/**
* Calculate possible hull of a pair of polygons
*
* @param a
* @param b
* @return possible hull
*/
private static EdPolygon calcPHull(EdPolygon aPoly, EdPolygon bPoly) {
final boolean db = true;
if (db && T.update())
T.msg(
"calc possible hull of two polygons"
+ T.show(aPoly, MyColor.cBLUE, STRK_THICK, -1)
+ T.show(bPoly, MyColor.cDARKGREEN, STRK_THICK, -1));
PtEntry a = PtEntry.buildFrom(aPoly);
PtEntry b = PtEntry.buildFrom(bPoly);
PtEntry aHull = PtEntry.convexHull(a);
PtEntry bHull = PtEntry.convexHull(b);
inf = Inf.create();
if (db && T.update()) {
T.msg(
"convex hulls"
+ T.show(aHull.toPolygon(), MyColor.cBLUE, STRK_THICK, -1)
+ T.show(bHull.toPolygon(), MyColor.cDARKGREEN, STRK_THICK, -1));
}
PtEntry ph = hullOfPolygons(a, b, aHull, bHull);
traceHullPt = ph;
insertValleys(ph, a.source(), b.source());
expandHull(ph, aHull, bHull, true);
expandHull(ph, aHull, bHull, false);
return ph.toPolygon();
}
/**
* Calc possible hull from a set of polygons
*
* @param polySet set of polygons
* @param first first polygon to include
* @param last last polygon to include
* @return polygon containing possible hull
*/
private static EdPolygon calcPHullRange(EdPolygon[] polySet, int first, int last) {
final boolean db = true;
int len = last + 1 - first;
if (len == 1) return polySet[first];
if (len > 2) {
if (db && T.update()) {
DArray a = new DArray();
for (int i = first; i <= last; i++) a.add(polySet[i]);
T.msg("calc possible hull of multiple polygons" + T.show(a, MyColor.cRED, STRK_THICK, -1));
}
int n = len / 2;
return calcPHull(
calcPHullRange(polySet, first, first + n - 1), calcPHullRange(polySet, first + n, last));
}
return calcPHull(polySet[first], polySet[first + 1]);
}
private void construct(EdDisc a, EdDisc b) {
this.discA = a;
this.discB = b;
if (EdDisc.partiallyDisjoint(a, b)) {
// if (!UHullMain.oldBitanMethod())
{
final boolean db = false;
if (a.getRadius() == b.getRadius()) {
FPoint2 oa = a.getOrigin(), ob = b.getOrigin();
FPoint2 n = new FPoint2(-(ob.y - oa.y), ob.x - oa.x);
n.normalize();
n.x *= a.getRadius();
n.y *= a.getRadius();
seg = new DirSeg(FPoint2.add(oa, n, null), FPoint2.add(ob, n, null));
return;
}
boolean swap = a.getRadius() > b.getRadius();
if (swap) {
b = (EdDisc) discA;
a = (EdDisc) discB;
}
if (db && T.update())
T.msg(
"BiTangent construct, arad="
+ Tools.f(a.getRadius())
+ " brad="
+ Tools.f(b.getRadius())
+ " swap="
+ swap
+ " origin.a="
+ T.show(a.getOrigin()));
FPoint2 oa = a.getOrigin();
FPoint2 ob = b.getOrigin();
double U = ob.x, V = ob.y;
double A = oa.x - U, B = oa.y - V;
double R1 = a.getRadius();
double R2 = b.getRadius();
double S = R2 - R1;
double x1, y1, x2, y2;
x1 = A;
y1 = B;
boolean secondRoot;
boolean altSlope = Math.abs(B) < Math.abs(A);
if (!altSlope) {
double C1 = S * S / B, C2 = -A / B;
double qA = 1 + C2 * C2, qB = 2 * C1 * C2, qC = C1 * C1 - S * S;
double root = Math.sqrt(qB * qB - 4 * qA * qC);
x2 = (-qB - root) / (2 * qA);
y2 = C1 + C2 * x2;
secondRoot = MyMath.sideOfLine(x2, y2, A, B, 0, 0) < 0;
if (swap ^ secondRoot) {
x2 = (-qB + root) / (2 * qA);
y2 = C1 + C2 * x2;
}
} else {
double C1 = S * S / A, C2 = -B / A;
double qA = 1 + C2 * C2, qB = 2 * C1 * C2, qC = C1 * C1 - S * S;
double root = Math.sqrt(qB * qB - 4 * qA * qC);
y2 = (-qB - root) / (2 * qA);
x2 = C1 + C2 * y2;
secondRoot = MyMath.sideOfLine(x2, y2, A, B, 0, 0) < 0;
if (swap ^ secondRoot) {
y2 = (-qB + root) / (2 * qA);
x2 = C1 + C2 * y2;
}
}
// now grow both discs back to r1, r2
double tx = U;
double ty = V;
// if (S == 0) {
// FPoint2 unit = new FPoint2(-A, -B);
// if (swap) {
// unit.x = -unit.x;
// unit.y = -unit.y;
// }
// unit.normalize();
// tx += -unit.y * R1;
// ty += unit.x * R1;
// } else
{
double F = R1 / S;
tx += x2 * F;
ty += y2 * F;
}
if (db && T.update())
T.msg("adding offset to both points: " + tx + ", " + ty + T.show(new FPoint2(tx, ty)));
x1 += tx;
y1 += ty;
x2 += tx;
y2 += ty;
FPoint2 p1 = new FPoint2(x1, y1);
FPoint2 p2 = new FPoint2(x2, y2);
if (swap) {
FPoint2 tmp = p1;
p1 = p2;
p2 = tmp;
}
seg = new DirSeg(p1, p2);
if (db && T.update())
T.msg(
"swap="
+ swap
+ " altSlope="
+ altSlope
+ " secondRoot="
+ secondRoot
+ " dirseg="
+ EdSegment.showDirected(p1, p2));
}
// else {
//
// double th = calcTheta(a, b);
// LineEqn eqn = new LineEqn(a.polarPoint(th + Math.PI / 2), th);
// double ta = eqn.parameterFor(a.getOrigin());
// double tb = eqn.parameterFor(b.getOrigin());
// seg = new DirSeg(eqn.pt(ta), eqn.pt(tb));
//
// }
}
}
private static void OLDexpandHull(
PtEntry convHullEntry, PtEntry aHull, PtEntry bHull, boolean ccw) {
boolean db__OLD = C.vb(DB_HULLEXPAND);
if (db__OLD && T.update()) T.msg("expandHull" + T.show(convHullEntry) + " ccw=" + ccw);
PtEntry[] opp = new PtEntry[2];
opp[0] = aHull;
opp[1] = bHull;
PtEntry old____hEnt = convHullEntry;
boolean advanced = false;
do {
if (old____hEnt != convHullEntry) advanced = true;
inf.update();
if (old____hEnt.source() == null) {
if (db__OLD && T.update())
T.msg("expandHull, source unknown, guaranteed not convex" + T.show(old____hEnt));
old____hEnt = old____hEnt.next(ccw);
continue;
}
int w = (old____hEnt.source() == opp[0].source()) ? 1 : 0;
PtEntry oppEnt = opp[w];
boolean isTangent =
!COper3.right(old____hEnt, oppEnt, oppEnt.next(true), ccw)
&& !COper3.right(old____hEnt, oppEnt, oppEnt.prev(true), ccw);
if (!isTangent) {
if (db__OLD && T.update())
T.msg(
"expandHull, advance tangent line"
+ T.show(oppEnt.toPolygon(), MyColor.cDARKGRAY, -1, MARK_X)
+ T.show(old____hEnt)
+ tl(old____hEnt, oppEnt));
opp[w] = oppEnt.next(ccw);
continue;
}
if (COper3.left(old____hEnt, oppEnt, old____hEnt.next(ccw), ccw)
&& COper3.left(old____hEnt, oppEnt, old____hEnt.prev(ccw), ccw)) {
DArray dispPts = new DArray();
// delete points until cross tangent line
PtEntry next = old____hEnt.next(ccw);
while (true) {
PtEntry prev = next;
dispPts.add(prev);
next = prev.delete(ccw);
inf.update();
if (COper3.right(old____hEnt, oppEnt, next, ccw)) {
FPoint2 cross = MyMath.linesIntersection(old____hEnt, oppEnt, prev, next, null);
old____hEnt = old____hEnt.insert(new PtEntry(cross), ccw);
if (db__OLD && T.update())
T.msg(
"expandHull, clipped to shadow region"
+ tl(old____hEnt, oppEnt)
+ T.show(old____hEnt)
+ T.show(dispPts));
break;
}
}
} else {
if (db__OLD && T.update())
T.msg(
"expandHull, not dipping into shadow region"
+ T.show(old____hEnt.next(ccw))
+ tl(old____hEnt, oppEnt));
}
old____hEnt = old____hEnt.next(ccw);
} while (!advanced || old____hEnt != convHullEntry);
}
/**
* 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;
}
private static void insertValleys(
PtEntry hullPt, Object aSrc, Object bSrc) { // pa, MyPolygon pb) {
boolean db = C.vb(DB_INSERTVALLEY);
PtEntry ent = hullPt;
if (db && T.update()) T.msg("insertValleys");
do {
PtEntry next = ent.next(true);
if (ent.source() == next.source()) {
PtEntry orig = ent.orig();
if (orig.next(true) != next.orig()) {
PtEntry vPeak0 = ent;
PtEntry vPeak1 = next;
EdPolygon opp = (EdPolygon) (vPeak0.source() == aSrc ? bSrc : aSrc);
FPoint2 kernelPt = opp.getPointMod(C.vi(KERNELVERT));
// construct a chain from the vertices of the valley
PtEntry handle = new PtEntry(vPeak0);
PtEntry hNext = handle;
PtEntry e = vPeak0.orig();
while (e != vPeak1.orig()) {
inf.update();
e = e.next(true);
hNext = hNext.insert(new PtEntry(e), true);
}
if (C.vb(SKIPCONTOUR)) {
PtEntry h0 = handle.next(true);
PtEntry h1 = hNext.prev(true);
PtEntry.join(vPeak0, h0);
PtEntry.join(h1, vPeak1);
if (db && T.update())
T.msg("inserted unmodified valley" + T.show(vPeak0) + T.show(vPeak1));
} else {
if (!C.vb(DB_CONTOUR)) T.disable();
PtEntry hull = COper3.buildHullForChain(handle, kernelPt);
if (!C.vb(DB_CONTOUR)) T.enable();
// find entries corresponding to start, end of hull
PtEntry peak0 = null, peak1 = null;
{
PtEntry hEnt = hull;
while (peak0 == null || peak1 == null) {
inf.update();
if (hEnt.orig() == vPeak0.orig()) peak0 = hEnt;
if (hEnt.orig() == vPeak1.orig()) peak1 = hEnt;
hEnt = hEnt.next(true);
}
}
PtEntry.join(vPeak0, peak0.next(true));
PtEntry.join(peak1.prev(true), vPeak1);
if (db && T.update())
T.msg("inserted monotonic valley" + T.show(vPeak0) + T.show(vPeak1));
}
}
}
ent = next;
} while (ent != hullPt);
}
/**
* Apply hull expansion procedure
*
* @param convHullEntry an entry of the hull (should be on the convex hull, so it is not deleted
* or replaced and is still valid for subsequent calls)
* @param aHull entry on convex hull of polygon A
* @param bHull entry on convex hull of polygon B
* @param ccw true to move in ccw direction, else cw
*/
private static void expandHull(PtEntry convHullEntry, PtEntry aHull, PtEntry bHull, boolean ccw) {
if (C.vb(OLDMETHOD)) {
OLDexpandHull(convHullEntry, aHull, bHull, ccw);
return;
}
boolean db = C.vb(DB_HULLEXPAND);
if (db && T.update()) T.msg("expandHull" + T.show(convHullEntry) + " ccw=" + ccw);
// tangent points for A, B
PtEntry[] tangentPoints = new PtEntry[2];
tangentPoints[0] = aHull;
tangentPoints[1] = bHull;
PtEntry hEnt = convHullEntry;
do {
inf.update();
// calculate tangent ray R
PtEntry tangentPt = null;
while (true) {
int tanIndex = (hEnt.source() == tangentPoints[0].source()) ? 1 : 0;
tangentPt = tangentPoints[tanIndex];
if (!COper3.right(hEnt, tangentPt, tangentPt.next(true), ccw)
&& !COper3.right(hEnt, tangentPt, tangentPt.prev(true), ccw)) break;
tangentPt = tangentPt.next(ccw);
if (db && T.update())
T.msg(
"expandHull, advance tangent line"
+ T.show(tangentPt.toPolygon(), MyColor.cDARKGRAY, -1, MARK_DISC)
+ T.show(hEnt)
+ tl(hEnt, tangentPt));
tangentPoints[tanIndex] = tangentPt;
}
if (COper3.left(hEnt, tangentPt, hEnt.next(ccw), ccw)) {
DArray dispPts = new DArray();
// delete points until cross tangent line
PtEntry next = hEnt.next(ccw);
while (true) {
PtEntry prev = next;
dispPts.add(prev);
next = prev.delete(ccw);
if (COper3.right(hEnt, tangentPt, next, ccw)) {
FPoint2 cross = MyMath.linesIntersection(hEnt, tangentPt, prev, next, null);
hEnt = hEnt.insert(new PtEntry(cross), ccw);
if (db && T.update())
T.msg(
"expandHull, clipped to shadow region"
+ tl(hEnt, tangentPt)
+ T.show(hEnt)
+ T.show(dispPts));
break;
}
}
} else {
if (db && T.update())
T.msg(
"expandHull, not dipping into shadow region"
+ T.show(hEnt.next(ccw))
+ tl(hEnt, tangentPt));
}
while (true) {
hEnt = hEnt.next(ccw);
if (COper3.left(hEnt.prev(ccw), hEnt, hEnt.next(ccw), ccw)) break;
if (db && T.update()) T.msg("skipping reflex vertex" + T.show(hEnt));
}
} while (hEnt != convHullEntry);
}