/*
* Smallest enclosing circle - Library (Java)
*
* Copyright (c) 2020 Project Nayuki
* https://www.nayuki.io/page/smallest-enclosing-circle
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program (see COPYING.txt and COPYING.LESSER.txt).
* If not, see .
*/
import java.util.ArrayList;
import java.util.Collection;
import java.util.Collections;
import java.util.List;
import java.util.Random;
public final class SmallestEnclosingCircle {
/*
* Returns the smallest circle that encloses all the given points. Runs in expected O(n) time, randomized.
* Note: If 0 points are given, null is returned. If 1 point is given, a circle of radius 0 is returned.
*/
// Initially: No boundary points known
public static Circle makeCircle(List points) {
// Clone list to preserve the caller's data, randomize order
List shuffled = new ArrayList<>(points);
Collections.shuffle(shuffled, new Random());
// Progressively add points to circle or recompute circle
Circle c = null;
for (int i = 0; i < shuffled.size(); i++) {
Point p = shuffled.get(i);
if (c == null || !c.contains(p))
c = makeCircleOnePoint(shuffled.subList(0, i + 1), p);
}
return c;
}
// One boundary point known
private static Circle makeCircleOnePoint(List points, Point p) {
Circle c = new Circle(p, 0);
for (int i = 0; i < points.size(); i++) {
Point q = points.get(i);
if (!c.contains(q)) {
if (c.r == 0)
c = makeDiameter(p, q);
else
c = makeCircleTwoPoints(points.subList(0, i + 1), p, q);
}
}
return c;
}
// Two boundary points known
private static Circle makeCircleTwoPoints(List points, Point p, Point q) {
Circle circ = makeDiameter(p, q);
Circle left = null;
Circle right = null;
// For each point not in the two-point circle
Point pq = q.subtract(p);
for (Point r : points) {
if (circ.contains(r))
continue;
// Form a circumcircle and classify it on left or right side
double cross = pq.cross(r.subtract(p));
Circle c = makeCircumcircle(p, q, r);
if (c == null)
continue;
else if (cross > 0 && (left == null || pq.cross(c.c.subtract(p)) > pq.cross(left.c.subtract(p))))
left = c;
else if (cross < 0 && (right == null || pq.cross(c.c.subtract(p)) < pq.cross(right.c.subtract(p))))
right = c;
}
// Select which circle to return
if (left == null && right == null)
return circ;
else if (left == null)
return right;
else if (right == null)
return left;
else
return left.r <= right.r ? left : right;
}
static Circle makeDiameter(Point a, Point b) {
Point c = new Point((a.x + b.x) / 2, (a.y + b.y) / 2);
return new Circle(c, Math.max(c.distance(a), c.distance(b)));
}
static Circle makeCircumcircle(Point a, Point b, Point c) {
// Mathematical algorithm from Wikipedia: Circumscribed circle
double ox = (Math.min(Math.min(a.x, b.x), c.x) + Math.max(Math.max(a.x, b.x), c.x)) / 2;
double oy = (Math.min(Math.min(a.y, b.y), c.y) + Math.max(Math.max(a.y, b.y), c.y)) / 2;
double ax = a.x - ox, ay = a.y - oy;
double bx = b.x - ox, by = b.y - oy;
double cx = c.x - ox, cy = c.y - oy;
double d = (ax * (by - cy) + bx * (cy - ay) + cx * (ay - by)) * 2;
if (d == 0)
return null;
double x = ((ax*ax + ay*ay) * (by - cy) + (bx*bx + by*by) * (cy - ay) + (cx*cx + cy*cy) * (ay - by)) / d;
double y = ((ax*ax + ay*ay) * (cx - bx) + (bx*bx + by*by) * (ax - cx) + (cx*cx + cy*cy) * (bx - ax)) / d;
Point p = new Point(ox + x, oy + y);
double r = Math.max(Math.max(p.distance(a), p.distance(b)), p.distance(c));
return new Circle(p, r);
}
}
final class Circle {
private static final double MULTIPLICATIVE_EPSILON = 1 + 1e-14;
public final Point c; // Center
public final double r; // Radius
public Circle(Point c, double r) {
this.c = c;
this.r = r;
}
public boolean contains(Point p) {
return c.distance(p) <= r * MULTIPLICATIVE_EPSILON;
}
public boolean contains(Collection ps) {
for (Point p : ps) {
if (!contains(p))
return false;
}
return true;
}
public String toString() {
return String.format("Circle(x=%g, y=%g, r=%g)", c.x, c.y, r);
}
}
final class Point {
public final double x;
public final double y;
public Point(double x, double y) {
this.x = x;
this.y = y;
}
public Point subtract(Point p) {
return new Point(x - p.x, y - p.y);
}
public double distance(Point p) {
return Math.hypot(x - p.x, y - p.y);
}
// Signed area / determinant thing
public double cross(Point p) {
return x * p.y - y * p.x;
}
public String toString() {
return String.format("Point(%g, %g)", x, y);
}
}