public AlgoCircleThreePoints(Construction cons, GeoPointND A, GeoPointND B, GeoPointND C) {
super(cons);
setPoints(A, B, C);
createCircle();
circle.addPointOnConic(getA());
circle.addPointOnConic(getB());
circle.addPointOnConic(getC());
// temp: line bisectors
s0 = new GeoLine(cons);
s1 = new GeoLine(cons);
center = new GeoPoint(cons);
setInputOutput(); // for AlgoElement
compute();
}
// compute incircle of triangle A, B, C
@Override
public void compute() {
// bisector of angle ABC
double dAB = getA().distance(getB());
double dAC = getA().distance(getC());
double dBC = getB().distance(getC());
double dmax = dAB > dBC ? dAB : dBC;
A1.setCoords(
dmax / dAB * (getA().inhomX - getB().inhomX) + getB().inhomX,
dmax / dAB * (getA().inhomY - getB().inhomY) + getB().inhomY,
1.0d);
C1.setCoords(
dmax / dBC * (getC().inhomX - getB().inhomX) + getB().inhomX,
dmax / dBC * (getC().inhomY - getB().inhomY) + getB().inhomY,
1.0d);
B1.setCoords((A1.inhomX + C1.inhomX) / 2.0d, (A1.inhomY + C1.inhomY) / 2.0d, 1.0d);
GeoVec3D.lineThroughPoints(getB(), B1, bisectorB);
// bisector of angle BCA
dmax = dAC > dBC ? dAC : dBC;
A1.setCoords(
dmax / dAC * (getA().inhomX - getC().inhomX) + getC().inhomX,
dmax / dAC * (getA().inhomY - getC().inhomY) + getC().inhomY,
1.0d);
B1.setCoords(
dmax / dBC * (getB().inhomX - getC().inhomX) + getC().inhomX,
dmax / dBC * (getB().inhomY - getC().inhomY) + getC().inhomY,
1.0d);
C1.setCoords((A1.inhomX + B1.inhomX) / 2.0d, (A1.inhomY + B1.inhomY) / 2.0d, 1.0d);
GeoVec3D.lineThroughPoints(getC(), C1, bisectorC);
// intersect angle bisectors to get incenter
GeoVec3D.lineThroughPoints(getB(), getC(), sideBC);
GeoVec3D.cross(bisectorB, bisectorC, incenter);
GeoVec3D.cross(incenter, sideBC.x, sideBC.y, 0.0, heightBC);
GeoVec3D.cross(sideBC, heightBC, heightFoot);
double dist = incenter.distance(heightFoot);
circle.setCircle(incenter, dist);
}
public AlgoIncircle(Construction cons, String label, GeoPointND A, GeoPointND B, GeoPointND C) {
this(cons, A, B, C);
circle.setLabel(label);
}
protected AlgoCircleThreePoints(
Construction cons, String label, GeoPointND A, GeoPointND B, GeoPointND C) {
this(cons, A, B, C);
circle.setLabel(label);
}
// 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()));
}
}