gfx/2d/PathHelpers.cpp

   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 "PathHelpers.h"
   8
   9 namespace mozilla {
  10 namespace gfx {
  11
  12 UserDataKey sDisablePixelSnapping;
  13
  14 void AppendRectToPath(PathBuilder* aPathBuilder, const Rect& aRect,
  15                       bool aDrawClockwise) {
  16   if (aDrawClockwise) {
  17     aPathBuilder->MoveTo(aRect.TopLeft());
  18     aPathBuilder->LineTo(aRect.TopRight());
  19     aPathBuilder->LineTo(aRect.BottomRight());
  20     aPathBuilder->LineTo(aRect.BottomLeft());
  21   } else {
  22     aPathBuilder->MoveTo(aRect.TopRight());
  23     aPathBuilder->LineTo(aRect.TopLeft());
  24     aPathBuilder->LineTo(aRect.BottomLeft());
  25     aPathBuilder->LineTo(aRect.BottomRight());
  26   }
  27   aPathBuilder->Close();
  28 }
  29
  30 void AppendRoundedRectToPath(PathBuilder* aPathBuilder, const Rect& aRect,
  31                              const RectCornerRadii& aRadii,
  32                              bool aDrawClockwise) {
  33   // For CW drawing, this looks like:
  34   //
  35   //  ...******0**      1    C
  36   //              ****
  37   //                  ***    2
  38   //                     **
  39   //                       *
  40   //                        *
  41   //                         3
  42   //                         *
  43   //                         *
  44   //
  45   // Where 0, 1, 2, 3 are the control points of the Bezier curve for
  46   // the corner, and C is the actual corner point.
  47   //
  48   // At the start of the loop, the current point is assumed to be
  49   // the point adjacent to the top left corner on the top
  50   // horizontal.  Note that corner indices start at the top left and
  51   // continue clockwise, whereas in our loop i = 0 refers to the top
  52   // right corner.
  53   //
  54   // When going CCW, the control points are swapped, and the first
  55   // corner that's drawn is the top left (along with the top segment).
  56   //
  57   // There is considerable latitude in how one chooses the four
  58   // control points for a Bezier curve approximation to an ellipse.
  59   // For the overall path to be continuous and show no corner at the
  60   // endpoints of the arc, points 0 and 3 must be at the ends of the
  61   // straight segments of the rectangle; points 0, 1, and C must be
  62   // collinear; and points 3, 2, and C must also be collinear.  This
  63   // leaves only two free parameters: the ratio of the line segments
  64   // 01 and 0C, and the ratio of the line segments 32 and 3C.  See
  65   // the following papers for extensive discussion of how to choose
  66   // these ratios:
  67   //
  68   //   Dokken, Tor, et al. "Good approximation of circles by
  69   //      curvature-continuous Bezier curves."  Computer-Aided
  70   //      Geometric Design 7(1990) 33--41.
  71   //   Goldapp, Michael. "Approximation of circular arcs by cubic
  72   //      polynomials." Computer-Aided Geometric Design 8(1991) 227--238.
  73   //   Maisonobe, Luc. "Drawing an elliptical arc using polylines,
  74   //      quadratic, or cubic Bezier curves."
  75   //      http://www.spaceroots.org/documents/ellipse/elliptical-arc.pdf
  76   //
  77   // We follow the approach in section 2 of Goldapp (least-error,
  78   // Hermite-type approximation) and make both ratios equal to
  79   //
  80   //          2   2 + n - sqrt(2n + 28)
  81   //  alpha = - * ---------------------
  82   //          3           n - 4
  83   //
  84   // where n = 3( cbrt(sqrt(2)+1) - cbrt(sqrt(2)-1) ).
  85   //
  86   // This is the result of Goldapp's equation (10b) when the angle
  87   // swept out by the arc is pi/2, and the parameter "a-bar" is the
  88   // expression given immediately below equation (21).
  89   //
  90   // Using this value, the maximum radial error for a circle, as a
  91   // fraction of the radius, is on the order of 0.2 x 10^-3.
  92   // Neither Dokken nor Goldapp discusses error for a general
  93   // ellipse; Maisonobe does, but his choice of control points
  94   // follows different constraints, and Goldapp's expression for
  95   // 'alpha' gives much smaller radial error, even for very flat
  96   // ellipses, than Maisonobe's equivalent.
  97   //
  98   // For the various corners and for each axis, the sign of this
  99   // constant changes, or it might be 0 -- it's multiplied by the
 100   // appropriate multiplier from the list before using.
 101
 102   const Float alpha = Float(0.55191497064665766025);
 103
 104   typedef struct {
 105     Float a, b;
 106   } twoFloats;
 107
 108   twoFloats cwCornerMults[4] = {{-1, 0},  // cc == clockwise
 109                                 {0, -1},
 110                                 {+1, 0},
 111                                 {0, +1}};
 112   twoFloats ccwCornerMults[4] = {{+1, 0},  // ccw == counter-clockwise
 113                                  {0, -1},
 114                                  {-1, 0},
 115                                  {0, +1}};
 116
 117   twoFloats* cornerMults = aDrawClockwise ? cwCornerMults : ccwCornerMults;
 118
 119   Point cornerCoords[] = {aRect.TopLeft(), aRect.TopRight(),
 120                           aRect.BottomRight(), aRect.BottomLeft()};
 121
 122   Point pc, p0, p1, p2, p3;
 123
 124   if (aDrawClockwise) {
 125     aPathBuilder->MoveTo(
 126         Point(aRect.X() + aRadii[eCornerTopLeft].width, aRect.Y()));
 127   } else {
 128     aPathBuilder->MoveTo(Point(
 129         aRect.X() + aRect.Width() - aRadii[eCornerTopRight].width, aRect.Y()));
 130   }
 131
 132   for (int i = 0; i < 4; ++i) {
 133     // the corner index -- either 1 2 3 0 (cw) or 0 3 2 1 (ccw)
 134     int c = aDrawClockwise ? ((i + 1) % 4) : ((4 - i) % 4);
 135
 136     // i+2 and i+3 respectively.  These are used to index into the corner
 137     // multiplier table, and were deduced by calculating out the long form
 138     // of each corner and finding a pattern in the signs and values.
 139     int i2 = (i + 2) % 4;
 140     int i3 = (i + 3) % 4;
 141
 142     pc = cornerCoords[c];
 143
 144     if (aRadii[c].width > 0.0 && aRadii[c].height > 0.0) {
 145       p0.x = pc.x + cornerMults[i].a * aRadii[c].width;
 146       p0.y = pc.y + cornerMults[i].b * aRadii[c].height;
 147
 148       p3.x = pc.x + cornerMults[i3].a * aRadii[c].width;
 149       p3.y = pc.y + cornerMults[i3].b * aRadii[c].height;
 150
 151       p1.x = p0.x + alpha * cornerMults[i2].a * aRadii[c].width;
 152       p1.y = p0.y + alpha * cornerMults[i2].b * aRadii[c].height;
 153
 154       p2.x = p3.x - alpha * cornerMults[i3].a * aRadii[c].width;
 155       p2.y = p3.y - alpha * cornerMults[i3].b * aRadii[c].height;
 156
 157       aPathBuilder->LineTo(p0);
 158       aPathBuilder->BezierTo(p1, p2, p3);
 159     } else {
 160       aPathBuilder->LineTo(pc);
 161     }
 162   }
 163
 164   aPathBuilder->Close();
 165 }
 166
 167 void AppendEllipseToPath(PathBuilder* aPathBuilder, const Point& aCenter,
 168                          const Size& aDimensions) {
 169   Size halfDim = aDimensions / 2.f;
 170   Rect rect(aCenter - Point(halfDim.width, halfDim.height), aDimensions);
 171   RectCornerRadii radii(halfDim.width, halfDim.height);
 172
 173   AppendRoundedRectToPath(aPathBuilder, rect, radii);
 174 }
 175
 176 bool SnapLineToDevicePixelsForStroking(Point& aP1, Point& aP2,
 177                                        const DrawTarget& aDrawTarget,
 178                                        Float aLineWidth) {
 179   Matrix mat = aDrawTarget.GetTransform();
 180   if (mat.HasNonTranslation()) {
 181     return false;
 182   }
 183   if (aP1.x != aP2.x && aP1.y != aP2.y) {
 184     return false;  // not a horizontal or vertical line
 185   }
 186   Point p1 = aP1 + mat.GetTranslation();  // into device space
 187   Point p2 = aP2 + mat.GetTranslation();
 188   p1.Round();
 189   p2.Round();
 190   p1 -= mat.GetTranslation();  // back into user space
 191   p2 -= mat.GetTranslation();
 192
 193   aP1 = p1;
 194   aP2 = p2;
 195
 196   bool lineWidthIsOdd = (int(aLineWidth) % 2) == 1;
 197   if (lineWidthIsOdd) {
 198     if (aP1.x == aP2.x) {
 199       // snap vertical line, adding 0.5 to align it to be mid-pixel:
 200       aP1 += Point(0.5, 0);
 201       aP2 += Point(0.5, 0);
 202     } else {
 203       // snap horizontal line, adding 0.5 to align it to be mid-pixel:
 204       aP1 += Point(0, 0.5);
 205       aP2 += Point(0, 0.5);
 206     }
 207   }
 208   return true;
 209 }
 210
 211 void StrokeSnappedEdgesOfRect(const Rect& aRect, DrawTarget& aDrawTarget,
 212                               const ColorPattern& aColor,
 213                               const StrokeOptions& aStrokeOptions) {
 214   if (aRect.IsEmpty()) {
 215     return;
 216   }
 217
 218   Point p1 = aRect.TopLeft();
 219   Point p2 = aRect.BottomLeft();
 220   SnapLineToDevicePixelsForStroking(p1, p2, aDrawTarget,
 221                                     aStrokeOptions.mLineWidth);
 222   aDrawTarget.StrokeLine(p1, p2, aColor, aStrokeOptions);
 223
 224   p1 = aRect.BottomLeft();
 225   p2 = aRect.BottomRight();
 226   SnapLineToDevicePixelsForStroking(p1, p2, aDrawTarget,
 227                                     aStrokeOptions.mLineWidth);
 228   aDrawTarget.StrokeLine(p1, p2, aColor, aStrokeOptions);
 229
 230   p1 = aRect.TopLeft();
 231   p2 = aRect.TopRight();
 232   SnapLineToDevicePixelsForStroking(p1, p2, aDrawTarget,
 233                                     aStrokeOptions.mLineWidth);
 234   aDrawTarget.StrokeLine(p1, p2, aColor, aStrokeOptions);
 235
 236   p1 = aRect.TopRight();
 237   p2 = aRect.BottomRight();
 238   SnapLineToDevicePixelsForStroking(p1, p2, aDrawTarget,
 239                                     aStrokeOptions.mLineWidth);
 240   aDrawTarget.StrokeLine(p1, p2, aColor, aStrokeOptions);
 241 }
 242
 243 // The logic for this comes from _cairo_stroke_style_max_distance_from_path
 244 Margin MaxStrokeExtents(const StrokeOptions& aStrokeOptions,
 245                         const Matrix& aTransform) {
 246   double styleExpansionFactor = 0.5f;
 247
 248   if (aStrokeOptions.mLineCap == CapStyle::SQUARE) {
 249     styleExpansionFactor = M_SQRT1_2;
 250   }
 251
 252   if (aStrokeOptions.mLineJoin == JoinStyle::MITER &&
 253       styleExpansionFactor < M_SQRT2 * aStrokeOptions.mMiterLimit) {
 254     styleExpansionFactor = M_SQRT2 * aStrokeOptions.mMiterLimit;
 255   }
 256
 257   styleExpansionFactor *= aStrokeOptions.mLineWidth;
 258
 259   double dx = styleExpansionFactor * hypot(aTransform._11, aTransform._21);
 260   double dy = styleExpansionFactor * hypot(aTransform._22, aTransform._12);
 261
 262   // Even if the stroke only partially covers a pixel, it must still render to
 263   // full pixels. Round up to compensate for this.
 264   dx = ceil(dx);
 265   dy = ceil(dy);
 266
 267   return Margin(dy, dx, dy, dx);
 268 }
 269
 270 }  // namespace gfx
 271 }  // namespace mozilla