gecko/dom/svg/SVGPathData.cpp

/* -*- Mode: C++; tab-width: 2; 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 "SVGPathData.h"

#include "gfx2DGlue.h"
#include "gfxPlatform.h"
#include "mozilla/gfx/2D.h"
#include "mozilla/gfx/Types.h"
#include "mozilla/gfx/Point.h"
#include "mozilla/RefPtr.h"
#include "nsError.h"
#include "nsString.h"
#include "nsSVGPathDataParser.h"
#include "nsSVGPathGeometryElement.h" // for nsSVGMark
#include <stdarg.h>
#include "nsStyleConsts.h"
#include "SVGContentUtils.h"
#include "SVGPathSegUtils.h"
#include <algorithm>

using namespace mozilla;
using namespace mozilla::gfx;

static bool IsMoveto(uint16_t aSegType)
{
  return aSegType == PATHSEG_MOVETO_ABS ||
         aSegType == PATHSEG_MOVETO_REL;
}

nsresult
SVGPathData::CopyFrom(const SVGPathData& rhs)
{
  if (!mData.SetCapacity(rhs.mData.Length())) {
    // Yes, we do want fallible alloc here
    return NS_ERROR_OUT_OF_MEMORY;
  }
  mData = rhs.mData;
  return NS_OK;
}

void
SVGPathData::GetValueAsString(nsAString& aValue) const
{
  // we need this function in DidChangePathSegList
  aValue.Truncate();
  if (!Length()) {
    return;
  }
  uint32_t i = 0;
  for (;;) {
    nsAutoString segAsString;
    SVGPathSegUtils::GetValueAsString(&mData[i], segAsString);
    // We ignore OOM, since it's not useful for us to return an error.
    aValue.Append(segAsString);
    i += 1 + SVGPathSegUtils::ArgCountForType(mData[i]);
    if (i >= mData.Length()) {
      NS_ABORT_IF_FALSE(i == mData.Length(), "Very, very bad - mData corrupt");
      return;
    }
    aValue.Append(' ');
  }
}

nsresult
SVGPathData::SetValueFromString(const nsAString& aValue)
{
  // We don't use a temp variable since the spec says to parse everything up to
  // the first error. We still return any error though so that callers know if
  // there's a problem.

  nsSVGPathDataParser pathParser(aValue, this);
  return pathParser.Parse() ? NS_OK : NS_ERROR_DOM_SYNTAX_ERR;
}

nsresult
SVGPathData::AppendSeg(uint32_t aType, ...)
{
  uint32_t oldLength = mData.Length();
  uint32_t newLength = oldLength + 1 + SVGPathSegUtils::ArgCountForType(aType);
  if (!mData.SetLength(newLength)) {
    return NS_ERROR_OUT_OF_MEMORY;
  }

  mData[oldLength] = SVGPathSegUtils::EncodeType(aType);
  va_list args;
  va_start(args, aType);
  for (uint32_t i = oldLength + 1; i < newLength; ++i) {
    // NOTE! 'float' is promoted to 'double' when passed through '...'!
    mData[i] = float(va_arg(args, double));
  }
  va_end(args);
  return NS_OK;
}

float
SVGPathData::GetPathLength() const
{
  SVGPathTraversalState state;

  uint32_t i = 0;
  while (i < mData.Length()) {
    SVGPathSegUtils::TraversePathSegment(&mData[i], state);
    i += 1 + SVGPathSegUtils::ArgCountForType(mData[i]);
  }

  NS_ABORT_IF_FALSE(i == mData.Length(), "Very, very bad - mData corrupt");

  return state.length;
}

#ifdef DEBUG
uint32_t
SVGPathData::CountItems() const
{
  uint32_t i = 0, count = 0;

  while (i < mData.Length()) {
    i += 1 + SVGPathSegUtils::ArgCountForType(mData[i]);
    count++;
  }

  NS_ABORT_IF_FALSE(i == mData.Length(), "Very, very bad - mData corrupt");

  return count;
}
#endif

bool
SVGPathData::GetSegmentLengths(nsTArray<double> *aLengths) const
{
  aLengths->Clear();
  SVGPathTraversalState state;

  uint32_t i = 0;
  while (i < mData.Length()) {
    state.length = 0.0;
    SVGPathSegUtils::TraversePathSegment(&mData[i], state);
    if (!aLengths->AppendElement(state.length)) {
      aLengths->Clear();
      return false;
    }
    i += 1 + SVGPathSegUtils::ArgCountForType(mData[i]);
  }

  NS_ABORT_IF_FALSE(i == mData.Length(), "Very, very bad - mData corrupt");

  return true;
}

bool
SVGPathData::GetDistancesFromOriginToEndsOfVisibleSegments(FallibleTArray<double> *aOutput) const
{
  SVGPathTraversalState state;

  aOutput->Clear();

  uint32_t i = 0;
  while (i < mData.Length()) {
    uint32_t segType = SVGPathSegUtils::DecodeType(mData[i]);
    SVGPathSegUtils::TraversePathSegment(&mData[i], state);

    // We skip all moveto commands except an initial moveto. See the text 'A
    // "move to" command does not count as an additional point when dividing up
    // the duration...':
    //
    // http://www.w3.org/TR/SVG11/animate.html#AnimateMotionElement
    //
    // This is important in the non-default case of calcMode="linear". In
    // this case an equal amount of time is spent on each path segment,
    // except on moveto segments which are jumped over immediately.

    if (i == 0 || (segType != PATHSEG_MOVETO_ABS &&
                   segType != PATHSEG_MOVETO_REL)) {
      if (!aOutput->AppendElement(state.length)) {
        return false;
      }
    }
    i += 1 + SVGPathSegUtils::ArgCountForType(segType);
  }

  NS_ABORT_IF_FALSE(i == mData.Length(), "Very, very bad - mData corrupt?");

  return true;
}

uint32_t
SVGPathData::GetPathSegAtLength(float aDistance) const
{
  // TODO [SVGWG issue] get specified what happen if 'aDistance' < 0, or
  // 'aDistance' > the length of the path, or the seg list is empty.
  // Return -1? Throwing would better help authors avoid tricky bugs (DOM
  // could do that if we return -1).

  uint32_t i = 0, segIndex = 0;
  SVGPathTraversalState state;

  while (i < mData.Length()) {
    SVGPathSegUtils::TraversePathSegment(&mData[i], state);
    if (state.length >= aDistance) {
      return segIndex;
    }
    i += 1 + SVGPathSegUtils::ArgCountForType(mData[i]);
    segIndex++;
  }

  NS_ABORT_IF_FALSE(i == mData.Length(), "Very, very bad - mData corrupt");

  return std::max(0U, segIndex - 1); // -1 because while loop takes us 1 too far
}

/**
 * The SVG spec says we have to paint stroke caps for zero length subpaths:
 *
 *   http://www.w3.org/TR/SVG11/implnote.html#PathElementImplementationNotes
 *
 * Cairo only does this for |stroke-linecap: round| and not for
 * |stroke-linecap: square| (since that's what Adobe Acrobat has always done).
 * Most likely the other backends that DrawTarget uses have the same behavior.
 *
 * To help us conform to the SVG spec we have this helper function to draw an
 * approximation of square caps for zero length subpaths. It does this by
 * inserting a subpath containing a single user space axis aligned straight
 * line that is as small as it can be while minimizing the risk of it being
 * thrown away by the DrawTarget's backend for being too small to affect
 * rendering. The idea is that we'll then get stroke caps drawn for this axis
 * aligned line, creating an axis aligned rectangle that approximates the
 * square that would ideally be drawn.
 *
 * Since we don't have any information about transforms from user space to
 * device space, we choose the length of the small line that we insert by
 * making it a small percentage of the stroke width of the path. This should
 * hopefully allow us to make the line as long as possible (to avoid rounding
 * issues in the backend resulting in the backend seeing it as having zero
 * length) while still avoiding the small rectangle being noticably different
 * from a square.
 *
 * Note that this function inserts a subpath into the current gfx path that
 * will be present during both fill and stroke operations.
 */
static void
ApproximateZeroLengthSubpathSquareCaps(PathBuilder* aPB,
                                       const Point& aPoint,
                                       Float aStrokeWidth)
{
  // Note that caps are proportional to stroke width, so if stroke width is
  // zero it's actually fine for |tinyLength| below to end up being zero.
  // However, it would be a waste to inserting a LineTo in that case, so better
  // not to.
  MOZ_ASSERT(aStrokeWidth > 0.0f,
             "Make the caller check for this, or check it here");

  // The fraction of the stroke width that we choose for the length of the
  // line is rather arbitrary, other than being chosen to meet the requirements
  // described in the comment above.

  Float tinyLength = aStrokeWidth / 512;

  aPB->LineTo(aPoint + Point(tinyLength, 0));
  aPB->MoveTo(aPoint);
}

#define MAYBE_APPROXIMATE_ZERO_LENGTH_SUBPATH_SQUARE_CAPS_TO_DT               \
  do {                                                                        \
    if (!subpathHasLength && hasLineCaps && aStrokeWidth > 0 &&               \
        subpathContainsNonMoveTo &&                                           \
        SVGPathSegUtils::IsValidType(prevSegType) &&                          \
        (!IsMoveto(prevSegType) || segType == PATHSEG_CLOSEPATH)) {           \
      ApproximateZeroLengthSubpathSquareCaps(builder, segStart, aStrokeWidth);\
    }                                                                         \
  } while(0)

TemporaryRef<Path>
SVGPathData::BuildPath(PathBuilder* builder,
                       uint8_t aStrokeLineCap,
                       Float aStrokeWidth) const
{
  if (mData.IsEmpty() || !IsMoveto(SVGPathSegUtils::DecodeType(mData[0]))) {
    return nullptr; // paths without an initial moveto are invalid
  }

  bool hasLineCaps = aStrokeLineCap != NS_STYLE_STROKE_LINECAP_BUTT;
  bool subpathHasLength = false;  // visual length
  bool subpathContainsNonMoveTo = false;

  uint32_t segType     = PATHSEG_UNKNOWN;
  uint32_t prevSegType = PATHSEG_UNKNOWN;
  Point pathStart(0.0, 0.0); // start point of [sub]path
  Point segStart(0.0, 0.0);
  Point segEnd;
  Point cp1, cp2;            // previous bezier's control points
  Point tcp1, tcp2;          // temporaries

  // Regarding cp1 and cp2: If the previous segment was a cubic bezier curve,
  // then cp2 is its second control point. If the previous segment was a
  // quadratic curve, then cp1 is its (only) control point.

  uint32_t i = 0;
  while (i < mData.Length()) {
    segType = SVGPathSegUtils::DecodeType(mData[i++]);
    uint32_t argCount = SVGPathSegUtils::ArgCountForType(segType);

    switch (segType)
    {
    case PATHSEG_CLOSEPATH:
      // set this early to allow drawing of square caps for "M{x},{y} Z":
      subpathContainsNonMoveTo = true;
      MAYBE_APPROXIMATE_ZERO_LENGTH_SUBPATH_SQUARE_CAPS_TO_DT;
      segEnd = pathStart;
      builder->Close();
      break;

    case PATHSEG_MOVETO_ABS:
      MAYBE_APPROXIMATE_ZERO_LENGTH_SUBPATH_SQUARE_CAPS_TO_DT;
      pathStart = segEnd = Point(mData[i], mData[i+1]);
      builder->MoveTo(segEnd);
      subpathHasLength = false;
      break;

    case PATHSEG_MOVETO_REL:
      MAYBE_APPROXIMATE_ZERO_LENGTH_SUBPATH_SQUARE_CAPS_TO_DT;
      pathStart = segEnd = segStart + Point(mData[i], mData[i+1]);
      builder->MoveTo(segEnd);
      subpathHasLength = false;
      break;

    case PATHSEG_LINETO_ABS:
      segEnd = Point(mData[i], mData[i+1]);
      if (segEnd != segStart) {
        subpathHasLength = true;
        builder->LineTo(segEnd);
      }
      break;

    case PATHSEG_LINETO_REL:
      segEnd = segStart + Point(mData[i], mData[i+1]);
      if (segEnd != segStart) {
        subpathHasLength = true;
        builder->LineTo(segEnd);
      }
      break;

    case PATHSEG_CURVETO_CUBIC_ABS:
      cp1 = Point(mData[i], mData[i+1]);
      cp2 = Point(mData[i+2], mData[i+3]);
      segEnd = Point(mData[i+4], mData[i+5]);
      if (segEnd != segStart || segEnd != cp1 || segEnd != cp2) {
        subpathHasLength = true;
        builder->BezierTo(cp1, cp2, segEnd);
      }
      break;

    case PATHSEG_CURVETO_CUBIC_REL:
      cp1 = segStart + Point(mData[i], mData[i+1]);
      cp2 = segStart + Point(mData[i+2], mData[i+3]);
      segEnd = segStart + Point(mData[i+4], mData[i+5]);
      if (segEnd != segStart || segEnd != cp1 || segEnd != cp2) {
        subpathHasLength = true;
        builder->BezierTo(cp1, cp2, segEnd);
      }
      break;

    case PATHSEG_CURVETO_QUADRATIC_ABS:
      cp1 = Point(mData[i], mData[i+1]);
      // Convert quadratic curve to cubic curve:
      tcp1 = segStart + (cp1 - segStart) * 2 / 3;
      segEnd = Point(mData[i+2], mData[i+3]); // set before setting tcp2!
      tcp2 = cp1 + (segEnd - cp1) / 3;
      if (segEnd != segStart || segEnd != cp1) {
        subpathHasLength = true;
        builder->BezierTo(tcp1, tcp2, segEnd);
      }
      break;

    case PATHSEG_CURVETO_QUADRATIC_REL:
      cp1 = segStart + Point(mData[i], mData[i+1]);
      // Convert quadratic curve to cubic curve:
      tcp1 = segStart + (cp1 - segStart) * 2 / 3;
      segEnd = segStart + Point(mData[i+2], mData[i+3]); // set before setting tcp2!
      tcp2 = cp1 + (segEnd - cp1) / 3;
      if (segEnd != segStart || segEnd != cp1) {
        subpathHasLength = true;
        builder->BezierTo(tcp1, tcp2, segEnd);
      }
      break;

    case PATHSEG_ARC_ABS:
    case PATHSEG_ARC_REL:
    {
      Point radii(mData[i], mData[i+1]);
      segEnd = Point(mData[i+5], mData[i+6]);
      if (segType == PATHSEG_ARC_REL) {
        segEnd += segStart;
      }
      if (segEnd != segStart) {
        subpathHasLength = true;
        if (radii.x == 0.0f || radii.y == 0.0f) {
          builder->LineTo(segEnd);
        } else {
          nsSVGArcConverter converter(segStart, segEnd, radii, mData[i+2],
                                      mData[i+3] != 0, mData[i+4] != 0);
          while (converter.GetNextSegment(&cp1, &cp2, &segEnd)) {
            builder->BezierTo(cp1, cp2, segEnd);
          }
        }
      }
      break;
    }

    case PATHSEG_LINETO_HORIZONTAL_ABS:
      segEnd = Point(mData[i], segStart.y);
      if (segEnd != segStart) {
        subpathHasLength = true;
        builder->LineTo(segEnd);
      }
      break;

    case PATHSEG_LINETO_HORIZONTAL_REL:
      segEnd = segStart + Point(mData[i], 0.0f);
      if (segEnd != segStart) {
        subpathHasLength = true;
        builder->LineTo(segEnd);
      }
      break;

    case PATHSEG_LINETO_VERTICAL_ABS:
      segEnd = Point(segStart.x, mData[i]);
      if (segEnd != segStart) {
        subpathHasLength = true;
        builder->LineTo(segEnd);
      }
      break;

    case PATHSEG_LINETO_VERTICAL_REL:
      segEnd = segStart + Point(0.0f, mData[i]);
      if (segEnd != segStart) {
        subpathHasLength = true;
        builder->LineTo(segEnd);
      }
      break;

    case PATHSEG_CURVETO_CUBIC_SMOOTH_ABS:
      cp1 = SVGPathSegUtils::IsCubicType(prevSegType) ? segStart * 2 - cp2 : segStart;
      cp2 = Point(mData[i],   mData[i+1]);
      segEnd = Point(mData[i+2], mData[i+3]);
      if (segEnd != segStart || segEnd != cp1 || segEnd != cp2) {
        subpathHasLength = true;
        builder->BezierTo(cp1, cp2, segEnd);
      }
      break;

    case PATHSEG_CURVETO_CUBIC_SMOOTH_REL:
      cp1 = SVGPathSegUtils::IsCubicType(prevSegType) ? segStart * 2 - cp2 : segStart;
      cp2 = segStart + Point(mData[i], mData[i+1]);
      segEnd = segStart + Point(mData[i+2], mData[i+3]);
      if (segEnd != segStart || segEnd != cp1 || segEnd != cp2) {
        subpathHasLength = true;
        builder->BezierTo(cp1, cp2, segEnd);
      }
      break;

    case PATHSEG_CURVETO_QUADRATIC_SMOOTH_ABS:
      cp1 = SVGPathSegUtils::IsQuadraticType(prevSegType) ? segStart * 2 - cp1 : segStart;
      // Convert quadratic curve to cubic curve:
      tcp1 = segStart + (cp1 - segStart) * 2 / 3;
      segEnd = Point(mData[i], mData[i+1]); // set before setting tcp2!
      tcp2 = cp1 + (segEnd - cp1) / 3;
      if (segEnd != segStart || segEnd != cp1) {
        subpathHasLength = true;
        builder->BezierTo(tcp1, tcp2, segEnd);
      }
      break;

    case PATHSEG_CURVETO_QUADRATIC_SMOOTH_REL:
      cp1 = SVGPathSegUtils::IsQuadraticType(prevSegType) ? segStart * 2 - cp1 : segStart;
      // Convert quadratic curve to cubic curve:
      tcp1 = segStart + (cp1 - segStart) * 2 / 3;
      segEnd = segStart + Point(mData[i], mData[i+1]); // changed before setting tcp2!
      tcp2 = cp1 + (segEnd - cp1) / 3;
      if (segEnd != segStart || segEnd != cp1) {
        subpathHasLength = true;
        builder->BezierTo(tcp1, tcp2, segEnd);
      }
      break;

    default:
      NS_NOTREACHED("Bad path segment type");
      return nullptr; // according to spec we'd use everything up to the bad seg anyway
    }

    subpathContainsNonMoveTo = segType != PATHSEG_MOVETO_ABS &&
                               segType != PATHSEG_MOVETO_REL;
    i += argCount;
    prevSegType = segType;
    segStart = segEnd;
  }

  NS_ABORT_IF_FALSE(i == mData.Length(), "Very, very bad - mData corrupt");
  NS_ABORT_IF_FALSE(prevSegType == segType,
                    "prevSegType should be left at the final segType");

  MAYBE_APPROXIMATE_ZERO_LENGTH_SUBPATH_SQUARE_CAPS_TO_DT;

  return builder->Finish();
}

TemporaryRef<Path>
SVGPathData::BuildPathForMeasuring() const
{
  // Since the path that we return will not be used for painting it doesn't
  // matter what we pass to CreatePathBuilder as aFillRule. Hawever, we do want
  // to pass something other than NS_STYLE_STROKE_LINECAP_SQUARE as
  // aStrokeLineCap to avoid the insertion of extra little lines (by
  // ApproximateZeroLengthSubpathSquareCaps), in which case the value that we
  // pass as aStrokeWidth doesn't matter (since it's only used to determine the
  // length of those extra little lines).

  RefPtr<DrawTarget> drawTarget =
    gfxPlatform::GetPlatform()->ScreenReferenceDrawTarget();
  RefPtr<PathBuilder> builder =
    drawTarget->CreatePathBuilder(FillRule::FILL_WINDING);
  return BuildPath(builder, NS_STYLE_STROKE_LINECAP_BUTT, 0);
}

static double
AngleOfVector(const Point& aVector)
{
  // C99 says about atan2 "A domain error may occur if both arguments are
  // zero" and "On a domain error, the function returns an implementation-
  // defined value". In the case of atan2 the implementation-defined value
  // seems to commonly be zero, but it could just as easily be a NaN value.
  // We specifically want zero in this case, hence the check:

  return (aVector != Point(0.0, 0.0)) ? atan2(aVector.y, aVector.x) : 0.0;
}

static float
AngleOfVectorF(const Point& aVector)
{
  return static_cast<float>(AngleOfVector(aVector));
}

void
SVGPathData::GetMarkerPositioningData(nsTArray<nsSVGMark> *aMarks) const
{
  // This code should assume that ANY type of segment can appear at ANY index.
  // It should also assume that segments such as M and Z can appear in weird
  // places, and repeat multiple times consecutively.

  // info on current [sub]path (reset every M command):
  Point pathStart(0.0, 0.0);
  float pathStartAngle = 0.0f;

  // info on previous segment:
  uint16_t prevSegType = PATHSEG_UNKNOWN;
  Point prevSegEnd(0.0, 0.0);
  float prevSegEndAngle = 0.0f;
  Point prevCP; // if prev seg was a bezier, this was its last control point

  uint32_t i = 0;
  while (i < mData.Length()) {

    // info on current segment:
    uint16_t segType =
      SVGPathSegUtils::DecodeType(mData[i++]); // advances i to args
    Point& segStart = prevSegEnd;
    Point segEnd;
    float segStartAngle, segEndAngle;

    switch (segType) // to find segStartAngle, segEnd and segEndAngle
    {
    case PATHSEG_CLOSEPATH:
      segEnd = pathStart;
      segStartAngle = segEndAngle = AngleOfVectorF(segEnd - segStart);
      break;

    case PATHSEG_MOVETO_ABS:
    case PATHSEG_MOVETO_REL:
      if (segType == PATHSEG_MOVETO_ABS) {
        segEnd = Point(mData[i], mData[i+1]);
      } else {
        segEnd = segStart + Point(mData[i], mData[i+1]);
      }
      pathStart = segEnd;
      // If authors are going to specify multiple consecutive moveto commands
      // with markers, me might as well make the angle do something useful:
      segStartAngle = segEndAngle = AngleOfVectorF(segEnd - segStart);
      i += 2;
      break;

    case PATHSEG_LINETO_ABS:
    case PATHSEG_LINETO_REL:
      if (segType == PATHSEG_LINETO_ABS) {
        segEnd = Point(mData[i], mData[i+1]);
      } else {
        segEnd = segStart + Point(mData[i], mData[i+1]);
      }
      segStartAngle = segEndAngle = AngleOfVectorF(segEnd - segStart);
      i += 2;
      break;

    case PATHSEG_CURVETO_CUBIC_ABS:
    case PATHSEG_CURVETO_CUBIC_REL:
    {
      Point cp1, cp2; // control points
      if (segType == PATHSEG_CURVETO_CUBIC_ABS) {
        cp1 = Point(mData[i], mData[i+1]);
        cp2 = Point(mData[i+2], mData[i+3]);
        segEnd = Point(mData[i+4], mData[i+5]);
      } else {
        cp1 = segStart + Point(mData[i], mData[i+1]);
        cp2 = segStart + Point(mData[i+2], mData[i+3]);
        segEnd = segStart + Point(mData[i+4], mData[i+5]);
      }
      prevCP = cp2;
      if (cp1 == segStart) {
        cp1 = cp2;
      }
      if (cp2 == segEnd) {
        cp2 = cp1;
      }
      segStartAngle = AngleOfVectorF(cp1 - segStart);
      segEndAngle = AngleOfVectorF(segEnd - cp2);
      i += 6;
      break;
    }

    case PATHSEG_CURVETO_QUADRATIC_ABS:
    case PATHSEG_CURVETO_QUADRATIC_REL:
    {
      Point cp1, cp2; // control points
      if (segType == PATHSEG_CURVETO_QUADRATIC_ABS) {
        cp1 = Point(mData[i], mData[i+1]);
        segEnd = Point(mData[i+2], mData[i+3]);
      } else {
        cp1 = segStart + Point(mData[i], mData[i+1]);
        segEnd = segStart + Point(mData[i+2], mData[i+3]);
      }
      prevCP = cp1;
      segStartAngle = AngleOfVectorF(cp1 - segStart);
      segEndAngle = AngleOfVectorF(segEnd - cp1);
      i += 4;
      break;
    }

    case PATHSEG_ARC_ABS:
    case PATHSEG_ARC_REL:
    {
      double rx = mData[i];
      double ry = mData[i+1];
      double angle = mData[i+2];
      bool largeArcFlag = mData[i+3] != 0.0f;
      bool sweepFlag = mData[i+4] != 0.0f;
      if (segType == PATHSEG_ARC_ABS) {
        segEnd = Point(mData[i+5], mData[i+6]);
      } else {
        segEnd = segStart + Point(mData[i+5], mData[i+6]);
      }

      // See section F.6 of SVG 1.1 for details on what we're doing here:
      // http://www.w3.org/TR/SVG11/implnote.html#ArcImplementationNotes

      if (segStart == segEnd) {
        // F.6.2 says "If the endpoints (x1, y1) and (x2, y2) are identical,
        // then this is equivalent to omitting the elliptical arc segment
        // entirely." We take that very literally here, not adding a mark, and
        // not even setting any of the 'prev' variables so that it's as if this
        // arc had never existed; note the difference this will make e.g. if
        // the arc is proceeded by a bezier curve and followed by a "smooth"
        // bezier curve of the same degree!
        i += 7;
        continue;
      }

      // Below we have funny interleaving of F.6.6 (Correction of out-of-range
      // radii) and F.6.5 (Conversion from endpoint to center parameterization)
      // which is designed to avoid some unnecessary calculations.

      if (rx == 0.0 || ry == 0.0) {
        // F.6.6 step 1 - straight line or coincidental points
        segStartAngle = segEndAngle = AngleOfVectorF(segEnd - segStart);
        i += 7;
        break;
      }
      rx = fabs(rx); // F.6.6.1
      ry = fabs(ry);

      // F.6.5.1:
      angle = angle * M_PI/180.0;
      double x1p =  cos(angle) * (segStart.x - segEnd.x) / 2.0
                  + sin(angle) * (segStart.y - segEnd.y) / 2.0;
      double y1p = -sin(angle) * (segStart.x - segEnd.x) / 2.0
                  + cos(angle) * (segStart.y - segEnd.y) / 2.0;

      // This is the root in F.6.5.2 and the numerator under that root:
      double root;
      double numerator = rx*rx*ry*ry - rx*rx*y1p*y1p - ry*ry*x1p*x1p;

      if (numerator >= 0.0) {
        root = sqrt(numerator/(rx*rx*y1p*y1p + ry*ry*x1p*x1p));
        if (largeArcFlag == sweepFlag)
          root = -root;
      } else {
        // F.6.6 step 3 - |numerator < 0.0|. This is equivalent to the result
        // of F.6.6.2 (lamedh) being greater than one. What we have here is
        // ellipse radii that are too small for the ellipse to reach between
        // segStart and segEnd. We scale the radii up uniformly so that the
        // ellipse is just big enough to fit (i.e. to the point where there is
        // exactly one solution).

        double lamedh = 1.0 - numerator/(rx*rx*ry*ry); // equiv to eqn F.6.6.2
        double s = sqrt(lamedh);
        rx *= s;  // F.6.6.3
        ry *= s;
        root = 0.0;
      }

      double cxp =  root * rx * y1p / ry;  // F.6.5.2
      double cyp = -root * ry * x1p / rx;

      double theta, delta;
      theta = AngleOfVector(Point((x1p-cxp)/rx, (y1p-cyp)/ry));    // F.6.5.5
      delta = AngleOfVector(Point((-x1p-cxp)/rx, (-y1p-cyp)/ry)) - // F.6.5.6
              theta;
      if (!sweepFlag && delta > 0)
        delta -= 2.0 * M_PI;
      else if (sweepFlag && delta < 0)
        delta += 2.0 * M_PI;

      double tx1, ty1, tx2, ty2;
      tx1 = -cos(angle)*rx*sin(theta) - sin(angle)*ry*cos(theta);
      ty1 = -sin(angle)*rx*sin(theta) + cos(angle)*ry*cos(theta);
      tx2 = -cos(angle)*rx*sin(theta+delta) - sin(angle)*ry*cos(theta+delta);
      ty2 = -sin(angle)*rx*sin(theta+delta) + cos(angle)*ry*cos(theta+delta);

      if (delta < 0.0f) {
        tx1 = -tx1;
        ty1 = -ty1;
        tx2 = -tx2;
        ty2 = -ty2;
      }

      segStartAngle = static_cast<float>(atan2(ty1, tx1));
      segEndAngle = static_cast<float>(atan2(ty2, tx2));
      i += 7;
      break;
    }

    case PATHSEG_LINETO_HORIZONTAL_ABS:
    case PATHSEG_LINETO_HORIZONTAL_REL:
      if (segType == PATHSEG_LINETO_HORIZONTAL_ABS) {
        segEnd = Point(mData[i++], segStart.y);
      } else {
        segEnd = segStart + Point(mData[i++], 0.0f);
      }
      segStartAngle = segEndAngle = AngleOfVectorF(segEnd - segStart);
      break;

    case PATHSEG_LINETO_VERTICAL_ABS:
    case PATHSEG_LINETO_VERTICAL_REL:
      if (segType == PATHSEG_LINETO_VERTICAL_ABS) {
        segEnd = Point(segStart.x, mData[i++]);
      } else {
        segEnd = segStart + Point(0.0f, mData[i++]);
      }
      segStartAngle = segEndAngle = AngleOfVectorF(segEnd - segStart);
      break;

    case PATHSEG_CURVETO_CUBIC_SMOOTH_ABS:
    case PATHSEG_CURVETO_CUBIC_SMOOTH_REL:
    {
      Point cp1 = SVGPathSegUtils::IsCubicType(prevSegType) ?
                       segStart * 2 - prevCP : segStart;
      Point cp2;
      if (segType == PATHSEG_CURVETO_CUBIC_SMOOTH_ABS) {
        cp2 = Point(mData[i], mData[i+1]);
        segEnd = Point(mData[i+2], mData[i+3]);
      } else {
        cp2 = segStart + Point(mData[i], mData[i+1]);
        segEnd = segStart + Point(mData[i+2], mData[i+3]);
      }
      prevCP = cp2;
      if (cp1 == segStart) {
        cp1 = cp2;
      }
      if (cp2 == segEnd) {
        cp2 = cp1;
      }
      segStartAngle = AngleOfVectorF(cp1 - segStart);
      segEndAngle = AngleOfVectorF(segEnd - cp2);
      i += 4;
      break;
    }

    case PATHSEG_CURVETO_QUADRATIC_SMOOTH_ABS:
    case PATHSEG_CURVETO_QUADRATIC_SMOOTH_REL:
    {
      Point cp1 = SVGPathSegUtils::IsQuadraticType(prevSegType) ?
                       segStart * 2 - prevCP : segStart;
      Point cp2;
      if (segType == PATHSEG_CURVETO_QUADRATIC_SMOOTH_ABS) {
        segEnd = Point(mData[i], mData[i+1]);
      } else {
        segEnd = segStart + Point(mData[i], mData[i+1]);
      }
      prevCP = cp1;
      segStartAngle = AngleOfVectorF(cp1 - segStart);
      segEndAngle = AngleOfVectorF(segEnd - cp1);
      i += 2;
      break;
    }

    default:
      // Leave any existing marks in aMarks so we have a visual indication of
      // when things went wrong.
      NS_ABORT_IF_FALSE(false, "Unknown segment type - path corruption?");
      return;
    }

    // Set the angle of the mark at the start of this segment:
    if (aMarks->Length()) {
      nsSVGMark &mark = aMarks->LastElement();
      if (!IsMoveto(segType) && IsMoveto(prevSegType)) {
        // start of new subpath
        pathStartAngle = mark.angle = segStartAngle;
      } else if (IsMoveto(segType) && !IsMoveto(prevSegType)) {
        // end of a subpath
        if (prevSegType != PATHSEG_CLOSEPATH)
          mark.angle = prevSegEndAngle;
      } else {
        if (!(segType == PATHSEG_CLOSEPATH &&
              prevSegType == PATHSEG_CLOSEPATH))
          mark.angle = SVGContentUtils::AngleBisect(prevSegEndAngle, segStartAngle);
      }
    }

    // Add the mark at the end of this segment, and set its position:
    if (!aMarks->AppendElement(nsSVGMark(static_cast<float>(segEnd.x),
                                         static_cast<float>(segEnd.y),
                                         0.0f,
                                         nsSVGMark::eMid))) {
      aMarks->Clear(); // OOM, so try to free some
      return;
    }

    if (segType == PATHSEG_CLOSEPATH &&
        prevSegType != PATHSEG_CLOSEPATH) {
      aMarks->LastElement().angle =
        //aMarks->ElementAt(pathStartIndex).angle =
        SVGContentUtils::AngleBisect(segEndAngle, pathStartAngle);
    }

    prevSegType = segType;
    prevSegEnd = segEnd;
    prevSegEndAngle = segEndAngle;
  }

  NS_ABORT_IF_FALSE(i == mData.Length(), "Very, very bad - mData corrupt");

  if (aMarks->Length()) {
    if (prevSegType != PATHSEG_CLOSEPATH) {
      aMarks->LastElement().angle = prevSegEndAngle;
    }
    aMarks->LastElement().type = nsSVGMark::eEnd;
    aMarks->ElementAt(0).type = nsSVGMark::eStart;
  }
}

size_t
SVGPathData::SizeOfExcludingThis(MallocSizeOf aMallocSizeOf) const
{
  return mData.SizeOfExcludingThis(aMallocSizeOf);
}

size_t
SVGPathData::SizeOfIncludingThis(MallocSizeOf aMallocSizeOf) const
{
  return aMallocSizeOf(this) + SizeOfExcludingThis(aMallocSizeOf);
}