public double thetaP() {
return MyMath.normalizeAnglePositive(theta());
}
/**
* Determine convex hull of two polygons, using rotating calipers method
*
* @param pa first polygon
* @param pb second polygon
* @return convex hull structure
*/
private static PtEntry hullOfPolygons(PtEntry pa, PtEntry pb, PtEntry aHull, PtEntry bHull) {
boolean db = C.vb(DB_INITIALHULL);
if (db && T.update())
T.msg(
"construct convex hull of polygons"
+ T.show(pa, MyColor.cBLUE, STRK_THICK, -1)
+ T.show(pb, MyColor.cDARKGREEN, STRK_THICK, -1));
PtEntry hullVertex = null;
// A hull vertex and index
PtEntry av = rightMostVertex(aHull);
// B hull vertex and index
PtEntry bv = rightMostVertex(bHull);
double theta = Math.PI / 2;
LineEqn aLine = new LineEqn(av, theta);
int bSide = aLine.sideOfLine(bv);
boolean bActive = (bSide == 0) ? (bv.y > av.y) : bSide < 0;
if (db && T.update()) T.msg("rightmost vertices" + T.show(av) + T.show(bv));
// construct initial vertex of hull
hullVertex = new PtEntry(!bActive ? av : bv);
// if (db && T.update())
// T.msg("constructed initial hull vertex: " + hullVertex);
PtEntry.join(hullVertex, hullVertex);
PtEntry firstEnt = hullVertex;
while (true) {
Inf.update(inf);
PtEntry av2 = av.next(true);
PtEntry bv2 = bv.next(true);
// next vertex is either A advance, B advance, or bridge
double anga = MyMath.polarAngle(av, av2);
double angb = MyMath.polarAngle(bv, bv2);
double angBridge = bActive ? MyMath.polarAngle(bv, av) : MyMath.polarAngle(av, bv);
double ta = MyMath.normalizeAnglePositive(anga - theta);
double tb = MyMath.normalizeAnglePositive(angb - theta);
double tc = MyMath.normalizeAnglePositive(angBridge - theta);
// precision problem: if A and B tangent lines are parallel, both can
// reach near zero simultaneously
final double MAX = Math.PI * 2 - 1e-3;
if (ta >= MAX) ta = 0;
if (tb >= MAX) tb = 0;
if (tc >= MAX) tc = 0;
theta += Math.min(ta, Math.min(tb, tc));
if (db && T.update())
T.msg("caliper" + T.show(hullVertex) + tr(hullVertex, theta) + tp(av) + tp(bv));
PtEntry newPoint = null;
if (ta <= tb && ta <= tc) {
if (db && T.update()) T.msg("A vertex is nearest" + tl(av, av2));
// ai++;
av = av2;
if (!bActive) newPoint = av;
} else if (tb <= ta && tb <= tc) {
if (db && T.update()) T.msg("B vertex is nearest" + tl(bv, bv2));
// bi++;
bv = bv2;
if (bActive) newPoint = bv;
} else {
if (db && T.update())
T.msg("Bridge vertex is nearest" + tl(bActive ? bv : av, bActive ? av : bv));
bActive ^= true;
newPoint = bActive ? bv : av;
}
if (newPoint != null) {
if (PtEntry.samePoint(newPoint, firstEnt)) {
break;
}
// construct new vertex for hull of the two;
// remember, use original vertex, not the convex hull
hullVertex = hullVertex.insert(new PtEntry(newPoint), true);
if (db && T.update()) T.msg("adding new caliper vertex " + T.show(hullVertex));
}
}
return hullVertex;
}