diff options
Diffstat (limited to 'basegfx')
| -rw-r--r-- | basegfx/source/polygon/b2dpolygontools.cxx | 44 |
1 files changed, 28 insertions, 16 deletions
diff --git a/basegfx/source/polygon/b2dpolygontools.cxx b/basegfx/source/polygon/b2dpolygontools.cxx index e0cfcdba1933..f005f2519026 100644 --- a/basegfx/source/polygon/b2dpolygontools.cxx +++ b/basegfx/source/polygon/b2dpolygontools.cxx @@ -1490,6 +1490,21 @@ namespace basegfx return false; } + // Calculates distance of curve point to its control point for a Bézier curve, that + // approximates a unit circle arc. fAngle is the center angle of the circle arc. The + // constrain 0<=fAngle<=pi/2 must not be violated to give a useful accuracy. For details + // and alternatives read document "ApproxCircleInfo.odt", attachment of bug tdf#121425. + static double impDistanceBezierPointToControl(double fAngle) + { + SAL_WARN_IF(fAngle < 0 || fAngle > F_PI2,"basegfx","angle not suitable for approximate circle"); + if (0 <= fAngle && fAngle <= F_PI2) + { + return 4.0/3.0 * ( tan(fAngle/4.0)); + } + else + return 0; + } + B2DPolygon createPolygonFromRect( const B2DRectangle& rRect, double fRadiusX, double fRadiusY ) { const double fZero(0.0); @@ -1549,7 +1564,7 @@ namespace basegfx B2DPolygon aRetval; const double fBowX((rRect.getWidth() / 2.0) * fRadiusX); const double fBowY((rRect.getHeight() / 2.0) * fRadiusY); - const double fKappa((M_SQRT2 - 1.0) * 4.0 / 3.0); + const double fKappa(impDistanceBezierPointToControl(F_PI2)); // create start point at bottom center if(!rtl::math::approxEqual(fOne, fRadiusX)) @@ -1657,13 +1672,12 @@ namespace basegfx static B2DPolygon impCreateUnitCircle(sal_uInt32 nStartQuadrant) { B2DPolygon aUnitCircle; - const double fKappa((M_SQRT2 - 1.0) * 4.0 / 3.0); - const double fScaledKappa(fKappa * (1.0 / STEPSPERQUARTER)); + const double fSegmentKappa = impDistanceBezierPointToControl(F_PI2 / STEPSPERQUARTER); const B2DHomMatrix aRotateMatrix(createRotateB2DHomMatrix(F_PI2 / STEPSPERQUARTER)); B2DPoint aPoint(1.0, 0.0); - B2DPoint aForward(1.0, fScaledKappa); - B2DPoint aBackward(1.0, -fScaledKappa); + B2DPoint aForward(1.0, fSegmentKappa); + B2DPoint aBackward(1.0, -fSegmentKappa); if(nStartQuadrant != 0) { @@ -1697,12 +1711,11 @@ namespace basegfx B2DPolygon operator()() { B2DPolygon aUnitHalfCircle; - const double fKappa((M_SQRT2 - 1.0) * 4.0 / 3.0); - const double fScaledKappa(fKappa * (1.0 / STEPSPERQUARTER)); + const double fSegmentKappa(impDistanceBezierPointToControl(F_PI2 / STEPSPERQUARTER)); const B2DHomMatrix aRotateMatrix(createRotateB2DHomMatrix(F_PI2 / STEPSPERQUARTER)); B2DPoint aPoint(1.0, 0.0); - B2DPoint aForward(1.0, fScaledKappa); - B2DPoint aBackward(1.0, -fScaledKappa); + B2DPoint aForward(1.0, fSegmentKappa); + B2DPoint aBackward(1.0, -fSegmentKappa); aUnitHalfCircle.append(aPoint); @@ -1815,8 +1828,7 @@ namespace basegfx const double fAnglePerSegment(F_PI2 / STEPSPERQUARTER); const sal_uInt32 nStartSegment(sal_uInt32(fStart / fAnglePerSegment) % nSegments); const sal_uInt32 nEndSegment(sal_uInt32(fEnd / fAnglePerSegment) % nSegments); - const double fKappa((M_SQRT2 - 1.0) * 4.0 / 3.0); - const double fScaledKappa(fKappa * (1.0 / STEPSPERQUARTER)); + const double fSegmentKappa(impDistanceBezierPointToControl(fAnglePerSegment)); B2DPoint aSegStart(cos(fStart), sin(fStart)); aRetval.append(aSegStart); @@ -1825,7 +1837,7 @@ namespace basegfx { // start and end in one sector and in the right order, create in one segment const B2DPoint aSegEnd(cos(fEnd), sin(fEnd)); - const double fFactor(fScaledKappa * ((fEnd - fStart) / fAnglePerSegment)); + const double fFactor(impDistanceBezierPointToControl(fEnd - fStart)); aRetval.appendBezierSegment( aSegStart + (B2DPoint(-aSegStart.getY(), aSegStart.getX()) * fFactor), @@ -1835,7 +1847,7 @@ namespace basegfx else { double fSegEndRad((nStartSegment + 1) * fAnglePerSegment); - double fFactor(fScaledKappa * ((fSegEndRad - fStart) / fAnglePerSegment)); + double fFactor(impDistanceBezierPointToControl(fSegEndRad - fStart)); B2DPoint aSegEnd(cos(fSegEndRad), sin(fSegEndRad)); aRetval.appendBezierSegment( @@ -1853,8 +1865,8 @@ namespace basegfx aSegEnd = B2DPoint(cos(fSegEndRad), sin(fSegEndRad)); aRetval.appendBezierSegment( - aSegStart + (B2DPoint(-aSegStart.getY(), aSegStart.getX()) * fScaledKappa), - aSegEnd - (B2DPoint(-aSegEnd.getY(), aSegEnd.getX()) * fScaledKappa), + aSegStart + (B2DPoint(-aSegStart.getY(), aSegStart.getX()) * fSegmentKappa), + aSegEnd - (B2DPoint(-aSegEnd.getY(), aSegEnd.getX()) * fSegmentKappa), aSegEnd); nSegment = (nSegment + 1) % nSegments; @@ -1863,7 +1875,7 @@ namespace basegfx // End in this sector const double fSegStartRad(nSegment * fAnglePerSegment); - fFactor = fScaledKappa * ((fEnd - fSegStartRad) / fAnglePerSegment); + fFactor= impDistanceBezierPointToControl(fEnd - fSegStartRad); aSegEnd = B2DPoint(cos(fEnd), sin(fEnd)); aRetval.appendBezierSegment( |