/**
* Calculate angle of tangent line at a particular point
*
* @param t : parameter
* @return angle
*/
public double calcDirectionAt(double t) {
final boolean db = false;
calcTangentAt(t, workPt);
double a = Math.atan2(workPt.y, workPt.x);
if (db) {
System.out.println("calcDirectionAt " + Tools.f(t) + " a=" + Tools.fa(a));
}
return a;
}
/**
* Clip out a section of the arm, using internal parameter values
*
* @param c0 : start of section to clip out
* @param c1 : end of section to clip out; if < c0, c0 & c1 are swapped
*/
private void clip0(double c0, double c1) {
final boolean db = false;
if (c0 > c1) {
double t = c0;
c0 = c1;
c1 = t;
}
// array to store new clip elements in
DArray nc = new DArray();
if (db) {
System.out.println("clip " + Tools.f(c0) + "..." + Tools.f(c1));
}
for (int i = 0; i < visSeg.size(); i += 2) {
double t0 = visSeg.getDouble(i), t1 = visSeg.getDouble(i + 1);
if (db) {
System.out.println(" seg " + i + " " + Tools.f(t0) + "..." + Tools.f(t1));
}
// if this seg is outside clip region, leave intact (add it)
if (t0 >= c1 || t1 <= c0) {
nc.addDouble(t0);
nc.addDouble(t1);
continue;
}
if (t0 >= c0 && t1 <= c1) {
if (db) {
System.out.println(" clipping entire segment");
}
// remove entire segment, by skipping it
continue;
}
// add unclipped portion
if (t0 < c0) {
nc.addDouble(t0);
nc.addDouble(c0);
}
if (t1 > c1) {
nc.addDouble(c1);
nc.addDouble(t1);
}
}
visSeg = nc;
if (db) {
System.out.println(" after clipping:" + visSeg);
}
}
public void render(Color c, int stroke, int markType) {
if (c == null) c = Color.RED;
V.pushColor(c);
if (defined()) {
seg.render(c, stroke, markType);
} else {
for (int i = 0; i < 2; i++) {
if (i == 1 && discA == discB) continue;
EdObject obj = object(i);
if (obj instanceof EdDisc) {
EdDisc d = (EdDisc) obj;
stroke = STRK_RUBBERBAND;
V.pushStroke(stroke);
double r = Math.max(d.getRadius() - 4, 2.0);
V.drawCircle(d.getOrigin(), r);
V.popStroke();
} else {
Tools.unimp("rendering undefined bitangents of polygons");
}
}
}
V.popColor();
}
/**
* 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);
}
/**
* 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;
}
public String visString() {
StringBuilder sb = new StringBuilder();
if (visSeg != null) {
for (int i = 0; i < visSeg.size(); i += 2) {
double t0 = 0, t1 = 0;
if (flipped()) {
int j = visSeg.size() - i - 2;
t0 = toExt(visSeg.getDouble(j + 1));
t1 = toExt(visSeg.getDouble(j));
} else {
t0 = visSeg.getDouble(i);
t1 = visSeg.getDouble(i + 1);
}
sb.append("<");
sb.append(Tools.f(t0));
sb.append("..");
sb.append(Tools.f(t1));
sb.append("> ");
}
}
return sb.toString();
}
/**
* 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());
}
}
}
/**
* Calculate a point on the hyperbola
*
* @param t : parameter in internal space (after flipping has occurred)
* @param dest : where to store the calculated point
*/
private FPoint2 calcPointInternal(double t, FPoint2 dest) {
final boolean db = false;
if (!valid) throw new FPError("calcPoint of invalid hyperbola");
// Tools.ASSERT(valid, "calcPoint of invalid hyperbola");
// final FPoint2 work = new FPoint2();
//
// work.setLocation(Polyn.sqrt(A + t * t * B), t);
dest = toW2.apply(Polyn.sqrt(A + t * t * B), t, dest);
//
// if (dest == null)
// dest = new FPoint2();
// Matrix.apply(toW2, work, dest);
if (db) {
System.out.println(
"calcPoint t="
+ Tools.f(toExt(t)) // + " armsp=" + work
+ " world="
+ dest);
}
return dest;
}
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));
//
// }
}
}
/**
* Construct a string
*
* @param javaMode : if true, generates java code to construct it
* @return String
*/
private String toString(boolean javaMode) {
StringBuilder sb = new StringBuilder();
// sb.setLength(0);
if (javaMode) {
sb.append(
"new Hyperbola(new FPoint2("
+ foci[RIGHT].x
+ ","
+ foci[RIGHT].y
+ "), new FPoint2("
+ foci[LEFT].x
+ ","
+ foci[LEFT].y
+ "), new FPoint2("
+ pt.x
+ ","
+ pt.y
+ "));");
} else {
sb.append("hyperbola: ");
if (!valid) {
sb.append("***INVALID***");
} else {
sb.append(
"f(r)="
+ foci[RIGHT]
+ " f(l)="
+ foci[LEFT]
+ " a="
+ Tools.f(a)
+ " c="
+ Tools.f(c));
sb.append(" flip=" + Tools.f(flipped()));
if (visSeg != null) {
sb.append("\nVisible segments: ");
for (int i = 0; i < visSeg.size(); i += 2) {
double t0 = 0, t1 = 0;
if (flipped()) {
int j = visSeg.size() - i - 2;
t0 = toExt(visSeg.getDouble(j + 1));
t1 = toExt(visSeg.getDouble(j));
} else {
t0 = visSeg.getDouble(i);
t1 = visSeg.getDouble(i + 1);
}
sb.append("<");
sb.append(Tools.f(t0));
sb.append("..");
sb.append(Tools.f(t1));
sb.append("> ");
}
sb.append("\n");
}
}
}
return sb.toString();
}
/**
* Find intersections of hyperbolic arm with an axes-aligned line segment. Arm must intersect
* segment, not its underlying (infinite) line. The intersection points are sorted into increasing
* parameter values w.r.t. the arm.
*
* @param s0 : start of line segment
* @param s1 : end of line segment
* @param ipts : intersection points returned here
* @param reverseOrder : if true, points are sorted by decreasing parameter values
* @param dbFlag : true to print debug information
*/
public void findOrthogonalIntersect(
FPoint2 s0, FPoint2 s1, DArray ipts, boolean reverseOrder, boolean dbFlag) {
final boolean db = true && dbFlag;
if (db) {
System.out.println(
"findOrthogonalIntersect " + s0 + " -> " + s1 + " rev:" + Tools.f(reverseOrder));
}
// Determine whether this is a vertical or horizontal line segment.
boolean vert = (Math.abs(s1.y - s0.y) > Math.abs(s1.x - s0.x));
if (db) {
System.out.println(" vert=" + Tools.f(vert));
}
// Find the quadratic to solve.
Polyn p;
PlaneCurve cv = getCurve();
if (vert) {
p = cv.solveForX(s0.x);
} else {
p = cv.solveForY(s0.y);
}
DArray lst = new DArray();
p.solve(lst);
if (db) {
System.out.println(" curve=" + cv.toString(true));
System.out.println(" polyn=" + p.toString(true));
System.out.println(" roots=" + Tools.d(lst));
}
// Sort points, discarding those not on line segment,
// and those not on the correct arm.
ipts.clear();
for (int i = 0; i < lst.size(); i++) {
double ta = lst.getDouble(i);
FPoint2 pt;
if (vert) {
pt = new FPoint2(s0.x, ta);
} else {
pt = new FPoint2(ta, s0.y);
}
if (db) {
System.out.println(" position on arm for ta=" + ta + " is " + pt);
}
double t = MyMath.positionOnSegment(pt, s0, s1);
if (db) {
System.out.println(" pt=" + pt + " t=" + t);
}
if (t < 0 || t > 1) {
if (db) {
System.out.println(" not on segment, skipping");
}
continue;
}
FPoint2 cpt = toCurveSpace(pt, null);
if (db) {
System.out.println(" curveSpace=" + cpt);
}
if (cpt.x < 0) {
if (db) {
System.out.println(" skipping...");
}
continue;
}
double t1 = calcParameter(pt);
int j = 0;
while (true) {
if (j == ipts.size()) {
break;
}
double t2 = calcParameter(ipts.getFPoint2(j));
if (!reverseOrder) {
if (t1 < t2) {
break;
}
} else if (t1 > t2) {
break;
}
j++;
}
ipts.add(j, pt);
}
if (db) {
System.out.println(" ipts=" + Tools.d(ipts));
}
}
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();
}
}
}