QList<RVector> RShape::getIntersectionPointsLT(const RLine& line1,
const RTriangle& triangle2, bool limited) {
QList<RVector> res;
RVector normal = triangle2.getNormal();
if (normal.getMagnitude() < 1.0e-12) {
return res;
}
if (line1.getLength() < 1.0e-12) {
return res;
}
double t = RVector::getDotProduct(normal, triangle2.getCorner(2) - line1.getStartPoint())
/ RVector::getDotProduct(normal, (line1.getEndPoint() - line1.getStartPoint()));
// check if intersection point is on the line:
if (limited && (t < 0.0 || t > 1.0)) {
return res;
}
// intersection point:
RVector ip = line1.getStartPoint() + (line1.getEndPoint() - line1.getStartPoint()) * t;
// check if intersection point is inside the triangle:
if (!limited || triangle2.isPointInTriangle(ip)) {
res.push_back(ip);
}
return res;
}
void RPainterPathExporter::exportLineSegment(const RLine& line, double angle) {
if (line.getLength()<RS::PointTolerance) {
if (exportZeroLinesAsPoints) {
path.addPoint(line.getStartPoint());
}
else {
// Qt won't export a zero length line as point:
// e.g. dot in a dash/dot line:
RVector startPoint = line.startPoint - RVector::createPolar(0.01, angle);
RVector endPoint = line.endPoint + RVector::createPolar(0.01, angle);
path.moveTo(startPoint);
path.lineTo(endPoint);
// path.moveTo(line.getStartPoint()-RVector(0.01,0));
// path.lineTo(line.getEndPoint()+RVector(0.01, 0));
// path.moveTo(line.getStartPoint()-RVector(0,0.01));
// path.lineTo(line.getEndPoint()+RVector(0, 0.01));
}
}
else {
if (!path.isAtPosition(line.getStartPoint())) {
path.moveTo(line.getStartPoint());
}
path.lineTo(line.getEndPoint());
}
}
void RPainterPathExporter::exportLineSegment(const RLine& line) {
if (line.getLength()<RS::PointTolerance) {
path.addPoint(line.getStartPoint());
}
else {
path.moveTo(line.getStartPoint());
path.lineTo(line.getEndPoint());
}
}
RVector RVector::rotate3D(const RLine& axis, double rotation) {
RVector off = -axis.getStartPoint();
RVector ret = *this;
ret.move(off);
RVector ax = axis.getStartPoint() - axis.getEndPoint();
QQuaternion quat = QQuaternion::fromAxisAndAngle(ax.x, ax.y, ax.z, RMath::rad2deg(rotation));
QVector3D qv = quat.rotatedVector(QVector3D(ret.x, ret.y, ret.z));
ret = RVector(qv.x(), qv.y(), qv.z());
ret.move(-off);
*this = ret;
return *this;
}
void RSpline::appendToExploded(const RLine& line) const {
if (line.getLength()<1.0e-6) {
return;
}
if (!exploded.isEmpty()) {
// compare angle of this sement with last segment and
// modify last segment if angle is the same (straight line):
QSharedPointer<RLine> prev = exploded.last().dynamicCast<RLine>();
if (!prev.isNull()) {
if (RMath::fuzzyCompare(prev->getAngle(), prev->getStartPoint().getAngleTo(line.getEndPoint()))) {
prev->setEndPoint(line.getEndPoint());
return;
}
}
}
exploded.append(QSharedPointer<RShape>(new RLine(line)));
}
QList<RVector> RShape::getIntersectionPointsLE(const RLine& line1,
const REllipse& ellipse2, bool limited) {
QList<RVector> res;
// find out if line1 is (almost) a tangent:
QList<RLine> tangents = ellipse2.getTangents(line1.getMiddlePoint());
for (int i=0; i<tangents.length(); i++) {
double a = tangents[i].getAngle();
double ad1 = fabs(RMath::getAngleDifference180(a, line1.getDirection1()));
double ad2 = fabs(RMath::getAngleDifference180(a, line1.getDirection2()));
if (ad1 < 1.0e-2 || ad2 < 1.0e-2) {
res.append(tangents[i].getEndPoint());
// no need to continue: max. one tangent possible:
return res;
}
}
// rotate into normal position:
double ang = ellipse2.getAngle();
double rx = ellipse2.getMajorRadius();
double ry = ellipse2.getMinorRadius();
RVector center = ellipse2.getCenter();
RVector a1 = line1.getStartPoint();
a1.rotate(-ang, center);
RVector a2 = line1.getEndPoint();
a2.rotate(-ang, center);
RVector origin = a1;
RVector dir = a2-a1;
RVector diff = origin - center;
RVector mDir = RVector(dir.x/(rx*rx), dir.y/(ry*ry));
RVector mDiff = RVector(diff.x/(rx*rx), diff.y/(ry*ry));
double a = RVector::getDotProduct(dir, mDir);
double b = RVector::getDotProduct(dir, mDiff);
double c = RVector::getDotProduct(diff, mDiff) - 1.0;
double d = b*b - a*c;
RVector res1 = RVector::invalid;
RVector res2 = RVector::invalid;
if (d < 0) {
// no solution
} else if ( d > 0 ) {
double root = sqrt(d);
double t_a = (-b - root) / a;
double t_b = (-b + root) / a;
res1 = a1.getLerp(a2, t_a).rotate(ang, center);
res2 = a1.getLerp(a2, t_b).rotate(ang, center);
} else {
double t = -b/a;
if ( 0 <= t && t <= 1 ) {
// one solution:
res1 = a1.getLerp(a2, t).rotate(ang, center);
} else {
// no solution
}
}
if (res1.isValid()) {
if (!limited || (line1.isOnShape(res1) && ellipse2.isOnShape(res1))) {
res.append(res1);
}
}
if (res2.isValid()) {
if (!limited || (line1.isOnShape(res2) && ellipse2.isOnShape(res2))) {
res.append(res2);
}
}
return res;
}
QList<RVector> RShape::getIntersectionPointsLC(const RLine& line1,
const RCircle& circle2, bool limited) {
QList<RVector> res;
RVector vLineCenter = line1.getVectorTo(circle2.getCenter(), false);
double dist = vLineCenter.getMagnitude();
// special case: arc touches line (tangent):
if (fabs(dist - circle2.getRadius()) < 1.0e-4) {
res.append(circle2.getCenter() - vLineCenter);
// ret.setTangent(true);
return res;
}
RVector p = line1.getStartPoint();
RVector d = line1.getEndPoint() - line1.getStartPoint();
if (d.getMagnitude() < 1.0e-6) {
return res;
}
RVector delta = p - circle2.getCenter();
// root term:
double term = RMath::pow(RVector::getDotProduct(d, delta), 2.0)
- RMath::pow(d.getMagnitude(), 2.0)
* (RMath::pow(delta.getMagnitude(), 2.0) - RMath::pow(circle2.getRadius(), 2.0));
// no intersection:
if (term<0.0) {
return res;
}
// one or two intersections:
double t1 = (- RVector::getDotProduct(d, delta) + sqrt(term))
/ RMath::pow(d.getMagnitude(), 2.0);
double t2;
bool tangent = false;
// only one intersection:
if (fabs(term) < RS::PointTolerance) {
t2 = t1;
tangent = true;
}
// two intersections
else {
t2 = (-RVector::getDotProduct(d, delta) - sqrt(term))
/ RMath::pow(d.getMagnitude(), 2.0);
}
RVector sol1;
RVector sol2 = RVector::invalid;
sol1 = p + d * t1;
if (!tangent) {
sol2 = p + d * t2;
}
if (!limited || line1.isOnShape(sol1)) {
res.append(sol1);
}
if (sol2.isValid()) {
if (!limited || line1.isOnShape(sol2)) {
res.append(sol2);
}
}
// ret.setTangent(tangent);
return res;
}
RXLine::RXLine(const RLine& line) :
basePoint(line.getStartPoint()), directionVector(line.getEndPoint()-line.getStartPoint()) {
}