/* -*- Mode: C++; tab-width: 20; indent-tabs-mode: nil; c-basic-offset: 4 -*- * ***** BEGIN LICENSE BLOCK ***** * Version: MPL 1.1/GPL 2.0/LGPL 2.1 * * The contents of this file are subject to the Mozilla Public License Version * 1.1 (the "License"); you may not use this file except in compliance with * the License. You may obtain a copy of the License at * http://www.mozilla.org/MPL/ * * Software distributed under the License is distributed on an "AS IS" basis, * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License * for the specific language governing rights and limitations under the * License. * * The Original Code is Oracle Corporation code. * * The Initial Developer of the Original Code is Oracle Corporation. * Portions created by the Initial Developer are Copyright (C) 2005 * the Initial Developer. All Rights Reserved. * * Contributor(s): * Stuart Parmenter * Vladimir Vukicevic * * Alternatively, the contents of this file may be used under the terms of * either the GNU General Public License Version 2 or later (the "GPL"), or * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"), * in which case the provisions of the GPL or the LGPL are applicable instead * of those above. If you wish to allow use of your version of this file only * under the terms of either the GPL or the LGPL, and not to allow others to * use your version of this file under the terms of the MPL, indicate your * decision by deleting the provisions above and replace them with the notice * and other provisions required by the GPL or the LGPL. If you do not delete * the provisions above, a recipient may use your version of this file under * the terms of any one of the MPL, the GPL or the LGPL. * * ***** END LICENSE BLOCK ***** */ #ifdef _MSC_VER #define _USE_MATH_DEFINES #endif #include #ifndef M_PI #define M_PI 3.14159265358979323846 #endif #include "cairo.h" #include "gfxContext.h" #include "gfxColor.h" #include "gfxMatrix.h" #include "gfxASurface.h" #include "gfxPattern.h" #include "gfxPlatform.h" #include "gfxTeeSurface.h" gfxContext::gfxContext(gfxASurface *surface) : mSurface(surface) { MOZ_COUNT_CTOR(gfxContext); mCairo = cairo_create(surface->CairoSurface()); mFlags = surface->GetDefaultContextFlags(); } gfxContext::~gfxContext() { cairo_destroy(mCairo); MOZ_COUNT_DTOR(gfxContext); } gfxASurface * gfxContext::OriginalSurface() { return mSurface; } already_AddRefed gfxContext::CurrentSurface(gfxFloat *dx, gfxFloat *dy) { cairo_surface_t *s = cairo_get_group_target(mCairo); if (s == mSurface->CairoSurface()) { if (dx && dy) cairo_surface_get_device_offset(s, dx, dy); gfxASurface *ret = mSurface; NS_ADDREF(ret); return ret; } if (dx && dy) cairo_surface_get_device_offset(s, dx, dy); return gfxASurface::Wrap(s); } void gfxContext::Save() { cairo_save(mCairo); } void gfxContext::Restore() { cairo_restore(mCairo); } // drawing void gfxContext::NewPath() { cairo_new_path(mCairo); } void gfxContext::ClosePath() { cairo_close_path(mCairo); } already_AddRefed gfxContext::CopyPath() const { nsRefPtr path = new gfxPath(cairo_copy_path(mCairo)); return path.forget(); } void gfxContext::AppendPath(gfxPath* path) { if (path->mPath->status == CAIRO_STATUS_SUCCESS && path->mPath->num_data != 0) cairo_append_path(mCairo, path->mPath); } gfxPoint gfxContext::CurrentPoint() const { double x, y; cairo_get_current_point(mCairo, &x, &y); return gfxPoint(x, y); } void gfxContext::Stroke() { cairo_stroke_preserve(mCairo); } void gfxContext::Fill() { cairo_fill_preserve(mCairo); } void gfxContext::FillWithOpacity(gfxFloat aOpacity) { // This method exists in the hope that one day cairo gets a direct // API for this, and then we would change this method to use that // API instead. if (aOpacity != 1.0) { gfxContextAutoSaveRestore saveRestore(this); Clip(); Paint(aOpacity); } else { Fill(); } } void gfxContext::MoveTo(const gfxPoint& pt) { cairo_move_to(mCairo, pt.x, pt.y); } void gfxContext::NewSubPath() { cairo_new_sub_path(mCairo); } void gfxContext::LineTo(const gfxPoint& pt) { cairo_line_to(mCairo, pt.x, pt.y); } void gfxContext::CurveTo(const gfxPoint& pt1, const gfxPoint& pt2, const gfxPoint& pt3) { cairo_curve_to(mCairo, pt1.x, pt1.y, pt2.x, pt2.y, pt3.x, pt3.y); } void gfxContext::QuadraticCurveTo(const gfxPoint& pt1, const gfxPoint& pt2) { double cx, cy; cairo_get_current_point(mCairo, &cx, &cy); cairo_curve_to(mCairo, (cx + pt1.x * 2.0) / 3.0, (cy + pt1.y * 2.0) / 3.0, (pt1.x * 2.0 + pt2.x) / 3.0, (pt1.y * 2.0 + pt2.y) / 3.0, pt2.x, pt2.y); } void gfxContext::Arc(const gfxPoint& center, gfxFloat radius, gfxFloat angle1, gfxFloat angle2) { cairo_arc(mCairo, center.x, center.y, radius, angle1, angle2); } void gfxContext::NegativeArc(const gfxPoint& center, gfxFloat radius, gfxFloat angle1, gfxFloat angle2) { cairo_arc_negative(mCairo, center.x, center.y, radius, angle1, angle2); } void gfxContext::Line(const gfxPoint& start, const gfxPoint& end) { MoveTo(start); LineTo(end); } // XXX snapToPixels is only valid when snapping for filled // rectangles and for even-width stroked rectangles. // For odd-width stroked rectangles, we need to offset x/y by // 0.5... void gfxContext::Rectangle(const gfxRect& rect, PRBool snapToPixels) { if (snapToPixels) { gfxRect snappedRect(rect); if (UserToDevicePixelSnapped(snappedRect, PR_TRUE)) { cairo_matrix_t mat; cairo_get_matrix(mCairo, &mat); cairo_identity_matrix(mCairo); Rectangle(snappedRect); cairo_set_matrix(mCairo, &mat); return; } } cairo_rectangle(mCairo, rect.X(), rect.Y(), rect.Width(), rect.Height()); } void gfxContext::Ellipse(const gfxPoint& center, const gfxSize& dimensions) { gfxSize halfDim = dimensions / 2.0; gfxRect r(center - gfxPoint(halfDim.width, halfDim.height), dimensions); gfxCornerSizes c(halfDim, halfDim, halfDim, halfDim); RoundedRectangle (r, c); } void gfxContext::Polygon(const gfxPoint *points, PRUint32 numPoints) { if (numPoints == 0) return; cairo_move_to(mCairo, points[0].x, points[0].y); for (PRUint32 i = 1; i < numPoints; ++i) { cairo_line_to(mCairo, points[i].x, points[i].y); } } void gfxContext::DrawSurface(gfxASurface *surface, const gfxSize& size) { cairo_save(mCairo); cairo_set_source_surface(mCairo, surface->CairoSurface(), 0, 0); cairo_new_path(mCairo); // pixel-snap this Rectangle(gfxRect(gfxPoint(0.0, 0.0), size), PR_TRUE); cairo_fill(mCairo); cairo_restore(mCairo); } // transform stuff void gfxContext::Translate(const gfxPoint& pt) { cairo_translate(mCairo, pt.x, pt.y); } void gfxContext::Scale(gfxFloat x, gfxFloat y) { cairo_scale(mCairo, x, y); } void gfxContext::Rotate(gfxFloat angle) { cairo_rotate(mCairo, angle); } void gfxContext::Multiply(const gfxMatrix& matrix) { const cairo_matrix_t& mat = reinterpret_cast(matrix); cairo_transform(mCairo, &mat); } void gfxContext::SetMatrix(const gfxMatrix& matrix) { const cairo_matrix_t& mat = reinterpret_cast(matrix); cairo_set_matrix(mCairo, &mat); } void gfxContext::IdentityMatrix() { cairo_identity_matrix(mCairo); } gfxMatrix gfxContext::CurrentMatrix() const { cairo_matrix_t mat; cairo_get_matrix(mCairo, &mat); return gfxMatrix(*reinterpret_cast(&mat)); } void gfxContext::NudgeCurrentMatrixToIntegers() { cairo_matrix_t mat; cairo_get_matrix(mCairo, &mat); gfxMatrix(*reinterpret_cast(&mat)).NudgeToIntegers(); cairo_set_matrix(mCairo, &mat); } gfxPoint gfxContext::DeviceToUser(const gfxPoint& point) const { gfxPoint ret = point; cairo_device_to_user(mCairo, &ret.x, &ret.y); return ret; } gfxSize gfxContext::DeviceToUser(const gfxSize& size) const { gfxSize ret = size; cairo_device_to_user_distance(mCairo, &ret.width, &ret.height); return ret; } gfxRect gfxContext::DeviceToUser(const gfxRect& rect) const { gfxRect ret = rect; cairo_device_to_user(mCairo, &ret.x, &ret.y); cairo_device_to_user_distance(mCairo, &ret.width, &ret.height); return ret; } gfxPoint gfxContext::UserToDevice(const gfxPoint& point) const { gfxPoint ret = point; cairo_user_to_device(mCairo, &ret.x, &ret.y); return ret; } gfxSize gfxContext::UserToDevice(const gfxSize& size) const { gfxSize ret = size; cairo_user_to_device_distance(mCairo, &ret.width, &ret.height); return ret; } gfxRect gfxContext::UserToDevice(const gfxRect& rect) const { double xmin = rect.X(), ymin = rect.Y(), xmax = rect.XMost(), ymax = rect.YMost(); double x[3], y[3]; x[0] = xmin; y[0] = ymax; x[1] = xmax; y[1] = ymax; x[2] = xmax; y[2] = ymin; cairo_user_to_device(mCairo, &xmin, &ymin); xmax = xmin; ymax = ymin; for (int i = 0; i < 3; i++) { cairo_user_to_device(mCairo, &x[i], &y[i]); xmin = NS_MIN(xmin, x[i]); xmax = NS_MAX(xmax, x[i]); ymin = NS_MIN(ymin, y[i]); ymax = NS_MAX(ymax, y[i]); } return gfxRect(xmin, ymin, xmax - xmin, ymax - ymin); } PRBool gfxContext::UserToDevicePixelSnapped(gfxRect& rect, PRBool ignoreScale) const { if (GetFlags() & FLAG_DISABLE_SNAPPING) return PR_FALSE; // if we're not at 1.0 scale, don't snap, unless we're // ignoring the scale. If we're not -just- a scale, // never snap. const gfxFloat epsilon = 0.0000001; #define WITHIN_E(a,b) (fabs((a)-(b)) < epsilon) cairo_matrix_t mat; cairo_get_matrix(mCairo, &mat); if (!ignoreScale && (!WITHIN_E(mat.xx,1.0) || !WITHIN_E(mat.yy,1.0) || !WITHIN_E(mat.xy,0.0) || !WITHIN_E(mat.yx,0.0))) return PR_FALSE; #undef WITHIN_E gfxPoint p1 = UserToDevice(rect.TopLeft()); gfxPoint p2 = UserToDevice(rect.TopRight()); gfxPoint p3 = UserToDevice(rect.BottomRight()); // Check that the rectangle is axis-aligned. For an axis-aligned rectangle, // two opposite corners define the entire rectangle. So check if // the axis-aligned rectangle with opposite corners p1 and p3 // define an axis-aligned rectangle whose other corners are p2 and p4. // We actually only need to check one of p2 and p4, since an affine // transform maps parallelograms to parallelograms. if (p2 == gfxPoint(p1.x, p3.y) || p2 == gfxPoint(p3.x, p1.y)) { p1.Round(); p3.Round(); rect.MoveTo(gfxPoint(NS_MIN(p1.x, p3.x), NS_MIN(p1.y, p3.y))); rect.SizeTo(gfxSize(NS_MAX(p1.x, p3.x) - rect.X(), NS_MAX(p1.y, p3.y) - rect.Y())); return PR_TRUE; } return PR_FALSE; } PRBool gfxContext::UserToDevicePixelSnapped(gfxPoint& pt, PRBool ignoreScale) const { if (GetFlags() & FLAG_DISABLE_SNAPPING) return PR_FALSE; // if we're not at 1.0 scale, don't snap, unless we're // ignoring the scale. If we're not -just- a scale, // never snap. cairo_matrix_t mat; cairo_get_matrix(mCairo, &mat); if ((!ignoreScale && (mat.xx != 1.0 || mat.yy != 1.0)) || (mat.xy != 0.0 || mat.yx != 0.0)) return PR_FALSE; pt = UserToDevice(pt); pt.Round(); return PR_TRUE; } void gfxContext::PixelSnappedRectangleAndSetPattern(const gfxRect& rect, gfxPattern *pattern) { gfxRect r(rect); // Bob attempts to pixel-snap the rectangle, and returns true if // the snapping succeeds. If it does, we need to set up an // identity matrix, because the rectangle given back is in device // coordinates. // // We then have to call a translate to dr.pos afterwards, to make // sure the image lines up in the right place with our pixel // snapped rectangle. // // If snapping wasn't successful, we just translate to where the // pattern would normally start (in app coordinates) and do the // same thing. gfxMatrix mat = CurrentMatrix(); if (UserToDevicePixelSnapped(r)) { IdentityMatrix(); } Translate(r.TopLeft()); r.MoveTo(gfxPoint(0, 0)); Rectangle(r); SetPattern(pattern); SetMatrix(mat); } void gfxContext::SetAntialiasMode(AntialiasMode mode) { if (mode == MODE_ALIASED) { cairo_set_antialias(mCairo, CAIRO_ANTIALIAS_NONE); } else if (mode == MODE_COVERAGE) { cairo_set_antialias(mCairo, CAIRO_ANTIALIAS_DEFAULT); } } gfxContext::AntialiasMode gfxContext::CurrentAntialiasMode() const { cairo_antialias_t aa = cairo_get_antialias(mCairo); if (aa == CAIRO_ANTIALIAS_NONE) return MODE_ALIASED; return MODE_COVERAGE; } void gfxContext::SetDash(gfxLineType ltype) { static double dash[] = {5.0, 5.0}; static double dot[] = {1.0, 1.0}; switch (ltype) { case gfxLineDashed: SetDash(dash, 2, 0.0); break; case gfxLineDotted: SetDash(dot, 2, 0.0); break; case gfxLineSolid: default: SetDash(nsnull, 0, 0.0); break; } } void gfxContext::SetDash(gfxFloat *dashes, int ndash, gfxFloat offset) { cairo_set_dash(mCairo, dashes, ndash, offset); } //void getDash() const; void gfxContext::SetLineWidth(gfxFloat width) { cairo_set_line_width(mCairo, width); } gfxFloat gfxContext::CurrentLineWidth() const { return cairo_get_line_width(mCairo); } void gfxContext::SetOperator(GraphicsOperator op) { if (mFlags & FLAG_SIMPLIFY_OPERATORS) { if (op != OPERATOR_SOURCE && op != OPERATOR_CLEAR && op != OPERATOR_OVER) op = OPERATOR_OVER; } cairo_set_operator(mCairo, (cairo_operator_t)op); } gfxContext::GraphicsOperator gfxContext::CurrentOperator() const { return (GraphicsOperator)cairo_get_operator(mCairo); } void gfxContext::SetLineCap(GraphicsLineCap cap) { cairo_set_line_cap(mCairo, (cairo_line_cap_t)cap); } gfxContext::GraphicsLineCap gfxContext::CurrentLineCap() const { return (GraphicsLineCap)cairo_get_line_cap(mCairo); } void gfxContext::SetLineJoin(GraphicsLineJoin join) { cairo_set_line_join(mCairo, (cairo_line_join_t)join); } gfxContext::GraphicsLineJoin gfxContext::CurrentLineJoin() const { return (GraphicsLineJoin)cairo_get_line_join(mCairo); } void gfxContext::SetMiterLimit(gfxFloat limit) { cairo_set_miter_limit(mCairo, limit); } gfxFloat gfxContext::CurrentMiterLimit() const { return cairo_get_miter_limit(mCairo); } void gfxContext::SetFillRule(FillRule rule) { cairo_set_fill_rule(mCairo, (cairo_fill_rule_t)rule); } gfxContext::FillRule gfxContext::CurrentFillRule() const { return (FillRule)cairo_get_fill_rule(mCairo); } // clipping void gfxContext::Clip(const gfxRect& rect) { cairo_new_path(mCairo); cairo_rectangle(mCairo, rect.X(), rect.Y(), rect.Width(), rect.Height()); cairo_clip(mCairo); } void gfxContext::Clip() { cairo_clip_preserve(mCairo); } void gfxContext::ResetClip() { cairo_reset_clip(mCairo); } void gfxContext::UpdateSurfaceClip() { NewPath(); // we paint an empty rectangle to ensure the clip is propagated to // the destination surface SetDeviceColor(gfxRGBA(0,0,0,0)); Rectangle(gfxRect(0,1,1,0)); Fill(); } gfxRect gfxContext::GetClipExtents() { double xmin, ymin, xmax, ymax; cairo_clip_extents(mCairo, &xmin, &ymin, &xmax, &ymax); return gfxRect(xmin, ymin, xmax - xmin, ymax - ymin); } // rendering sources void gfxContext::SetColor(const gfxRGBA& c) { if (gfxPlatform::GetCMSMode() == eCMSMode_All) { gfxRGBA cms; gfxPlatform::TransformPixel(c, cms, gfxPlatform::GetCMSRGBTransform()); // Use the original alpha to avoid unnecessary float->byte->float // conversion errors cairo_set_source_rgba(mCairo, cms.r, cms.g, cms.b, c.a); } else cairo_set_source_rgba(mCairo, c.r, c.g, c.b, c.a); } void gfxContext::SetDeviceColor(const gfxRGBA& c) { cairo_set_source_rgba(mCairo, c.r, c.g, c.b, c.a); } PRBool gfxContext::GetDeviceColor(gfxRGBA& c) { return cairo_pattern_get_rgba(cairo_get_source(mCairo), &c.r, &c.g, &c.b, &c.a) == CAIRO_STATUS_SUCCESS; } void gfxContext::SetSource(gfxASurface *surface, const gfxPoint& offset) { NS_ASSERTION(surface->GetAllowUseAsSource(), "Surface not allowed to be used as source!"); cairo_set_source_surface(mCairo, surface->CairoSurface(), offset.x, offset.y); } void gfxContext::SetPattern(gfxPattern *pattern) { cairo_set_source(mCairo, pattern->CairoPattern()); } already_AddRefed gfxContext::GetPattern() { cairo_pattern_t *pat = cairo_get_source(mCairo); NS_ASSERTION(pat, "I was told this couldn't be null"); gfxPattern *wrapper = nsnull; if (pat) wrapper = new gfxPattern(pat); else wrapper = new gfxPattern(gfxRGBA(0,0,0,0)); NS_IF_ADDREF(wrapper); return wrapper; } // masking void gfxContext::Mask(gfxPattern *pattern) { cairo_mask(mCairo, pattern->CairoPattern()); } void gfxContext::Mask(gfxASurface *surface, const gfxPoint& offset) { cairo_mask_surface(mCairo, surface->CairoSurface(), offset.x, offset.y); } void gfxContext::Paint(gfxFloat alpha) { cairo_paint_with_alpha(mCairo, alpha); } // groups void gfxContext::PushGroup(gfxASurface::gfxContentType content) { cairo_push_group_with_content(mCairo, (cairo_content_t) content); } static gfxRect GetRoundOutDeviceClipExtents(gfxContext* aCtx) { gfxContextMatrixAutoSaveRestore save(aCtx); aCtx->IdentityMatrix(); gfxRect r = aCtx->GetClipExtents(); r.RoundOut(); return r; } /** * Copy the contents of aSrc to aDest, translated by aTranslation. */ static void CopySurface(gfxASurface* aSrc, gfxASurface* aDest, const gfxPoint& aTranslation) { cairo_t *cr = cairo_create(aDest->CairoSurface()); cairo_set_source_surface(cr, aSrc->CairoSurface(), aTranslation.x, aTranslation.y); cairo_set_operator(cr, CAIRO_OPERATOR_SOURCE); cairo_paint(cr); cairo_destroy(cr); } void gfxContext::PushGroupAndCopyBackground(gfxASurface::gfxContentType content) { if (content == gfxASurface::CONTENT_COLOR_ALPHA && !(GetFlags() & FLAG_DISABLE_COPY_BACKGROUND)) { nsRefPtr s = CurrentSurface(); if ((s->GetAllowUseAsSource() || s->GetType() == gfxASurface::SurfaceTypeTee) && (s->GetContentType() == gfxASurface::CONTENT_COLOR || s->GetOpaqueRect().Contains(GetRoundOutDeviceClipExtents(this)))) { cairo_push_group_with_content(mCairo, CAIRO_CONTENT_COLOR); nsRefPtr d = CurrentSurface(); if (d->GetType() == gfxASurface::SurfaceTypeTee) { NS_ASSERTION(s->GetType() == gfxASurface::SurfaceTypeTee, "Mismatched types"); nsAutoTArray,2> ss; nsAutoTArray,2> ds; static_cast(s.get())->GetSurfaces(&ss); static_cast(d.get())->GetSurfaces(&ds); NS_ASSERTION(ss.Length() == ds.Length(), "Mismatched lengths"); gfxPoint translation = d->GetDeviceOffset() - s->GetDeviceOffset(); for (PRUint32 i = 0; i < ss.Length(); ++i) { CopySurface(ss[i], ds[i], translation); } } else { CopySurface(s, d, gfxPoint(0, 0)); } d->SetOpaqueRect(s->GetOpaqueRect()); return; } } cairo_push_group_with_content(mCairo, (cairo_content_t) content); } already_AddRefed gfxContext::PopGroup() { cairo_pattern_t *pat = cairo_pop_group(mCairo); gfxPattern *wrapper = new gfxPattern(pat); cairo_pattern_destroy(pat); NS_IF_ADDREF(wrapper); return wrapper; } void gfxContext::PopGroupToSource() { cairo_pop_group_to_source(mCairo); } PRBool gfxContext::PointInFill(const gfxPoint& pt) { return cairo_in_fill(mCairo, pt.x, pt.y); } PRBool gfxContext::PointInStroke(const gfxPoint& pt) { return cairo_in_stroke(mCairo, pt.x, pt.y); } gfxRect gfxContext::GetUserPathExtent() { double xmin, ymin, xmax, ymax; cairo_path_extents(mCairo, &xmin, &ymin, &xmax, &ymax); return gfxRect(xmin, ymin, xmax - xmin, ymax - ymin); } gfxRect gfxContext::GetUserFillExtent() { double xmin, ymin, xmax, ymax; cairo_fill_extents(mCairo, &xmin, &ymin, &xmax, &ymax); return gfxRect(xmin, ymin, xmax - xmin, ymax - ymin); } gfxRect gfxContext::GetUserStrokeExtent() { double xmin, ymin, xmax, ymax; cairo_stroke_extents(mCairo, &xmin, &ymin, &xmax, &ymax); return gfxRect(xmin, ymin, xmax - xmin, ymax - ymin); } already_AddRefed gfxContext::GetFlattenedPath() { gfxFlattenedPath *path = new gfxFlattenedPath(cairo_copy_path_flat(mCairo)); NS_IF_ADDREF(path); return path; } PRBool gfxContext::HasError() { return cairo_status(mCairo) != CAIRO_STATUS_SUCCESS; } void gfxContext::RoundedRectangle(const gfxRect& rect, const gfxCornerSizes& corners, PRBool draw_clockwise) { // // 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 gfxFloat alpha = 0.55191497064665766025; typedef struct { gfxFloat a, b; } twoFloats; twoFloats cwCornerMults[4] = { { -1, 0 }, { 0, -1 }, { +1, 0 }, { 0, +1 } }; twoFloats ccwCornerMults[4] = { { +1, 0 }, { 0, -1 }, { -1, 0 }, { 0, +1 } }; twoFloats *cornerMults = draw_clockwise ? cwCornerMults : ccwCornerMults; gfxPoint pc, p0, p1, p2, p3; if (draw_clockwise) cairo_move_to(mCairo, rect.X() + corners[NS_CORNER_TOP_LEFT].width, rect.Y()); else cairo_move_to(mCairo, rect.X() + rect.Width() - corners[NS_CORNER_TOP_RIGHT].width, rect.Y()); NS_FOR_CSS_CORNERS(i) { // the corner index -- either 1 2 3 0 (cw) or 0 3 2 1 (ccw) mozilla::css::Corner c = mozilla::css::Corner(draw_clockwise ? ((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 = rect.AtCorner(c); if (corners[c].width > 0.0 && corners[c].height > 0.0) { p0.x = pc.x + cornerMults[i].a * corners[c].width; p0.y = pc.y + cornerMults[i].b * corners[c].height; p3.x = pc.x + cornerMults[i3].a * corners[c].width; p3.y = pc.y + cornerMults[i3].b * corners[c].height; p1.x = p0.x + alpha * cornerMults[i2].a * corners[c].width; p1.y = p0.y + alpha * cornerMults[i2].b * corners[c].height; p2.x = p3.x - alpha * cornerMults[i3].a * corners[c].width; p2.y = p3.y - alpha * cornerMults[i3].b * corners[c].height; cairo_line_to (mCairo, p0.x, p0.y); cairo_curve_to (mCairo, p1.x, p1.y, p2.x, p2.y, p3.x, p3.y); } else { cairo_line_to (mCairo, pc.x, pc.y); } } cairo_close_path (mCairo); }