/** * \return List of splines which approximate the given arc. */ QList<RSpline> RSpline::createSplinesFromArc(const RArc& arc) { RArc a = arc; if (a.isReversed()) { a.reverse(); } double startAngle = RMath::getNormalizedAngle(a.getStartAngle()); double endAngle = RMath::getNormalizedAngle(a.getEndAngle()); if (a.isFullCircle()) { startAngle = 0.0; endAngle = 2*M_PI; } // normalize startAngle, endAngle to [-2PI, 2PI] double twoPI = M_PI * 2; //double startAngle = RMath::getNormalizedAngle(a.getStartAngle()); //double endAngle = RMath::getNormalizedAngle(a.getEndAngle()); if (startAngle>endAngle) { startAngle-=2*M_PI; } double radius = a.getRadius(); double EPSILON = 0.00001; // Compute the sequence of arc curves, up to PI/2 at a time. Total arc angle // is less than 2PI. QList<RSpline> curves; double piOverTwo = M_PI_2; double segmentationAngle = piOverTwo/4; //double segmentationAngle = M_PI/8; double sgn = (startAngle < endAngle) ? +1 : -1; double a1 = startAngle; for (double totalAngle = qMin(twoPI, qAbs(endAngle - startAngle)); totalAngle > EPSILON; ) { double a2 = a1 + sgn * qMin(totalAngle, segmentationAngle); RSpline sp = RSpline::createBezierFromSmallArc(radius, a1, a2); sp.move(a.getCenter()); curves.append(sp); totalAngle -= qAbs(a2 - a1); a1 = a2; } return curves; }
void RExporter::exportArcSegment(const RArc& arc, bool allowForZeroLength) { if (allowForZeroLength && arc.isFullCircle()) { exportLineSegment(RLine(arc.getStartPoint(), arc.getEndPoint()), arc.getDirection1()); return; } double segmentLength; if (pixelSizeHint>0.0) { // approximate arc with segments with the length of 2 pixels: segmentLength = pixelSizeHint * 2; } else { segmentLength = arc.getRadius() / 40.0; } // avoid a segment length of 0: if (segmentLength<1.0e-4) { segmentLength = 1.0e-4; } double a1 = arc.getStartAngle(); double a2 = arc.getEndAngle(); RVector center = arc.getCenter(); double radius = arc.getRadius(); double aStep; if (radius<1.0e-3) { aStep = 0.1; } else { aStep = segmentLength / radius; if (aStep>1.0) { aStep = 1.0; } double minAStep = RSettings::getMinArcAngleStep(); if (draftMode) { minAStep *= 4; } if (aStep<minAStep) { aStep = minAStep; } } RVector prev = arc.getStartPoint(); RVector ci; double a; if (!arc.isReversed()) { // Arc Counterclockwise: if(a1>a2-RS::AngleTolerance) { a2+=2*M_PI; } for (a=a1+aStep; a<=a2; a+=aStep) { ci.x = center.x + cos(a) * radius; ci.y = center.y + sin(a) * radius; exportLineSegment(RLine(prev, ci), a+M_PI_2); prev = ci; } } else { // Arc Clockwise: if (a1<a2+RS::AngleTolerance) { a2-=2*M_PI; } for (a=a1-aStep; a>=a2; a-=aStep) { ci.x = center.x + cos(a) * radius; ci.y = center.y + sin(a) * radius; exportLineSegment(RLine(prev, ci), a+M_PI_2); prev = ci; } } this->exportLineSegment(RLine(prev, arc.getEndPoint()), arc.getEndAngle()+M_PI_2); }