// calc axes
protected final void compute() {
// only parabola has directrix
if (c.type == GeoConic.CONIC_PARABOLA) {
// directrix has direction of second eigenvector
// through point (b - p/2* eigenvec1)
directrix.x = -eigenvec[1].y;
directrix.y = eigenvec[1].x;
double px = b.x - c.p / 2.0 * eigenvec[0].x;
double py = b.y - c.p / 2.0 * eigenvec[0].y;
directrix.z = -(directrix.x * px + directrix.y * py);
P.setCoords(px, py, 1.0);
} else directrix.setUndefined();
}
// compute circle through A, B, C
protected void compute() {
// A, B or C undefined
if (!getA().isFinite() || !getB().isFinite() || !getC().isFinite()) {
circle.setUndefined();
return;
}
// get inhomogenous coords of points
ax = ((GeoPoint) getA()).inhomX;
ay = ((GeoPoint) getA()).inhomY;
bx = ((GeoPoint) getB()).inhomX;
by = ((GeoPoint) getB()).inhomY;
cx = ((GeoPoint) getC()).inhomX;
cy = ((GeoPoint) getC()).inhomY;
// A = B = C
if (kernel.isEqual(ax, bx)
&& kernel.isEqual(ax, cx)
&& kernel.isEqual(ay, by)
&& kernel.isEqual(ay, cy)) {
circle.setCircle((GeoPoint) getA(), 0.0); // single point
return;
}
// calc vectors AB, AC, BC
ABx = bx - ax;
ABy = by - ay;
ACx = cx - ax;
ACy = cy - ay;
BCx = cx - bx;
BCy = cy - by;
double lengthAB = GeoVec2D.length(ABx, ABy);
double lengthAC = GeoVec2D.length(ACx, ACy);
double lengthBC = GeoVec2D.length(BCx, BCy);
// find the two bisectors with max intersection angle
// i.e. maximum abs of determinant of directions
// max( abs(det(AB, AC)), abs(det(AC, BC)), abs(det(AB, BC)) )
det[0] = Math.abs(ABx * ACy - ABy * ACx) / (lengthAB * lengthAC);
// AB, AC
det[1] = Math.abs(ACx * BCy - ACy * BCx) / (lengthAC * lengthBC);
// AC, BC
det[2] = Math.abs(ABx * BCy - ABy * BCx) / (lengthAB * lengthBC);
// AB, BC
// take ip[0] as init minimum and find minimum case
maxDet = det[0];
casenr = 0;
if (det[1] > maxDet) {
casenr = 1;
maxDet = det[1];
}
if (det[2] > maxDet) {
casenr = 2;
maxDet = det[2];
}
// A, B, C are collinear: set M to infinite point
// in perpendicular direction of AB
if (kernel.isZero(maxDet)) {
center.setCoords(-ABy, ABx, 0.0d);
circle.setCircle(center, (GeoPoint) getA());
}
// standard case
else {
// intersect two line bisectors according to casenr
switch (casenr) {
case 0: // bisectors of AB, AC
s0.x = ABx;
s0.y = ABy;
s0.z = -((ax + bx) * s0.x + (ay + by) * s0.y) / 2.0;
s1.x = ACx;
s1.y = ACy;
s1.z = -((ax + cx) * s1.x + (ay + cy) * s1.y) / 2.0;
break;
case 1: // bisectors of AC, BC
s1.x = ACx;
s1.y = ACy;
s1.z = -((ax + cx) * s1.x + (ay + cy) * s1.y) / 2.0;
s0.x = BCx;
s0.y = BCy;
s0.z = -((bx + cx) * s0.x + (by + cy) * s0.y) / 2.0;
break;
case 2: // bisectors of AB, BC
s0.x = ABx;
s0.y = ABy;
s0.z = -((ax + bx) * s0.x + (ay + by) * s0.y) / 2.0;
s1.x = BCx;
s1.y = BCy;
s1.z = -((bx + cx) * s1.x + (by + cy) * s1.y) / 2.0;
break;
}
// intersect line bisectors to get midpoint
GeoVec3D.cross(s0, s1, center);
circle.setCircle(center, center.distance(getA()));
}
}