Add midpoint ellipse algorithm (#5870)

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

@@ -0,0 +1,131 @@
+package com.thealgorithms.geometry;
+
+import java.util.ArrayList;
+import java.util.Collection;
+import java.util.List;
+
+/**
+ * The MidpointEllipse class implements the Midpoint Ellipse Drawing Algorithm.
+ * This algorithm efficiently computes the points on an ellipse by dividing it into two regions
+ * and using decision parameters to determine the next point to plot.
+ */
+public final class MidpointEllipse {
+
+    private MidpointEllipse() {
+        // Private constructor to prevent instantiation
+    }
+
+    /**
+     * Draws an ellipse using the Midpoint Ellipse Algorithm.
+     *
+     * @param centerX the x-coordinate of the center of the ellipse
+     * @param centerY the y-coordinate of the center of the ellipse
+     * @param a the length of the semi-major axis (horizontal radius)
+     * @param b the length of the semi-minor axis (vertical radius)
+     * @return a list of points (represented as int arrays) that form the ellipse
+     */
+    public static List<int[]> drawEllipse(int centerX, int centerY, int a, int b) {
+        List<int[]> points = new ArrayList<>();
+
+        // Handle degenerate cases with early returns
+        if (a == 0 && b == 0) {
+            points.add(new int[] {centerX, centerY}); // Only the center point
+            return points;
+        }
+
+        if (a == 0) {
+            // Semi-major axis is zero, create a vertical line
+            for (int y = centerY - b; y <= centerY + b; y++) {
+                points.add(new int[] {centerX, y});
+            }
+            return points; // Early return
+        }
+
+        if (b == 0) {
+            // Semi-minor axis is zero, create a horizontal line
+            for (int x = centerX - a; x <= centerX + a; x++) {
+                points.add(new int[] {x, centerY});
+            }
+            return points; // Early return
+        }
+
+        // Normal case: Non-degenerate ellipse
+        computeEllipsePoints(points, centerX, centerY, a, b);
+
+        return points; // Return all calculated points of the ellipse
+    }
+
+    /**
+     * Computes points of a non-degenerate ellipse using the Midpoint Ellipse Algorithm.
+     *
+     * @param points    the list to which points will be added
+     * @param centerX  the x-coordinate of the center of the ellipse
+     * @param centerY  the y-coordinate of the center of the ellipse
+     * @param a        the length of the semi-major axis (horizontal radius)
+     * @param b        the length of the semi-minor axis (vertical radius)
+     */
+    private static void computeEllipsePoints(Collection<int[]> points, int centerX, int centerY, int a, int b) {
+        int x = 0; // Initial x-coordinate
+        int y = b; // Initial y-coordinate
+
+        // Region 1: Initial decision parameter
+        double d1 = (b * b) - (a * a * b) + (0.25 * a * a); // Decision variable for region 1
+        double dx = 2.0 * b * b * x; // Change in x
+        double dy = 2.0 * a * a * y; // Change in y
+
+        // Region 1: When the slope is less than 1
+        while (dx < dy) {
+            addEllipsePoints(points, centerX, centerY, x, y);
+
+            // Update decision parameter and variables
+            if (d1 < 0) {
+                x++;
+                dx += (2 * b * b); // Update x change
+                d1 += dx + (b * b); // Update decision parameter
+            } else {
+                x++;
+                y--;
+                dx += (2 * b * b); // Update x change
+                dy -= (2 * a * a); // Update y change
+                d1 += dx - dy + (b * b); // Update decision parameter
+            }
+        }
+
+        // Region 2: Initial decision parameter for the second region
+        double d2 = b * b * (x + 0.5) * (x + 0.5) + a * a * (y - 1) * (y - 1) - a * a * b * b;
+
+        // Region 2: When the slope is greater than or equal to 1
+        while (y >= 0) {
+            addEllipsePoints(points, centerX, centerY, x, y);
+
+            // Update decision parameter and variables
+            if (d2 > 0) {
+                y--;
+                dy -= (2 * a * a); // Update y change
+                d2 += (a * a) - dy; // Update decision parameter
+            } else {
+                y--;
+                x++;
+                dx += (2 * b * b); // Update x change
+                dy -= (2 * a * a); // Update y change
+                d2 += dx - dy + (a * a); // Update decision parameter
+            }
+        }
+    }
+
+    /**
+     * Adds points for all four quadrants of the ellipse based on symmetry.
+     *
+     * @param points    the list to which points will be added
+     * @param centerX  the x-coordinate of the center of the ellipse
+     * @param centerY  the y-coordinate of the center of the ellipse
+     * @param x        the x-coordinate relative to the center
+     * @param y        the y-coordinate relative to the center
+     */
+    private static void addEllipsePoints(Collection<int[]> points, int centerX, int centerY, int x, int 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 - x, centerY - y});
+    }
+}