public Point2DDouble[] intersect(Circle2DDouble c, DoubleComparator dblComp) {
double d = p.distance(c.p);
if (dblComp.compare(d, radius + c.radius) > 0
|| dblComp.compare(d + Math.min(radius, c.radius), Math.max(radius, c.radius)) < 0) {
return new Point2DDouble[0];
}
if (dblComp.compare(d, 0) == 0) {
return null;
}
double diff = (radius * radius - c.radius * c.radius) / d;
double d1 = (d + diff) * .5;
Point2DDouble v = c.p.subtract(p);
Point2DDouble v1 = v.multiply(d1 / v.length());
double z = radius * radius - d1 * d1;
Point2DDouble p0 = p.add(v1);
// if (dblComp.compare(z, 0) < 0) {
// System.out.println(this + " " + c);
// System.out.println(d + " " + (radius + c.radius));
// throw new AssertionError();
// }
if (dblComp.compare(z, 0) <= 0) {
return new Point2DDouble[] {p0};
}
z = Math.sqrt(z);
Point2DDouble v2 = new Point2DDouble(-v.y, v.x).multiply(z / v.length());
return new Point2DDouble[] {p0.add(v2), p0.subtract(v2)};
}
public Point2DDouble[][] getInternalTangents(Circle2DDouble c, DoubleComparator comp) {
double d = p.distance(c.p);
if (comp.compare(d, radius + c.radius) < 0) return new Point2DDouble[0][];
if (comp.compare(d, radius + c.radius) == 0) {
Point2DDouble v = c.p.subtract(p);
v = v.multiply(radius / v.length());
v = v.add(p);
return new Point2DDouble[][] {{v, v}};
}
double nRadius = radius + c.radius;
Point2DDouble[] tangentsFromPoint = new Circle2DDouble(p, nRadius).getTangents(c.p, comp);
Point2DDouble vn1 = tangentsFromPoint[0].subtract(c.p);
vn1 = new Point2DDouble(-vn1.y, vn1.x);
vn1 = vn1.multiply(c.radius / vn1.length());
Point2DDouble vn2 = tangentsFromPoint[1].subtract(c.p);
vn2 = new Point2DDouble(vn2.y, -vn2.x);
vn2 = vn2.multiply(c.radius / vn2.length());
Point2DDouble[][] ret =
new Point2DDouble[][] {
{tangentsFromPoint[0].add(vn1), c.p.add(vn1)},
{tangentsFromPoint[1].add(vn2), c.p.add(vn2)}
};
if (comp.compare(ret[0][0].distance(p), radius) != 0) throw new AssertionError();
if (comp.compare(ret[1][0].distance(p), radius) != 0) throw new AssertionError();
if (comp.compare(ret[0][1].distance(c.p), c.radius) != 0) throw new AssertionError();
if (comp.compare(ret[1][1].distance(c.p), c.radius) != 0) throw new AssertionError();
return ret;
}
public Point2DDouble[] getTangents(Point2DDouble q, DoubleComparator comp) {
double d = p.distance(q);
if (comp.compare(d, radius) < 0) {
return null;
}
if (comp.compare(d, radius) == 0) {
return new Point2DDouble[] {p};
}
double d1 = radius * radius / d;
Point2DDouble v = q.subtract(p);
Point2DDouble vn = new Point2DDouble(-v.y, v.x);
v = v.multiply(d1 / v.length());
Point2DDouble c = p.add(v);
double d2 = radius * radius - d1 * d1;
if (d2 < 0) d2 = 0;
d2 = Math.sqrt(d2);
vn = vn.multiply(d2 / vn.length());
return new Point2DDouble[] {c.add(vn), c.subtract(vn)};
}
public Point2DDouble[][] getExternalTangents(Circle2DDouble c, DoubleComparator comp) {
if (comp.compare(radius, c.radius) < 0) {
Point2DDouble[][] ret = c.getExternalTangents(this, comp);
for (Point2DDouble[] e : ret) {
Point2DDouble t = e[0];
e[0] = e[1];
e[1] = t;
}
if (comp.compare(ret[0][0].distance(p), radius) != 0) throw new AssertionError();
if (comp.compare(ret[1][0].distance(p), radius) != 0) throw new AssertionError();
if (comp.compare(ret[0][1].distance(c.p), c.radius) != 0) throw new AssertionError();
if (comp.compare(ret[1][1].distance(c.p), c.radius) != 0) throw new AssertionError();
if (comp.compare(GeometryAlgorithms.distanceToLine(ret[0][0], ret[0][1], p), radius) != 0)
throw new AssertionError();
if (comp.compare(GeometryAlgorithms.distanceToLine(ret[0][0], ret[0][1], c.p), c.radius) != 0)
throw new AssertionError();
if (comp.compare(GeometryAlgorithms.distanceToLine(ret[1][0], ret[1][1], p), radius) != 0)
throw new AssertionError();
if (comp.compare(GeometryAlgorithms.distanceToLine(ret[1][0], ret[1][1], c.p), c.radius) != 0)
throw new AssertionError();
return ret;
}
double d = p.distance(c.p);
if (comp.compare(d + Math.min(radius, c.radius), Math.max(radius, c.radius)) < 0) {
return new Point2DDouble[0][];
}
if (comp.compare(d + Math.min(radius, c.radius), Math.max(radius, c.radius)) == 0) {
Point2DDouble v = c.p.subtract(p);
v = v.multiply(radius / v.length());
v = v.add(p);
return new Point2DDouble[][] {{v, v}};
}
Point2DDouble[] tangentsFromPoint =
new Circle2DDouble(p, radius - c.radius).getTangents(c.p, comp);
Point2DDouble vn1 = tangentsFromPoint[0].subtract(c.p);
vn1 = new Point2DDouble(vn1.y, -vn1.x);
vn1 = vn1.multiply(c.radius / vn1.length());
Point2DDouble vn2 = tangentsFromPoint[1].subtract(c.p);
vn2 = new Point2DDouble(-vn2.y, vn2.x);
vn2 = vn2.multiply(c.radius / vn2.length());
Point2DDouble[][] ret =
new Point2DDouble[][] {
{tangentsFromPoint[0].add(vn1), c.p.add(vn1)},
{tangentsFromPoint[1].add(vn2), c.p.add(vn2)}
};
if (comp.compare(ret[0][0].distance(p), radius) != 0) throw new AssertionError();
if (comp.compare(ret[1][0].distance(p), radius) != 0) throw new AssertionError();
if (comp.compare(ret[0][1].distance(c.p), c.radius) != 0) throw new AssertionError();
if (comp.compare(ret[1][1].distance(c.p), c.radius) != 0) throw new AssertionError();
if (comp.compare(GeometryAlgorithms.distanceToLine(ret[0][0], ret[0][1], p), radius) != 0)
throw new AssertionError();
if (comp.compare(GeometryAlgorithms.distanceToLine(ret[0][0], ret[0][1], c.p), c.radius) != 0)
throw new AssertionError();
if (comp.compare(GeometryAlgorithms.distanceToLine(ret[1][0], ret[1][1], p), radius) != 0)
throw new AssertionError();
if (comp.compare(GeometryAlgorithms.distanceToLine(ret[1][0], ret[1][1], c.p), c.radius) != 0)
throw new AssertionError();
return ret;
}
public boolean containsOn(Point2DDouble p, DoubleComparator comp) {
return comp.compare(p.distanceSquared(this.p), radius * radius) == 0;
}
public void solve(int testNumber, FastScanner in, FastPrinter out) {
Circle2DDouble c =
new Circle2DDouble(new Point2DDouble(in.nextInt(), in.nextInt()), in.nextInt());
Point2DDouble p1 = new Point2DDouble(in.nextInt(), in.nextInt());
Point2DDouble p2 = new Point2DDouble(in.nextInt(), in.nextInt());
if (p1.x > p2.x) {
double t = p1.x;
p1.x = p2.x;
p2.x = t;
}
if (p1.y > p2.y) {
double t = p1.y;
p1.y = p2.y;
p2.y = t;
}
List<Point2DDouble> allPoints = new ArrayList<>();
allPoints.add(p1);
allPoints.add(p2);
allPoints.add(new Point2DDouble(p1.x, p2.y));
allPoints.add(new Point2DDouble(p2.x, p1.y));
allPoints.add(new Point2DDouble(c.p.x - c.radius, c.p.y));
allPoints.add(new Point2DDouble(c.p.x + c.radius, c.p.y));
allPoints.add(new Point2DDouble(c.p.x, c.p.y - c.radius));
allPoints.add(new Point2DDouble(c.p.x, c.p.y + c.radius));
for (double x : new double[] {p1.x, p2.x}) {
if (comp.compare(x, c.p.x - c.radius) > 0 && comp.compare(x, c.p.x + c.radius) < 0) {
double dx = c.p.x - x;
double dy = Math.sqrt(c.radius * c.radius - dx * dx);
allPoints.add(new Point2DDouble(x, c.p.y - dy));
allPoints.add(new Point2DDouble(x, c.p.y + dy));
}
}
for (double y : new double[] {p1.y, p2.y}) {
if (comp.compare(y, c.p.y - c.radius) > 0 && comp.compare(y, c.p.y + c.radius) < 0) {
double dy = c.p.y - y;
double dx = Math.sqrt(c.radius * c.radius - dy * dy);
allPoints.add(new Point2DDouble(c.p.x - dx, y));
allPoints.add(new Point2DDouble(c.p.x + dx, y));
}
}
List<Point2DDouble> onRect = new ArrayList<>();
for (Point2DDouble e : allPoints) {
if (inside(p1, p2, e)) {
if (comp.compare(p1.x, e.x) < 0
&& comp.compare(e.x, p2.x) < 0
&& comp.compare(p1.y, e.y) < 0
&& comp.compare(e.y, p2.y) < 0) {
continue;
}
onRect.add(e);
}
}
List<Point2DDouble> onCircle = new ArrayList<>();
for (Point2DDouble e : allPoints) {
if (comp.compare(e.distance(c.p), c.radius) == 0) {
onCircle.add(e);
}
}
final Point2DDouble centerRect = p1.add(p2).multiply(0.5);
Collections.sort(
onRect,
new Comparator<Point2DDouble>() {
int get(Point2DDouble e) {
int x = comp.compare(e.x, 0);
int y = comp.compare(e.y, 0);
if (x > 0) {
return y > 0 ? 2 : y < 0 ? 8 : 1;
} else if (x < 0) {
return y > 0 ? 4 : y < 0 ? 6 : 5;
} else {
return y > 0 ? 3 : y < 0 ? 7 : 0;
}
}
@Override
public int compare(Point2DDouble o1, Point2DDouble o2) {
o1 = o1.subtract(centerRect);
o2 = o2.subtract(centerRect);
int c = get(o1) - get(o2);
if (c != 0) return c;
return comp.compare(o2.vmul(o1), 0);
}
});
final Point2DDouble circleCenter = c.p;
Collections.sort(
onCircle,
new Comparator<Point2DDouble>() {
int get(Point2DDouble e) {
int x = comp.compare(e.x, 0);
int y = comp.compare(e.y, 0);
if (x > 0) {
return y > 0 ? 2 : y < 0 ? 8 : 1;
} else if (x < 0) {
return y > 0 ? 4 : y < 0 ? 6 : 5;
} else {
return y > 0 ? 3 : y < 0 ? 7 : 0;
}
}
@Override
public int compare(Point2DDouble o1, Point2DDouble o2) {
o1 = o1.subtract(circleCenter);
o2 = o2.subtract(circleCenter);
int c = get(o1) - get(o2);
if (c != 0) return c;
return comp.compare(o2.vmul(o1), 0);
}
});
List<Segment> allSegments = new ArrayList<>();
for (int i = 0; i < onRect.size(); i++) {
Point2DDouble r1 = onRect.get(i);
Point2DDouble r2 = onRect.get((i + 1) % onRect.size());
if (pointsEqual(r1, r2)) continue;
Point2DDouble r0 = r1.add(r2).multiply(0.5);
if (comp.compare(r0.distance(c.p), c.radius) < 0) {
allSegments.add(new Segment(r1, r2, 0));
}
}
for (int i = 0; i < onCircle.size(); i++) {
Point2DDouble r1 = onCircle.get(i);
Point2DDouble r2 = onCircle.get((i + 1) % onCircle.size());
if (pointsEqual(r1, r2)) continue;
r1 = r1.subtract(c.p);
r2 = r2.subtract(c.p);
Point2DDouble r0 = r1.add(r2);
r0 = r0.multiply(c.radius / r0.length());
r0 = r0.add(c.p);
if (inside(p1, p2, r0)) {
allSegments.add(new Segment(r1.add(c.p), r2.add(c.p), c.radius));
}
}
if (allSegments.isEmpty()) {
out.println(0);
return;
}
boolean[] was = new boolean[allSegments.size()];
List<Segment> sortedSegments = new ArrayList<>();
sortedSegments.add(allSegments.get(0));
was[0] = true;
Point2DDouble last = sortedSegments.get(sortedSegments.size() - 1).q;
// System.out.println(allSegments);
while (!pointsEqual(sortedSegments.get(0).p, last)) {
int id = -1;
for (int i = 0; i < allSegments.size(); i++) {
if (was[i]) continue;
Segment e = allSegments.get(i);
if (pointsEqual(e.p, last)) {
id = i;
break;
}
}
if (id < 0) throw new AssertionError();
was[id] = true;
sortedSegments.add(allSegments.get(id));
last = allSegments.get(id).q;
}
double area = 0;
for (Segment e : sortedSegments) {
area += e.p.vmul(e.q);
}
area = Math.abs(area) * .5;
for (Segment e : sortedSegments) {
if (comp.compare(e.r, 0) > 0) {
double dist = e.p.distance(e.q);
double sin = dist * .5 / c.radius;
if (sin > 1) sin = 1;
else if (sin < -1) sin = -1;
double ang = Math.asin(sin) * 2;
area += c.radius * c.radius * .5 * (ang - Math.sin(ang));
}
}
out.println(area);
}
private boolean inside(Point2DDouble p1, Point2DDouble p2, Point2DDouble e) {
return comp.compare(p1.x, e.x) <= 0
&& comp.compare(e.x, p2.x) <= 0
&& comp.compare(p1.y, e.y) <= 0
&& comp.compare(e.y, p2.y) <= 0;
}
static boolean pointsEqual(Point2DDouble p, Point2DDouble q) {
return comp.compare(p.x, q.x) == 0 && comp.compare(p.y, q.y) == 0;
}