Length Toolbox::arcRadius(const Point& p1, const Point& p2,
const Angle& a) noexcept {
if (a == 0) {
return Length(0);
} else {
qreal x1 = p1.getX().toMm();
qreal y1 = p1.getY().toMm();
qreal x2 = p2.getX().toMm();
qreal y2 = p2.getY().toMm();
qreal angle = a.mappedTo180deg().toRad();
qreal d = qSqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1));
qreal r = d / (2 * qSin(angle / 2));
return Length::fromMm(r);
}
}
Point Toolbox::arcCenter(const Point& p1, const Point& p2,
const Angle& a) noexcept {
if (a == 0) {
// there is no arc center...just return the middle of start- and endpoint
return (p1 + p2) / 2;
} else {
// http://math.stackexchange.com/questions/27535/how-to-find-center-of-an-arc-given-start-point-end-point-radius-and-arc-direc
qreal x0 = p1.getX().toMm();
qreal y0 = p1.getY().toMm();
qreal x1 = p2.getX().toMm();
qreal y1 = p2.getY().toMm();
qreal angle = a.mappedTo180deg().toRad();
qreal angleSgn = (angle >= 0) ? 1 : -1;
qreal d = qSqrt((x1 - x0) * (x1 - x0) + (y1 - y0) * (y1 - y0));
qreal r = d / (2 * qSin(angle / 2));
qreal h = qSqrt(r * r - d * d / 4);
qreal u = (x1 - x0) / d;
qreal v = (y1 - y0) / d;
qreal a = ((x0 + x1) / 2) - h * v * angleSgn;
qreal b = ((y0 + y1) / 2) + h * u * angleSgn;
return Point::fromMm(a, b);
}
}