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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) {
// 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."
//
// 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) {
aPathBuilder->MoveTo(
Point(aRect.X() + aRadii[eCornerTopLeft].width, aRect.Y()));
} else {
aPathBuilder->MoveTo(Point(
aRect.X() + aRect.Width() - aRadii[eCornerTopRight].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 (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;
aPathBuilder->LineTo(p0);
aPathBuilder->BezierTo(p1, p2, p3);
} else {
aPathBuilder->LineTo(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