Add midpoint circle algorithm (#5868)

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

@@ -0,0 +1,85 @@
+package com.thealgorithms.geometry;
+
+import java.util.ArrayList;
+import java.util.Collection;
+import java.util.List;
+
+/**
+ * Class to represent the Midpoint Circle Algorithm.
+ * This algorithm calculates points on the circumference of a circle
+ * using integer arithmetic for efficient computation.
+ */
+public final class MidpointCircle {
+
+    private MidpointCircle() {
+        // Private Constructor to prevent instantiation.
+    }
+
+    /**
+     * Generates points on the circumference of a circle using the midpoint circle algorithm.
+     *
+     * @param centerX The x-coordinate of the circle's center.
+     * @param centerY The y-coordinate of the circle's center.
+     * @param radius  The radius of the circle.
+     * @return A list of points on the circle, each represented as an int[] with 2 elements [x, y].
+     */
+    public static List<int[]> generateCirclePoints(int centerX, int centerY, int radius) {
+        List<int[]> points = new ArrayList<>();
+
+        // Special case for radius 0, only the center point should be added.
+        if (radius == 0) {
+            points.add(new int[] {centerX, centerY});
+            return points;
+        }
+
+        // Start at (radius, 0)
+        int x = radius;
+        int y = 0;
+
+        // Decision parameter
+        int p = 1 - radius;
+
+        // Add the initial points in all octants
+        addSymmetricPoints(points, centerX, centerY, x, y);
+
+        // Iterate while x > y
+        while (x > y) {
+            y++;
+
+            if (p <= 0) {
+                // Midpoint is inside or on the circle
+                p = p + 2 * y + 1;
+            } else {
+                // Midpoint is outside the circle
+                x--;
+                p = p + 2 * y - 2 * x + 1;
+            }
+
+            // Add points for this (x, y)
+            addSymmetricPoints(points, centerX, centerY, x, y);
+        }
+
+        return points;
+    }
+
+    /**
+     * Adds the symmetric points in all octants of the circle based on the current x and y values.
+     *
+     * @param points  The list to which symmetric points will be added.
+     * @param centerX The x-coordinate of the circle's center.
+     * @param centerY The y-coordinate of the circle's center.
+     * @param x       The current x-coordinate on the circumference.
+     * @param y       The current y-coordinate on the circumference.
+     */
+    private static void addSymmetricPoints(Collection<int[]> points, int centerX, int centerY, int x, int y) {
+        // Octant symmetry points
+        points.add(new int[] {centerX + x, centerY + y});
+        points.add(new int[] {centerX - x, centerY + y});
+        points.add(new int[] {centerX + x, centerY - y});
+        points.add(new int[] {centerX - x, centerY - y});
+        points.add(new int[] {centerX + y, centerY + x});
+        points.add(new int[] {centerX - y, centerY + x});
+        points.add(new int[] {centerX + y, centerY - x});
+        points.add(new int[] {centerX - y, centerY - x});
+    }
+}