3 - CP2
  * Point a2 = CP4 - CP1
  *
  * Point d0 = a1 - a0
  * Point d1 = a2 - a1
  * Point e0 = d1 - d0
  *
  * this avoids any multiplications and may or may not be faster than the approach take below.
  *
  * "fast, precise flattening of cubic bezier path and ofset curves" by hain et. al
  * Point a = CP1 + 3 * CP2 - 3 * CP3 + CP4
  * Point b = 3 * CP1 - 6 * CP2 + 3 * CP3
  * Point c = -3 * CP1 + 3 * CP2
  * Point d = CP1
  * the a, b, c, d can be expressed in terms of a0, d0 and e0 defined above as:
  * c = 3 * a0
  * b = 3 * d0
  * a = e0
  *
  *
  * a = 3a = a.y * b.x - a.x * b.y
  * b = 3b = a.y * c.x - a.x * c.y
  * c = 9c = b.y * c.x - b.x * c.y
  *
  * The additional multiples of 3 cancel each other out as show below:
  *
  * x = (-b + sqrt(b * b - 4 * a * c)) / (2 * a)
  * x = (-3 * b + sqrt(3 * b * 3 * b - 4 * a * 3 * 9 * c / 3)) / (2 * 3 * a)
  * x = 3 * (-b + sqrt(b * b - 4 * a * c)) / (2 * 3 * a)
  * x = (-b + sqrt(b * b - 4 * a * c)) / (2 * a)
  *
  * I haven't looked into whether the formulation of the quadratic formula in
  * hain has any numerical advantages over the one used below.
  */
 static inline void
 FindInflectionPoints(const BezierControlPoints &aControlPoints,
                      Float *aT1, Float *aT2, uint32_t *aCount)
 {
   // Find inflection points.
   // See www.faculty.idc.ac.il/arik/quality/appendixa.html for an explanation
   // of this approach.
   Point A = aControlPoints.mCP2 - aControlPoints.mCP1;
   Point B = aControlPoints.mCP3 - (aControlPoints.mCP2 * 2) + aControlPoints.mCP1;
   Point C = aControlPoints.mCP4 - (aControlPoints.mCP3 * 3) + (aControlPoints.mCP2 * 3) - aControlPoints.mCP1;
   Float a = Float(B.x) * C.y - Float(B.y) * C.x;
   Float b = Float(A.x) * C.y - Float(A.y) * C.x;
   Float c = Float(A.x) * B.y - Float(A.y) * B.x;
   if (a == 0) {
     // Not a quadratic equation.
     if (b == 0) {
       // Instead of a linear acceleration change we have a constant
       // acceleration change. This means the equation has no solution
       // and there are no inflection points, unless the constant is 0.
       // In that case the curve is a straight line, but we'll let
       // FlattenBezierCurveSegment deal with this.
       *aCount = 0;
       return;
     }
     *aT1 = -c / b;
     *aCount = 1;
     return;
   } else {
     Float discriminant = b * b - 4 * a * c;
     if (discriminant < 0) {
       // No inflection points.
       *aCount = 0;
     } else if (discriminant == 0) {
       *aCount = 1;
       *aT1 = -b / (2 * a);
     } else {
       /* Use the following formula for computing the roots:
        *
        * q = -1/2 * (b + sign(b) * sqrt(b^2 - 4ac))
        * t1 = q / a
        * t2 = c / q
        */
       Float q = sqrtf(discriminant);
       if (b < 0) {
         q = b - q;
       } else {
         q = b + q;
       }
       q *= Float(-1./2);
       *aT1 = q / a;
       *aT2 = c / q;
       if (*aT1 > *aT2) {
         std::swap(*aT1, *aT2);
       }
       *aCount = 2;
     }
   }
   return;
 }
 void
 FlattenBezier(const BezierControlPoints &aControlPoints,
               PathSink *aSink, Float aTolerance)
 {
   Float t1;
   Float t2;
   uint32_t count;
   FindInflectionPoints(aControlPoints, &t1, &t2, &count);
   // Check that at least one of the inflection points is inside [0..1]
   if (count == 0 || ((t1 < 0 || t1 > 1.0) && ((t2 < 0 || t2 > 1.0) || count == 1)) ) {
     FlattenBezierCurveSegment(aControlPoints, aSink, aTolerance);
     return;
   }
   Float t1min = t1, t1max = t1, t2min = t2, t2max = t2;
   BezierControlPoints remainingCP = aControlPoints;
   // For both inflection points, calulate the range where they can be linearly
   // approximated if they are positioned within [0,1]
   if (count > 0 && t1 >= 0 && t1 < 1.0) {
     FindInflectionApproximationRange(aControlPoints, &t1min, &t1max, t1, aTolerance);
   }
   if (count > 1 && t2 >= 0 && t2 < 1.0) {
     FindInflectionApproximationRange(aControlPoints, &t2min, &t2max, t2, aTolerance);
   }
   BezierControlPoints nextCPs = aControlPoints;
   BezierControlPoints prevCPs;
   // Process ranges. [t1min, t1max] and [t2min, t2max] are approximated by line
   // segments.
   if (t1min > 0) {
     // Flatten the Bezier up until the first inflection point's approximation
     // point.
     SplitBezier(aControlPoints, &prevCPs,
                 &remainingCP, t1min);
     FlattenBezierCurveSegment(prevCPs, aSink, aTolerance);
   }
   if (t1max >= 0 && t1max < 1.0 && (count == 1 || t2min > t1max)) {
     // The second inflection point's approximation range begins after the end
     // of the first, approximate the first inflection point by a line and
     // subsequently flatten up until the end or the next inflection point.
     SplitBezier(aControlPoints, nullptr, &nextCPs, t1max);
     aSink->LineTo(nextCPs.mCP1);
     if (count == 1 || (count > 1 && t2min >= 1.0)) {
       // No more inflection points to deal with, flatten the rest of the curve.
       FlattenBezierCurveSegment(nextCPs, aSink, aTolerance);
     }
   } else if (count > 1 && t2min > 1.0) {
     // We've already concluded t2min <= t1max, so if this is true the
     // approximation range for the first inflection point runs past the
     // end of the curve, draw a line to the end and we're done.
     aSink->LineTo(aControlPoints.mCP4);
     return;
   }
   if (count > 1 && t2min < 1.0 && t2max > 0) {
     if (t2min > 0 && t2min < t1max) {
       // In this case the t2 approximation range starts inside the t1
       // approximation range.
       SplitBezier(aControlPoints, nullptr, &nextCPs, t1max);
       aSink->LineTo(nextCPs.mCP1);
     } else if (t2min > 0 && t1max > 0) {
       SplitBezier(aControlPoints, nullptr, &nextCPs, t1max);
       // Find a control points describing the portion of the curve between t1max and t2min.
       Float t2mina = (t2min - t1max) / (1 - t1max);
       SplitBezier(nextCPs, &prevCPs, &nextCPs, t2mina);
       FlattenBezierCurveSegment(prevCPs, aSink, aTolerance);
     } else if (t2min > 0) {
       // We have nothing interesting before t2min, find that bit and flatten it.
       SplitBezier(aControlPoints, &prevCPs, &nextCPs, t2min);
       FlattenBezierCurveSegment(prevCPs, aSink, aTolerance);
     }
     if (t2max < 1.0) {
       // Flatten the portion of the curve after t2max
       SplitBezier(aControlPoints, nullptr, &nextCPs, t2max);
       // Draw a line to the start, this is the approximation between t2min and
       // t2max.
       aSink->LineTo(nextCPs.mCP1);
       FlattenBezierCurveSegment(nextCPs, aSink, aTolerance);
     } else {
       // Our approximation range extends beyond the end of the curve.
       aSink->LineTo(aControlPoints.mCP4);
       return;
     }
   }
 }
 }
 }

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gfx/2d/Path.cpp@b8a032363ba2 (annotated)

gfx/2d/Path.cpp