feat: Add midpoint circle algorithm

Author: saahil-mahato

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

@@ -0,0 +1,77 @@
+package com.thealgorithms.geometry;
+
+import java.awt.Point;
+import java.util.ArrayList;
+import java.util.List;
+
+/**
+ * The {@code MidpointCircle} class implements the Midpoint Circle algorithm,
+ * which is an efficient way to determine the points of a circle
+ * centered at a given point with a specified radius in a 2D space.
+ *
+ * <p>This algorithm uses integer arithmetic to calculate the points,
+ * making it suitable for rasterization in computer graphics.</p>
+ */
+public final class MidpointCircle {
+
+    private MidpointCircle() {
+        // Private constructor to prevent instantiation.
+    }
+
+    /**
+     * Finds the list of points that form a circle centered at (xc, yc)
+     * with a given radius r.
+     *
+     * @param xc the x-coordinate of the center point
+     * @param yc the y-coordinate of the center point
+     * @param r  the radius of the circle
+     * @return a {@code List<Point>} containing all points on the circle
+     */
+    public static List<Point> drawCircle(int xc, int yc, int r) {
+        List<Point> circlePoints = new ArrayList<>();
+
+        int x = 0;
+        int y = r;
+        int p = 1 - r; // Initial decision parameter
+
+        // Function to add points based on symmetry
+        addCirclePoints(circlePoints, xc, yc, x, y);
+
+        while (x < y) {
+            x++;
+
+            // Update decision parameter
+            if (p < 0) {
+                p += 2 * x + 1; // Midpoint is inside the circle
+            } else {
+                y--; // Midpoint is outside the circle
+                p += 2 * x - 2 * y + 1;
+            }
+
+            // Add points based on symmetry
+            addCirclePoints(circlePoints, xc, yc, x, y);
+        }
+
+        return circlePoints; // Return the list of points forming the circle
+    }
+
+    /**
+     * Adds points to the list based on symmetry in all octants.
+     *
+     * @param points the list of points to add to
+     * @param xc    the x-coordinate of the center point
+     * @param yc    the y-coordinate of the center point
+     * @param x     current x coordinate in circle drawing
+     * @param y     current y coordinate in circle drawing
+     */
+    private static void addCirclePoints(List<Point> points, int xc, int yc, int x, int y) {
+        points.add(new Point(xc + x, yc + y));
+        points.add(new Point(xc - x, yc + y));
+        points.add(new Point(xc + x, yc - y));
+        points.add(new Point(xc - x, yc - y));
+        points.add(new Point(xc + y, yc + x));
+        points.add(new Point(xc - y, yc + x));
+        points.add(new Point(xc + y, yc - x));
+        points.add(new Point(xc - y, yc - x));
+    }
+}

src/test/java/com/thealgorithms/geometry/MidpointcircleTest.java

@@ -0,0 +1,59 @@
+package com.thealgorithms.geometry;
+
+import java.awt.Point;
+import java.util.Collection;
+import java.util.List;
+import java.util.stream.Stream;
+import org.junit.jupiter.api.Assertions;
+import org.junit.jupiter.params.ParameterizedTest;
+import org.junit.jupiter.params.provider.Arguments;
+import org.junit.jupiter.params.provider.MethodSource;
+
+/**
+ * The {@code MidpointCircleTest} class contains unit tests for the
+ * {@code MidpointCircle} class, specifically testing the
+ * {@code drawCircle} method.
+ *
+ * <p>This class uses parameterized tests to validate the output of
+ * the Midpoint Circle algorithm for various input parameters.</p>
+ */
+class MidpointCircleTest {
+
+    /**
+     * Provides test cases for the parameterized test.
+     *
+     * <p>Each test case includes center coordinates, radius,
+     * and the expected collection of points that should be generated by the
+     * {@code drawCircle} method.</p>
+     *
+     * @return a stream of arguments containing test cases
+     */
+    static Stream<Arguments> circlePointsProvider() {
+        return Stream.of(
+            Arguments.of(0, 0, 1, List.of(new Point(0, 1), new Point(1, 0), new Point(0, -1), new Point(-1, 0), new Point(1, 1), new Point(-1, -1), new Point(1, -1), new Point(-1, 1))),
+            Arguments.of(0, 0, 2, List.of(new Point(0, 2), new Point(2, 0), new Point(0, -2), new Point(-2, 0), new Point(2, 2), new Point(-2, -2), new Point(2, -2), new Point(-2, 2))),
+            Arguments.of(1, 1, 3, List.of(new Point(1, 4), new Point(4, 1), new Point(1, -2), new Point(-2, 1), new Point(4, 4), new Point(-2, -2), new Point(4, -2), new Point(-2, 4))),
+            Arguments.of(-3, -3, 4, List.of(new Point(-3, 1), new Point(1, -3), new Point(-3, -7), new Point(-7, -3), new Point(1, 1), new Point(-7, -7), new Point(1, -7), new Point(-7, 1)))
+        );
+    }
+
+    /**
+     * Tests the {@code drawCircle} method of the {@code MidpointCircle} class.
+     *
+     * <p>This parameterized test runs multiple times with different sets of
+     * center coordinates and radii to validate that the generated points
+     * match the expected output.</p>
+     *
+     * @param xc      the x-coordinate of the center point
+     * @param yc      the y-coordinate of the center point
+     * @param r       the radius of the circle
+     * @param expected a collection of expected points that should form a circle
+     */
+    @ParameterizedTest
+    @MethodSource("circlePointsProvider")
+    void testDrawCircle(int xc, int yc, int r, Collection<Point> expected) {
+        List<Point> actual = MidpointCircle.drawCircle(xc, yc, r);
+        Assertions.assertEquals(expected.size(), actual.size(), "The size of the points list should match.");
+        Assertions.assertTrue(expected.containsAll(actual) && actual.containsAll(expected), "The points generated should match the expected points.");
+    }
+}