Added RotatingCalipers to geometry

Author: Sushant Nadavade

src/main/java/com/thealgorithms/geometry/RotatingCalipers.java

@@ -0,0 +1,321 @@
+package com.thealgorithms.geometry;
+
+import java.util.ArrayList;
+import java.util.Collections;
+import java.util.List;
+
+/**
+ * A class implementing the Rotating Calipers algorithm for geometric computations on convex polygons.
+ * 
+ * The Rotating Calipers algorithm is an efficient technique for solving various geometric problems
+ * on convex polygons, including:
+ * - Computing the diameter (maximum distance between any two points)
+ * - Computing the width (minimum distance between parallel supporting lines)
+ * - Finding the minimum-area bounding rectangle
+ * 
+ * Algorithm Description:
+ * 1. Compute the convex hull of the given points
+ * 2. Use rotating calipers (parallel lines) that rotate around the convex hull
+ * 3. For each rotation, compute the desired geometric property
+ * 4. Return the optimal result
+ * 
+ * Time Complexity: O(n) where n is the number of points in the convex hull
+ * Space Complexity: O(n) for storing the convex hull
+ * 
+ * Reference:
+ * Shamos, M. I. (1978). Computational Geometry.
+ * 
+ * @author TheAlgorithms
+ */
+public final class RotatingCalipers {
+    
+    private RotatingCalipers() {
+    }
+    
+    /**
+     * Represents a pair of points with their distance.
+     */
+    public static record PointPair(Point p1, Point p2, double distance) {
+        @Override
+        public String toString() {
+            return String.format("PointPair(%s, %s, distance=%.2f)", p1, p2, distance);
+        }
+    }
+    
+    /**
+     * Represents a rectangle with its area.
+     */
+    public static record Rectangle(Point bottomLeft, Point topRight, double area) {
+        @Override
+        public String toString() {
+            return String.format("Rectangle(%s, %s, area=%.2f)", bottomLeft, topRight, area);
+        }
+    }
+    
+    /**
+     * Computes the diameter of a convex polygon using rotating calipers.
+     * The diameter is the maximum distance between any two points of the polygon.
+     * 
+     * @param points List of points representing a convex polygon
+     * @return PointPair containing the two points with maximum distance and the distance
+     * @throws IllegalArgumentException if points is null or has less than 2 points
+     */
+    public static PointPair computeDiameter(List<Point> points) {
+        if (points == null || points.size() < 2) {
+            throw new IllegalArgumentException("Points list must contain at least 2 points");
+        }
+        
+        List<Point> hull = ConvexHull.convexHullRecursive(new ArrayList<>(points));
+        if (hull.size() < 2) {
+            throw new IllegalArgumentException("Convex hull must contain at least 2 points");
+        }
+        
+        hull = ensureCounterClockwiseOrder(hull);
+        
+        if (hull.size() == 2) {
+            Point p1 = hull.get(0);
+            Point p2 = hull.get(1);
+            return new PointPair(p1, p2, distance(p1, p2));
+        }
+        
+        int n = hull.size();
+        PointPair maxPair = null;
+        double maxDistance = 0.0;
+        
+        int j = 1;
+        for (int i = 0; i < n; i++) {
+            Point p1 = hull.get(i);
+            
+            while (true) {
+                Point next = hull.get((j + 1) % n);
+                double dist1 = distance(p1, hull.get(j));
+                double dist2 = distance(p1, next);
+                
+                if (dist2 > dist1) {
+                    j = (j + 1) % n;
+                } else {
+                    break;
+                }
+            }
+            
+            double dist = distance(p1, hull.get(j));
+            if (dist > maxDistance) {
+                maxDistance = dist;
+                maxPair = new PointPair(p1, hull.get(j), dist);
+            }
+        }
+        
+        return maxPair;
+    }
+    
+    /**
+     * Computes the width of a convex polygon using rotating calipers.
+     * The width is the minimum distance between two parallel supporting lines.
+     * 
+     * @param points List of points representing a convex polygon
+     * @return The minimum width of the polygon
+     * @throws IllegalArgumentException if points is null or has less than 2 points
+     */
+    public static double computeWidth(List<Point> points) {
+        if (points == null || points.size() < 2) {
+            throw new IllegalArgumentException("Points list must contain at least 2 points");
+        }
+        
+        List<Point> hull = ConvexHull.convexHullRecursive(new ArrayList<>(points));
+        if (hull.size() < 2) {
+            throw new IllegalArgumentException("Convex hull must contain at least 2 points");
+        }
+        
+        hull = ensureCounterClockwiseOrder(hull);
+        
+        if (hull.size() == 2) {
+            return 0.0;
+        }
+        
+        int n = hull.size();
+        double minWidth = Double.MAX_VALUE;
+        
+        int j = 1;
+        for (int i = 0; i < n; i++) {
+            Point p1 = hull.get(i);
+            Point p2 = hull.get((i + 1) % n);
+            
+            while (true) {
+                Point next = hull.get((j + 1) % n);
+                double dist1 = distanceToLine(p1, p2, hull.get(j));
+                double dist2 = distanceToLine(p1, p2, next);
+                
+                if (dist2 > dist1) {
+                    j = (j + 1) % n;
+                } else {
+                    break;
+                }
+            }
+            
+            double width = distanceToLine(p1, p2, hull.get(j));
+            minWidth = Math.min(minWidth, width);
+        }
+        
+        return minWidth;
+    }
+    
+    /**
+     * Computes the minimum-area bounding rectangle of a convex polygon using rotating calipers.
+     * 
+     * @param points List of points representing a convex polygon
+     * @return Rectangle containing the minimum-area bounding rectangle
+     * @throws IllegalArgumentException if points is null or has less than 2 points
+     */
+    public static Rectangle computeMinimumAreaBoundingRectangle(List<Point> points) {
+        if (points == null || points.size() < 2) {
+            throw new IllegalArgumentException("Points list must contain at least 2 points");
+        }
+        
+        List<Point> hull = ConvexHull.convexHullRecursive(new ArrayList<>(points));
+        if (hull.size() < 2) {
+            throw new IllegalArgumentException("Convex hull must contain at least 2 points");
+        }
+        
+        hull = ensureCounterClockwiseOrder(hull);
+        
+        if (hull.size() == 2) {
+            Point p1 = hull.get(0);
+            Point p2 = hull.get(1);
+            return new Rectangle(p1, p2, 0.0);
+        }
+        
+        int n = hull.size();
+        double minArea = Double.MAX_VALUE;
+        Rectangle bestRectangle = null;
+        
+        for (int i = 0; i < n; i++) {
+            Point p1 = hull.get(i);
+            Point p2 = hull.get((i + 1) % n);
+            
+            int j = findAntipodalPoint(hull, i);
+            
+            double edgeLength = distance(p1, p2);
+            double height = distanceToLine(p1, p2, hull.get(j));
+            
+            double area = edgeLength * height;
+            
+            if (area < minArea) {
+                minArea = area;
+                Point bottomLeft = computeRectangleCorner(p1, p2, hull.get(j), true);
+                Point topRight = computeRectangleCorner(p1, p2, hull.get(j), false);
+                bestRectangle = new Rectangle(bottomLeft, topRight, area);
+            }
+        }
+        
+        return bestRectangle;
+    }
+    
+    /**
+     * Finds the antipodal point for a given edge using rotating calipers.
+     */
+    private static int findAntipodalPoint(List<Point> hull, int edgeStart) {
+        int n = hull.size();
+        int j = (edgeStart + 1) % n;
+        
+        Point p1 = hull.get(edgeStart);
+        Point p2 = hull.get((edgeStart + 1) % n);
+        
+        while (true) {
+            Point next = hull.get((j + 1) % n);
+            double dist1 = distanceToLine(p1, p2, hull.get(j));
+            double dist2 = distanceToLine(p1, p2, next);
+            
+            if (dist2 > dist1) {
+                j = (j + 1) % n;
+            } else {
+                break;
+            }
+        }
+        
+        return j;
+    }
+    
+    /**
+     * Computes a corner of the bounding rectangle.
+     */
+    private static Point computeRectangleCorner(Point p1, Point p2, Point antipodal, boolean isBottomLeft) {
+        int minX = Math.min(Math.min(p1.x(), p2.x()), antipodal.x());
+        int maxX = Math.max(Math.max(p1.x(), p2.x()), antipodal.x());
+        int minY = Math.min(Math.min(p1.y(), p2.y()), antipodal.y());
+        int maxY = Math.max(Math.max(p1.y(), p2.y()), antipodal.y());
+        
+        if (isBottomLeft) {
+            return new Point(minX, minY);
+        } else {
+            return new Point(maxX, maxY);
+        }
+    }
+    
+    /**
+     * Computes the Euclidean distance between two points.
+     */
+    private static double distance(Point p1, Point p2) {
+        int dx = p2.x() - p1.x();
+        int dy = p2.y() - p1.y();
+        return Math.sqrt(dx * dx + dy * dy);
+    }
+    
+    /**
+     * Computes the perpendicular distance from a point to a line defined by two points.
+     */
+    private static double distanceToLine(Point lineStart, Point lineEnd, Point point) {
+        int dx = lineEnd.x() - lineStart.x();
+        int dy = lineEnd.y() - lineStart.y();
+        
+        if (dx == 0 && dy == 0) {
+            return distance(lineStart, point);
+        }
+        
+        int px = point.x() - lineStart.x();
+        int py = point.y() - lineStart.y();
+        
+        double crossProduct = Math.abs(px * dy - py * dx);
+        double lineLength = Math.sqrt(dx * dx + dy * dy);
+        
+        return crossProduct / lineLength;
+    }
+    
+    /**
+     * Ensures the hull points are in counter-clockwise order for rotating calipers.
+     * The convex hull algorithm returns points sorted by natural order, but rotating calipers
+     * requires counter-clockwise ordering.
+     */
+    private static List<Point> ensureCounterClockwiseOrder(List<Point> hull) {
+        if (hull.size() <= 2) {
+            return hull;
+        }
+        
+        Point bottomMost = hull.get(0);
+        int bottomIndex = 0;
+        for (int i = 1; i < hull.size(); i++) {
+            Point p = hull.get(i);
+            if (p.y() < bottomMost.y() || (p.y() == bottomMost.y() && p.x() < bottomMost.x())) {
+                bottomMost = p;
+                bottomIndex = i;
+            }
+        }
+        
+        List<Point> orderedHull = new ArrayList<>();
+        for (int i = 0; i < hull.size(); i++) {
+            orderedHull.add(hull.get((bottomIndex + i) % hull.size()));
+        }
+        
+        if (orderedHull.size() >= 3) {
+            Point p1 = orderedHull.get(0);
+            Point p2 = orderedHull.get(1);
+            Point p3 = orderedHull.get(2);
+            
+            if (Point.orientation(p1, p2, p3) < 0) {
+                Collections.reverse(orderedHull);
+                Collections.rotate(orderedHull, 1);
+            }
+        }
+        
+        return orderedHull;
+    }
+}