Bug 931915, part 1 - Add an AppendRoundedRectToPath helper to Moz2D. r=Bas

gfx/2d/PathHelpers.cpp

@@ -0,0 +1,155 @@
+/* -*- 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 "PathHelpers.h"
+
+namespace mozilla {
+namespace gfx {
+
+void
+AppendRoundedRectToPath(PathBuilder* aPathBuilder,
+                        const Rect& aRect,
+                        // paren's needed due to operator precedence:
+                        const Size(& aCornerRadii)[4],
+                        bool aDrawClockwise)
+{
+  // For CW drawing, this looks like:
+  //
+  //  ...******0**      1    C
+  //              ****
+  //                  ***    2
+  //                     **
+  //                       *
+  //                        *
+  //                         3
+  //                         *
+  //                         *
+  //
+  // Where 0, 1, 2, 3 are the control points of the Bezier curve for
+  // the corner, and C is the actual corner point.
+  //
+  // At the start of the loop, the current point is assumed to be
+  // the point adjacent to the top left corner on the top
+  // horizontal.  Note that corner indices start at the top left and
+  // continue clockwise, whereas in our loop i = 0 refers to the top
+  // right corner.
+  //
+  // When going CCW, the control points are swapped, and the first
+  // corner that's drawn is the top left (along with the top segment).
+  //
+  // There is considerable latitude in how one chooses the four
+  // control points for a Bezier curve approximation to an ellipse.
+  // For the overall path to be continuous and show no corner at the
+  // endpoints of the arc, points 0 and 3 must be at the ends of the
+  // straight segments of the rectangle; points 0, 1, and C must be
+  // collinear; and points 3, 2, and C must also be collinear.  This
+  // leaves only two free parameters: the ratio of the line segments
+  // 01 and 0C, and the ratio of the line segments 32 and 3C.  See
+  // the following papers for extensive discussion of how to choose
+  // these ratios:
+  //
+  //   Dokken, Tor, et al. "Good approximation of circles by
+  //      curvature-continuous Bezier curves."  Computer-Aided
+  //      Geometric Design 7(1990) 33--41.
+  //   Goldapp, Michael. "Approximation of circular arcs by cubic
+  //      polynomials." Computer-Aided Geometric Design 8(1991) 227--238.
+  //   Maisonobe, Luc. "Drawing an elliptical arc using polylines,
+  //      quadratic, or cubic Bezier curves."
+  //      http://www.spaceroots.org/documents/ellipse/elliptical-arc.pdf
+  //
+  // We follow the approach in section 2 of Goldapp (least-error,
+  // Hermite-type approximation) and make both ratios equal to
+  //
+  //          2   2 + n - sqrt(2n + 28)
+  //  alpha = - * ---------------------
+  //          3           n - 4
+  //
+  // where n = 3( cbrt(sqrt(2)+1) - cbrt(sqrt(2)-1) ).
+  //
+  // This is the result of Goldapp's equation (10b) when the angle
+  // swept out by the arc is pi/2, and the parameter "a-bar" is the
+  // expression given immediately below equation (21).
+  //
+  // Using this value, the maximum radial error for a circle, as a
+  // fraction of the radius, is on the order of 0.2 x 10^-3.
+  // Neither Dokken nor Goldapp discusses error for a general
+  // ellipse; Maisonobe does, but his choice of control points
+  // follows different constraints, and Goldapp's expression for
+  // 'alpha' gives much smaller radial error, even for very flat
+  // ellipses, than Maisonobe's equivalent.
+  //
+  // For the various corners and for each axis, the sign of this
+  // constant changes, or it might be 0 -- it's multiplied by the
+  // appropriate multiplier from the list before using.
+
+  const Float alpha = Float(0.55191497064665766025);
+
+  typedef struct { Float a, b; } twoFloats;
+
+  twoFloats cwCornerMults[4] = { { -1,  0 },    // cc == clockwise
+                                 {  0, -1 },
+                                 { +1,  0 },
+                                 {  0, +1 } };
+  twoFloats ccwCornerMults[4] = { { +1,  0 },   // ccw == counter-clockwise
+                                  {  0, -1 },
+                                  { -1,  0 },
+                                  {  0, +1 } };
+
+  twoFloats *cornerMults = aDrawClockwise ? cwCornerMults : ccwCornerMults;
+
+  Point cornerCoords[] = { aRect.TopLeft(), aRect.TopRight(),
+                           aRect.BottomRight(), aRect.BottomLeft() };
+
+  Point pc, p0, p1, p2, p3;
+
+  // The indexes of the corners:
+  const int kTopLeft = 0, kTopRight = 1;
+
+  if (aDrawClockwise) {
+    aPathBuilder->MoveTo(Point(aRect.X() + aCornerRadii[kTopLeft].width,
+                               aRect.Y()));
+  } else {
+    aPathBuilder->MoveTo(Point(aRect.X() + aRect.Width() - aCornerRadii[kTopRight].width,
+                               aRect.Y()));
+  }
+
+  for (int i = 0; i < 4; ++i) {
+    // the corner index -- either 1 2 3 0 (cw) or 0 3 2 1 (ccw)
+    int c = aDrawClockwise ? ((i+1) % 4) : ((4-i) % 4);
+
+    // i+2 and i+3 respectively.  These are used to index into the corner
+    // multiplier table, and were deduced by calculating out the long form
+    // of each corner and finding a pattern in the signs and values.
+    int i2 = (i+2) % 4;
+    int i3 = (i+3) % 4;
+
+    pc = cornerCoords[c];
+
+    if (aCornerRadii[c].width > 0.0 && aCornerRadii[c].height > 0.0) {
+      p0.x = pc.x + cornerMults[i].a * aCornerRadii[c].width;
+      p0.y = pc.y + cornerMults[i].b * aCornerRadii[c].height;
+
+      p3.x = pc.x + cornerMults[i3].a * aCornerRadii[c].width;
+      p3.y = pc.y + cornerMults[i3].b * aCornerRadii[c].height;
+
+      p1.x = p0.x + alpha * cornerMults[i2].a * aCornerRadii[c].width;
+      p1.y = p0.y + alpha * cornerMults[i2].b * aCornerRadii[c].height;
+
+      p2.x = p3.x - alpha * cornerMults[i3].a * aCornerRadii[c].width;
+      p2.y = p3.y - alpha * cornerMults[i3].b * aCornerRadii[c].height;
+
+      aPathBuilder->LineTo(p0);
+      aPathBuilder->BezierTo(p1, p2, p3);
+    } else {
+      aPathBuilder->LineTo(pc);
+    }
+  }
+
+  aPathBuilder->Close();
+}
+
+} // namespace gfx
+} // namespace mozilla
+

gfx/2d/PathHelpers.h

@@ -81,7 +81,24 @@ void ArcToBezier(T* aSink, const Point &aOrigin, float aRadius, float aStartAngl
   }
 }
 
-}
-}
+/**
+ * Appends a path represending a rounded rectangle to the path being built by
+ * aPathBuilder.
+ *
+ * aRect           The rectangle to append.
+ * aCornerRadii    Contains the radii of the top-left, top-right, bottom-right
+ *                 and bottom-left corners, in that order.
+ * aDrawClockwise  If set to true, the path will start at the left of the top
+ *                 left edge and draw clockwise. If set to false the path will
+ *                 start at the right of the top left edge and draw counter-
+ *                 clockwise.
+ */
+GFX2D_API void AppendRoundedRectToPath(PathBuilder* aPathBuilder,
+                                       const Rect& aRect,
+                                       const Size(& aCornerRadii)[4],
+                                       bool aDrawClockwise = true);
+
+} // namespace gfx
+} // namespace mozilla
 
 #endif /* MOZILLA_GFX_PATHHELPERS_H_ */

gfx/2d/moz.build

@@ -89,6 +89,7 @@ SOURCES += [
     'ImageScaling.cpp',
     'Matrix.cpp',
     'PathCairo.cpp',
+    'PathHelpers.cpp',
     'PathRecording.cpp',
     'RecordedEvent.cpp',
     'Scale.cpp',