/**
* Creates an arc from 3 points.
*/
RArc RArc::createFrom3Points(const RVector& startPoint,
const RVector& point,
const RVector& endPoint) {
// intersection of two middle lines
// middle points between first two points:
RVector mp1 = RVector::getAverage(startPoint, point);
double a1 = startPoint.getAngleTo(point) + M_PI / 2.0;
// direction from middle point to center:
RVector dir1 = RVector::createPolar(1.0, a1);
// middle points between last two points:
RVector mp2 = RVector::getAverage(point, endPoint);
double a2 = point.getAngleTo(endPoint) + M_PI / 2.0;
// direction from middle point to center:
RVector dir2 = RVector::createPolar(1.0, a2);
RLine midLine1(mp1, mp1 + dir1);
RLine midLine2(mp2, mp2 + dir2);
QList<RVector> ips = midLine1.getIntersectionPoints(midLine2, false);
if (ips.length()!=1) {
//this.error = qsTr("No arc possible");
return RArc();
}
RVector center = ips[0];
double radius = center.getDistanceTo(endPoint);
double angle1 = center.getAngleTo(startPoint);
double angle2 = center.getAngleTo(endPoint);
bool reversed = RMath::isAngleBetween(center.getAngleTo(point),
angle1, angle2, true);
return RArc(center, radius, angle1, angle2, reversed);
}
RCircle RCircle::createFrom3Points(const RVector& p1,
const RVector& p2,
const RVector& p3) {
// intersection of two middle lines
// middle points between first two points:
RVector mp1 = RVector::getAverage(p1, p2);
double a1 = p1.getAngleTo(p2) + M_PI / 2.0;
// direction from middle point to center:
RVector dir1 = RVector::createPolar(1.0, a1);
// middle points between last two points:
RVector mp2 = RVector::getAverage(p2, p3);
double a2 = p2.getAngleTo(p3) + M_PI / 2.0;
// direction from middle point to center:
RVector dir2 = RVector::createPolar(1.0, a2);
RLine midLine1(mp1, mp1 + dir1);
RLine midLine2(mp2, mp2 + dir2);
QList<RVector> ips = midLine1.getIntersectionPoints(midLine2, false);
if (ips.length()!=1) {
return RCircle();
}
RVector center = ips[0];
double radius = center.getDistanceTo(p3);
// double angle1 = center.getAngleTo(p1);
// double angle2 = center.getAngleTo(p3);
// bool reversed = RMath::isAngleBetween(center.getAngleTo(p2),
// angle1, angle2, true);
return RCircle(center, radius);
}
/**
* Creates this arc from 3 given points which define the arc line.
*
* @param p1 1st point.
* @param p2 2nd point.
* @param p3 3rd point.
*/
bool RS_Arc::createFrom3P(const RS_Vector& p1, const RS_Vector& p2,
const RS_Vector& p3) {
if (p1.distanceTo(p2)>RS_TOLERANCE &&
p2.distanceTo(p3)>RS_TOLERANCE &&
p3.distanceTo(p1)>RS_TOLERANCE) {
// middle points between 3 points:
RS_Vector mp1, mp2;
RS_Vector dir1, dir2;
double a1, a2;
// intersection of two middle lines
mp1 = (p1 + p2)/2.0;
a1 = p1.angleTo(p2) + M_PI/2.0;
dir1.setPolar(100.0, a1);
mp2 = (p2 + p3)/2.0;
a2 = p2.angleTo(p3) + M_PI/2.0;
dir2.setPolar(100.0, a2);
RS_ConstructionLineData d1(mp1, mp1 + dir1);
RS_ConstructionLineData d2(mp2, mp2 + dir2);
RS_ConstructionLine midLine1(NULL, d1);
RS_ConstructionLine midLine2(NULL, d2);
RS_VectorSolutions sol =
RS_Information::getIntersection(&midLine1, &midLine2);
data.center = sol.get(0);
data.radius = data.center.distanceTo(p3);
data.angle1 = data.center.angleTo(p1);
data.angle2 = data.center.angleTo(p3);
data.reversed = RS_Math::isAngleBetween(data.center.angleTo(p2),
data.angle1, data.angle2, true);
if (sol.get(0).valid && data.radius<1.0e14 &&
data.radius>RS_TOLERANCE) {
calculateEndpoints();
calculateBorders();
return true;
} else {
RS_DEBUG->print("RS_Arc::createFrom3P(): "
"Cannot create an arc with inf radius.");
return false;
}
} else {
RS_DEBUG->print("RS_Arc::createFrom3P(): "
"Cannot create an arc with radius 0.0.");
return false;
}
}