/**
* Determine closest point on hyperbolic arm to a point pt
*
* @param pt : point
* @return t value for closest point; not necessarily within clipped range
*/
public double closestPointTo(FPoint2 pt) {
final boolean db = false;
pt = toCurveSpace(pt, null);
double U = B + 1;
double V = -pt.y;
double W = B * pt.x;
Polyn p =
new Polyn( //
B * U * U, //
2 * B * U * V, //
B * V * V + A * U * U - W * W, //
2 * A * U * V, //
A * V * V //
);
if (db) Streams.out.println("closestPointTo, pt=" + pt + "\n" + p);
double ret = 0;
try {
DArray r = new DArray();
if (Math.abs(p.c(0)) < 1e-5) r.addDouble(0);
else p.solve(r);
if (r.isEmpty()) {
throw new FPError("can't find closest point, poly=\n" + p);
}
double bestDist = 0;
for (int i = 0; i < r.size(); i++) {
double t = r.getDouble(i);
FPoint2 apt = calcPoint(t);
double dist = apt.distance(pt);
if (i == 0 || dist < bestDist) {
bestDist = dist;
ret = t;
}
}
} catch (FPError e) {
Tools.warn("caught FPError");
// Streams.out.println("caught:\n" + e);
ret = (this.minParameter() + this.maxParameter()) * .5;
}
return ret;
}
/**
* Calculate dx, dy values for a point
*
* @param t : parameter
* @param delta : where to store dx, dy values
*/
private void calcTangentAt(double t, FPoint2 delta) {
final boolean db = false;
if (db) {
System.out.println("calcTangentAt " + t);
}
t = toInt(t);
if (db) {
System.out.println(" flipped=" + flipped() + " ti=" + t);
}
double a = toW2.get(0, 0), b = toW2.get(0, 1), c = toW2.get(0, 2);
double d = toW2.get(1, 0), e = toW2.get(1, 1), f = toW2.get(1, 2);
if (db) {
System.out.println(" a=" + a + " b=" + b + " c=" + c + "\n d=" + d + " e=" + e + " f=" + f);
}
double rt = Polyn.sqrt(A + B * t * t);
double dx = a * B * t / rt + b;
double dy = d * B * t / rt + e;
if (flipped()) {
dx = -dx;
dy = -dy;
}
if (db) {
System.out.println(" dx=" + dx + "\n dy=" + dy);
System.out.println(" ratio=" + (dy / dx));
}
delta.setLocation(dx, dy);
}
/**
* Determine where point is relative to arm
*
* @param x :
* @param y : point to test
* @return an integer, which is 0 if it's on the arm, 1 if it's to the right of the arm, -1 if
* it's to the left of the arm
*/
public int testPoint(double x, double y) {
final FPoint2 ept = new FPoint2(), eps = new FPoint2();
eps.setLocation(x, y);
toCurveSpace(eps, ept);
FPoint2 as = calcPointInArmSpace(toExt(ept.y));
int out = 0;
double diff = ept.x - as.x;
if (diff > 0) {
out = 1;
} else if (diff < 0) {
out = -1;
}
if (flipped()) {
out = -out;
}
return out;
}
/**
* Construct a hyperbola
*
* @param f1 FPoint2 : first focus
* @param f2 FPoint2 : second focus
* @param interceptDistance : closest distance of point on arm to f1
*/
public Hyperbola(FPoint2 f1, FPoint2 f2, double interceptDistance) {
double fDist = f2.distance(f1);
if (!(interceptDistance >= 0 && interceptDistance <= fDist))
throw new FPError(
"Hyperbola construction: icept="
+ Tools.f(interceptDistance)
+ " of max "
+ Tools.f(fDist)
+ "\n f1="
+ f1
+ " f2="
+ f2);
double ratio = 0;
if (fDist > 0) {
ratio = interceptDistance / fDist;
}
FPoint2 pt = FPoint2.interpolate(f1, f2, ratio);
construct(f1, f2, pt);
}
/**
* Test program for Hyperbola class
*
* @param args String[]
*/
public static void main(String[] args) {
final double[] pts = { //
100, 0, -100, 0, 75, 20,
// 120, 30, -100, -10, 70, 50,
};
for (int i = 0; i < pts.length; i += 6) {
try {
Hyperbola h =
new Hyperbola(
new FPoint2(pts[i + 0], pts[i + 1]),
new FPoint2(pts[i + 2], pts[i + 3]),
new FPoint2(pts[i + 4], pts[i + 5]));
System.out.println("Constructed:\n" + h);
for (double t = -50; t <= 50; t += 10) {
FPoint2 pt = h.calcPoint(t);
FPoint2 pt2 = new FPoint2(pt.x, pt.y + 5);
double tClosest = h.closestPointTo(pt2);
System.out.println("t=" + Tools.f(t) + " pt=" + pt + " closest=" + tClosest);
if (t == -20) {
for (double t2 = tClosest - .1; t2 <= tClosest + .1; t2 += .01) {
FPoint2 pt3 = h.calcPoint(t2);
Streams.out.println("t2=" + t2 + " dist=" + pt3.distance(pt2));
}
}
}
} catch (TBError e) {
System.out.println(e.toString());
}
}
}
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));
//
// }
}
}
public void render(Color c, int stroke, int markType) {
final boolean db = false;
// Get array of visible segments. If no such array exists,
// use default.
DArray vseg = visSeg;
boolean dashed = false;
// if (step == 0) {
double step = renderStep();
// }
// vp V = TestBed.view();
if (db) Streams.out.println(" step=" + step);
// plot each visible segment
for (int seg = 0; seg < vseg.size(); seg += 2) {
double t0 = vseg.getDouble(seg + 0), t1 = vseg.getDouble(seg + 1);
t0 = MyMath.clamp(t0, -500.0, 500.0);
t1 = MyMath.clamp(t1, -500.0, 500.0);
// render() expects external parameters.
double s0 = toExt(t0), s1 = toExt(t1);
if (s0 > s1) {
double tmp = s0;
s0 = s1;
s1 = tmp;
}
FPoint2 p0 = calcPoint(s0), p1 = calcPoint(s1);
if (db) Streams.out.println(" p0=" + p0 + ", p1=" + p1);
if (isLine() && !dashed) {
V.drawLine(p0, p1);
} else {
/*
if (Math.abs(s0) >= 500
||Math.abs(s1) >= 500)
System.out.println("Rendering "+t0+" to "+t1+" step "+step);
*/
if (dashed) V.pushStroke(Globals.STRK_RUBBERBAND);
{
// int count = 0;
boolean first = true;
for (double t = t0; ; t += step) { // , count++) {
boolean last = (t >= t1);
if (last) {
t = t1;
}
calcPointInternal(t, p1);
if (!p1.isValid()) {
if (last) {
break;
}
continue;
}
if (db) {
System.out.println(" calcPt " + Tools.f(toExt(t)) + " = " + p1.x + "," + p1.y);
}
if (!first) {
V.drawLine(p0, p1);
if (false) {
Tools.warn("highlighting int");
V.mark(p0);
}
}
if (last) {
break;
}
p0.setLocation(p1);
first = false;
}
}
if (dashed) V.popStroke();
}
}
}
/**
* Constructor
*
* @param f1 FPoint2
* @param f2 FPoint2
* @param pt FPoint2, or null for bisector
*/
private void construct(FPoint2 f1, FPoint2 f2, FPoint2 pt) {
// userData[LEFT] = new DArray();
// userData[RIGHT] =new DArray();
final boolean db = false;
if (db) {
System.out.println("Hyperbola constructor\n f1=" + f1 + "\n f2=" + f2 + "\n pt=" + pt);
}
boolean bisector = (pt == null);
initializeVisibleSegments();
// if point on arm is closer to f2 than f1, swap f1 & f2.
if (!bisector && FPoint2.distanceSquared(f1, pt) > FPoint2.distanceSquared(f2, pt)) {
flipped = true;
}
this.foci[RIGHT] = new FPoint2(f1);
this.foci[LEFT] = new FPoint2(f2);
if (!bisector) {
this.pt = new FPoint2(pt);
}
double fociDist = FPoint2.distance(f1, f2);
if (fociDist == 0) {
throw new FPError("Hyperbola foci are same point");
}
c = fociDist * .5;
// calculate the translation of the hyperbola away from
// standard position.
FPoint2 rFocus = getFocus(0), lFocus = getFocus(1);
origin = new FPoint2(.5 * (rFocus.x + lFocus.x), .5 * (rFocus.y + lFocus.y));
// calculate the angle of rotation of the hyperbola away
// from the standard position.
double theta = Math.atan2(rFocus.y - lFocus.y, rFocus.x - lFocus.x);
Matrix fromCenterInW = Matrix.getTranslate(origin, true);
Matrix rotToE = Matrix.getRotate(-theta);
toE2 = rotToE;
Matrix.mult(toE2, fromCenterInW, toE2);
// calculate inverse
toW2 = toE2.invert(null);
// Matrix toCenterInW = Matrix.translationMatrix(origin, false);
// Matrix rotToW = Matrix.getRotate2D(theta);
//
// toW2 = toCenterInW;
// Matrix.mult(toW2, rotToW, toW2);
// Tools.warn("just invert matrix here");
//
if (bisector) {
valid = true;
} else {
// get the arm point in hyperbola space.
FPoint2 workPt = toE2.apply(pt, null);
double xs = workPt.x * workPt.x;
double cs = c * c;
Polyn q = new Polyn(1, -(cs + xs + workPt.y * workPt.y), cs * xs);
if (db) {
System.out.println("a2 quadratic:\n" + q);
}
final DArray qsoln = new DArray();
q.solve(qsoln);
if (db) {
Streams.out.println(qsoln);
}
double val = q.c(1) * -.5;
int ql = qsoln.size();
if (ql >= 1) {
val = qsoln.getDouble(0);
}
// choose the root that is less than c*c.
if (ql == 2) {
if (val > qsoln.getDouble(1)) {
val = qsoln.getDouble(1);
if (db) {
System.out.println(" two roots, choosing smaller.");
}
}
}
if (db) {
System.out.println(" root chosen=" + val);
}
a = Polyn.sqrt(val);
A = a * a;
B = A / (c * c - A);
}
valid = true;
if (db) {
System.out.println(" ==> " + this);
}
}