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+/* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
+/* vim: set ts=8 sts=2 et sw=2 tw=80: */
+/* 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 {
+
+UserDataKey sDisablePixelSnapping;
+
+void AppendRectToPath(PathBuilder* aPathBuilder, const Rect& aRect,
+ bool aDrawClockwise) {
+ if (aDrawClockwise) {
+ aPathBuilder->MoveTo(aRect.TopLeft());
+ aPathBuilder->LineTo(aRect.TopRight());
+ aPathBuilder->LineTo(aRect.BottomRight());
+ aPathBuilder->LineTo(aRect.BottomLeft());
+ } else {
+ aPathBuilder->MoveTo(aRect.TopRight());
+ aPathBuilder->LineTo(aRect.TopLeft());
+ aPathBuilder->LineTo(aRect.BottomLeft());
+ aPathBuilder->LineTo(aRect.BottomRight());
+ }
+ aPathBuilder->Close();
+}
+
+void AppendRoundedRectToPath(PathBuilder* aPathBuilder, const Rect& aRect,
+ const RectCornerRadii& aRadii, bool aDrawClockwise,
+ const Maybe<Matrix>& aTransform) {
+ // 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;
+
+ if (aDrawClockwise) {
+ Point pt(aRect.X() + aRadii[eCornerTopLeft].width, aRect.Y());
+ if (aTransform) {
+ pt = aTransform->TransformPoint(pt);
+ }
+ aPathBuilder->MoveTo(pt);
+ } else {
+ Point pt(aRect.X() + aRect.Width() - aRadii[eCornerTopRight].width,
+ aRect.Y());
+ if (aTransform) {
+ pt = aTransform->TransformPoint(pt);
+ }
+ aPathBuilder->MoveTo(pt);
+ }
+
+ 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 (aRadii[c].width > 0.0 && aRadii[c].height > 0.0) {
+ p0.x = pc.x + cornerMults[i].a * aRadii[c].width;
+ p0.y = pc.y + cornerMults[i].b * aRadii[c].height;
+
+ p3.x = pc.x + cornerMults[i3].a * aRadii[c].width;
+ p3.y = pc.y + cornerMults[i3].b * aRadii[c].height;
+
+ p1.x = p0.x + alpha * cornerMults[i2].a * aRadii[c].width;
+ p1.y = p0.y + alpha * cornerMults[i2].b * aRadii[c].height;
+
+ p2.x = p3.x - alpha * cornerMults[i3].a * aRadii[c].width;
+ p2.y = p3.y - alpha * cornerMults[i3].b * aRadii[c].height;
+
+ if (aTransform.isNothing()) {
+ aPathBuilder->LineTo(p0);
+ aPathBuilder->BezierTo(p1, p2, p3);
+ } else {
+ const Matrix& transform = *aTransform;
+ aPathBuilder->LineTo(transform.TransformPoint(p0));
+ aPathBuilder->BezierTo(transform.TransformPoint(p1),
+ transform.TransformPoint(p2),
+ transform.TransformPoint(p3));
+ }
+ } else {
+ if (aTransform.isNothing()) {
+ aPathBuilder->LineTo(pc);
+ } else {
+ aPathBuilder->LineTo(aTransform->TransformPoint(pc));
+ }
+ }
+ }
+
+ aPathBuilder->Close();
+}
+
+void AppendEllipseToPath(PathBuilder* aPathBuilder, const Point& aCenter,
+ const Size& aDimensions) {
+ Size halfDim = aDimensions / 2.f;
+ Rect rect(aCenter - Point(halfDim.width, halfDim.height), aDimensions);
+ RectCornerRadii radii(halfDim.width, halfDim.height);
+
+ AppendRoundedRectToPath(aPathBuilder, rect, radii);
+}
+
+bool SnapLineToDevicePixelsForStroking(Point& aP1, Point& aP2,
+ const DrawTarget& aDrawTarget,
+ Float aLineWidth) {
+ Matrix mat = aDrawTarget.GetTransform();
+ if (mat.HasNonTranslation()) {
+ return false;
+ }
+ if (aP1.x != aP2.x && aP1.y != aP2.y) {
+ return false; // not a horizontal or vertical line
+ }
+ Point p1 = aP1 + mat.GetTranslation(); // into device space
+ Point p2 = aP2 + mat.GetTranslation();
+ p1.Round();
+ p2.Round();
+ p1 -= mat.GetTranslation(); // back into user space
+ p2 -= mat.GetTranslation();
+
+ aP1 = p1;
+ aP2 = p2;
+
+ bool lineWidthIsOdd = (int(aLineWidth) % 2) == 1;
+ if (lineWidthIsOdd) {
+ if (aP1.x == aP2.x) {
+ // snap vertical line, adding 0.5 to align it to be mid-pixel:
+ aP1 += Point(0.5, 0);
+ aP2 += Point(0.5, 0);
+ } else {
+ // snap horizontal line, adding 0.5 to align it to be mid-pixel:
+ aP1 += Point(0, 0.5);
+ aP2 += Point(0, 0.5);
+ }
+ }
+ return true;
+}
+
+void StrokeSnappedEdgesOfRect(const Rect& aRect, DrawTarget& aDrawTarget,
+ const ColorPattern& aColor,
+ const StrokeOptions& aStrokeOptions) {
+ if (aRect.IsEmpty()) {
+ return;
+ }
+
+ Point p1 = aRect.TopLeft();
+ Point p2 = aRect.BottomLeft();
+ SnapLineToDevicePixelsForStroking(p1, p2, aDrawTarget,
+ aStrokeOptions.mLineWidth);
+ aDrawTarget.StrokeLine(p1, p2, aColor, aStrokeOptions);
+
+ p1 = aRect.BottomLeft();
+ p2 = aRect.BottomRight();
+ SnapLineToDevicePixelsForStroking(p1, p2, aDrawTarget,
+ aStrokeOptions.mLineWidth);
+ aDrawTarget.StrokeLine(p1, p2, aColor, aStrokeOptions);
+
+ p1 = aRect.TopLeft();
+ p2 = aRect.TopRight();
+ SnapLineToDevicePixelsForStroking(p1, p2, aDrawTarget,
+ aStrokeOptions.mLineWidth);
+ aDrawTarget.StrokeLine(p1, p2, aColor, aStrokeOptions);
+
+ p1 = aRect.TopRight();
+ p2 = aRect.BottomRight();
+ SnapLineToDevicePixelsForStroking(p1, p2, aDrawTarget,
+ aStrokeOptions.mLineWidth);
+ aDrawTarget.StrokeLine(p1, p2, aColor, aStrokeOptions);
+}
+
+// The logic for this comes from _cairo_stroke_style_max_distance_from_path
+Margin MaxStrokeExtents(const StrokeOptions& aStrokeOptions,
+ const Matrix& aTransform) {
+ double styleExpansionFactor = 0.5f;
+
+ if (aStrokeOptions.mLineCap == CapStyle::SQUARE) {
+ styleExpansionFactor = M_SQRT1_2;
+ }
+
+ if (aStrokeOptions.mLineJoin == JoinStyle::MITER &&
+ styleExpansionFactor < M_SQRT2 * aStrokeOptions.mMiterLimit) {
+ styleExpansionFactor = M_SQRT2 * aStrokeOptions.mMiterLimit;
+ }
+
+ styleExpansionFactor *= aStrokeOptions.mLineWidth;
+
+ double dx = styleExpansionFactor * hypot(aTransform._11, aTransform._21);
+ double dy = styleExpansionFactor * hypot(aTransform._22, aTransform._12);
+
+ // Even if the stroke only partially covers a pixel, it must still render to
+ // full pixels. Round up to compensate for this.
+ dx = ceil(dx);
+ dy = ceil(dy);
+
+ return Margin(dy, dx, dy, dx);
+}
+
+} // namespace gfx
+} // namespace mozilla
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