Create RayCasting.java

The Ray Casting algorithm, is used to determine whether a point lies inside a polygon.

Author: Somyagarg0309

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

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+package com.thealgorithms.geometry;
+
+import java.util.ArrayList;
+import java.util.List;
+
+/**
+ * A Java program that determines whether a point is inside a polygon using the Ray Casting algorithm.
+ * The time complexity is O(n), where n is the number of vertices in the polygon.
+ * The space complexity is O(1).
+ *
+ * References:
+ * https://en.wikipedia.org/wiki/Point_in_polygon
+ */
+public class RayCasting {
+
+    /**
+     * Determines if the given point is inside the polygon.
+     *
+     * @param polygon An array of points representing the vertices of the polygon.
+     * @param point   The point to check.
+     * @return true if the point is inside the polygon, false otherwise.
+     */
+    public static boolean isPointInPolygon(Point[] polygon, Point point) {
+        int n = polygon.length;
+        boolean inside = false;
+
+        for (int i = 0, j = n - 1; i < n; j = i++) {
+            if ((polygon[i].y > point.y) != (polygon[j].y > point.y) &&
+                (point.x < (polygon[j].x - polygon[i].x) * (point.y - polygon[i].y) /
+                (polygon[j].y - polygon[i].y) + polygon[i].x)) {
+                inside = !inside;
+            }
+        }
+        return inside;
+    }
+
+    /**
+     * A record representing a point in 2D space.
+     */
+    public record Point(int x, int y) {
+        /**
+         * @return A string representation of this point in the format (x, y)
+         */
+        @Override
+        public String toString() {
+            return String.format("(%d, %d)", x, y);
+        }
+    }
+
+    public static void main(String[] args) {
+        Point[] polygon = {
+            new Point(0, 0),
+            new Point(5, 0),
+            new Point(5, 5),
+            new Point(0, 5)
+        };
+        Point testPoint = new Point(3, 3);
+        System.out.println("Is point " + testPoint + " inside the polygon? " + isPointInPolygon(polygon, testPoint)); // true
+
+        Point outsidePoint = new Point(6, 3);
+        System.out.println("Is point " + outsidePoint + " inside the polygon? " + isPointInPolygon(polygon, outsidePoint)); // false
+    }
+}