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Add midpoint ellipse algorithm (#5870)
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Saahil Mahato
131
src/main/java/com/thealgorithms/geometry/MidpointEllipse.java
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131
src/main/java/com/thealgorithms/geometry/MidpointEllipse.java
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package com.thealgorithms.geometry;
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import java.util.ArrayList;
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import java.util.Collection;
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import java.util.List;
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/**
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* The MidpointEllipse class implements the Midpoint Ellipse Drawing Algorithm.
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* This algorithm efficiently computes the points on an ellipse by dividing it into two regions
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* and using decision parameters to determine the next point to plot.
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*/
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public final class MidpointEllipse {
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private MidpointEllipse() {
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// Private constructor to prevent instantiation
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}
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/**
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* Draws an ellipse using the Midpoint Ellipse Algorithm.
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*
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* @param centerX the x-coordinate of the center of the ellipse
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* @param centerY the y-coordinate of the center of the ellipse
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* @param a the length of the semi-major axis (horizontal radius)
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* @param b the length of the semi-minor axis (vertical radius)
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* @return a list of points (represented as int arrays) that form the ellipse
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*/
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public static List<int[]> drawEllipse(int centerX, int centerY, int a, int b) {
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List<int[]> points = new ArrayList<>();
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// Handle degenerate cases with early returns
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if (a == 0 && b == 0) {
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points.add(new int[] {centerX, centerY}); // Only the center point
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return points;
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}
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if (a == 0) {
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// Semi-major axis is zero, create a vertical line
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for (int y = centerY - b; y <= centerY + b; y++) {
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points.add(new int[] {centerX, y});
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}
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return points; // Early return
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}
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if (b == 0) {
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// Semi-minor axis is zero, create a horizontal line
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for (int x = centerX - a; x <= centerX + a; x++) {
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points.add(new int[] {x, centerY});
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}
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return points; // Early return
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}
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// Normal case: Non-degenerate ellipse
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computeEllipsePoints(points, centerX, centerY, a, b);
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return points; // Return all calculated points of the ellipse
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}
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/**
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* Computes points of a non-degenerate ellipse using the Midpoint Ellipse Algorithm.
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*
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* @param points the list to which points will be added
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* @param centerX the x-coordinate of the center of the ellipse
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* @param centerY the y-coordinate of the center of the ellipse
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* @param a the length of the semi-major axis (horizontal radius)
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* @param b the length of the semi-minor axis (vertical radius)
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*/
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private static void computeEllipsePoints(Collection<int[]> points, int centerX, int centerY, int a, int b) {
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int x = 0; // Initial x-coordinate
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int y = b; // Initial y-coordinate
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// Region 1: Initial decision parameter
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double d1 = (b * b) - (a * a * b) + (0.25 * a * a); // Decision variable for region 1
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double dx = 2.0 * b * b * x; // Change in x
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double dy = 2.0 * a * a * y; // Change in y
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// Region 1: When the slope is less than 1
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while (dx < dy) {
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addEllipsePoints(points, centerX, centerY, x, y);
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// Update decision parameter and variables
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if (d1 < 0) {
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x++;
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dx += (2 * b * b); // Update x change
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d1 += dx + (b * b); // Update decision parameter
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} else {
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x++;
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y--;
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dx += (2 * b * b); // Update x change
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dy -= (2 * a * a); // Update y change
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d1 += dx - dy + (b * b); // Update decision parameter
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}
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}
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// Region 2: Initial decision parameter for the second region
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double d2 = b * b * (x + 0.5) * (x + 0.5) + a * a * (y - 1) * (y - 1) - a * a * b * b;
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// Region 2: When the slope is greater than or equal to 1
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while (y >= 0) {
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addEllipsePoints(points, centerX, centerY, x, y);
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// Update decision parameter and variables
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if (d2 > 0) {
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y--;
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dy -= (2 * a * a); // Update y change
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d2 += (a * a) - dy; // Update decision parameter
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} else {
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y--;
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x++;
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dx += (2 * b * b); // Update x change
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dy -= (2 * a * a); // Update y change
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d2 += dx - dy + (a * a); // Update decision parameter
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}
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}
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}
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/**
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* Adds points for all four quadrants of the ellipse based on symmetry.
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*
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* @param points the list to which points will be added
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* @param centerX the x-coordinate of the center of the ellipse
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* @param centerY the y-coordinate of the center of the ellipse
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* @param x the x-coordinate relative to the center
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* @param y the y-coordinate relative to the center
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*/
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private static void addEllipsePoints(Collection<int[]> points, int centerX, int centerY, int x, int y) {
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points.add(new int[] {centerX + x, centerY + y});
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points.add(new int[] {centerX - x, centerY + y});
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points.add(new int[] {centerX + x, centerY - y});
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points.add(new int[] {centerX - x, centerY - y});
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}
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}
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package com.thealgorithms.geometry;
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import static org.junit.jupiter.api.Assertions.assertArrayEquals;
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import static org.junit.jupiter.api.Assertions.assertEquals;
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import java.util.List;
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import java.util.stream.Stream;
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import org.junit.jupiter.api.DisplayName;
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import org.junit.jupiter.params.ParameterizedTest;
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import org.junit.jupiter.params.provider.Arguments;
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import org.junit.jupiter.params.provider.MethodSource;
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/**
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* The {@code MidpointEllipseTest} class contains unit tests for the
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* {@code MidpointEllipse} class, specifically testing the
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* {@code drawEllipse} method.
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*
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* <p>This class uses parameterized tests to validate the output of
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* Midpoint Ellipse algorithm for various input points.</p>
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*/
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class MidpointEllipseTest {
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/**
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* Provides test cases for the drawEllipse method.
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* Each argument contains: centerX, centerY, a, b, and expected points.
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*
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* @return a stream of arguments for parameterized testing
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*/
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static Stream<Arguments> ellipseTestProvider() {
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return Stream.of(
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Arguments.of(0, 0, 5, 3, new int[][] {{0, 3}, {0, 3}, {0, -3}, {0, -3}, {1, 3}, {-1, 3}, {1, -3}, {-1, -3}, {2, 3}, {-2, 3}, {2, -3}, {-2, -3}, {3, 2}, {-3, 2}, {3, -2}, {-3, -2}, {4, 2}, {-4, 2}, {4, -2}, {-4, -2}, {5, 1}, {-5, 1}, {5, -1}, {-5, -1}, {5, 0}, {-5, 0}, {5, 0}, {-5, 0}}),
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Arguments.of(0, 0, 0, 5,
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new int[][] {
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{0, -5}, {0, -4}, {0, -3}, {0, -2}, {0, -1}, {0, 0}, {0, 1}, {0, 2}, {0, 3}, {0, 4}, {0, 5} // Only vertical line points and center
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}),
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Arguments.of(0, 0, 5, 0,
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new int[][] {
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{-5, 0}, {-4, 0}, {-3, 0}, {-2, 0}, {-1, 0}, {0, 0}, {1, 0}, {2, 0}, {3, 0}, {4, 0}, {5, 0} // Only horizontal line points and center
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}),
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Arguments.of(0, 0, 0, 0,
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new int[][] {
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{0, 0} // Only center point
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}),
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Arguments.of(0, 0, 4, 4,
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new int[][] {
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{0, 4},
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{0, 4},
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{0, -4},
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{0, -4},
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{1, 4},
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{-1, 4},
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{1, -4},
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{-1, -4},
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{2, 3},
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{-2, 3},
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{2, -3},
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{-2, -3},
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{3, 3},
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{-3, 3},
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{3, -3},
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{-3, -3},
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{3, 2},
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{-3, 2},
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{3, -2},
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{-3, -2},
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{4, 1},
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{-4, 1},
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{4, -1},
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{-4, -1},
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{4, 0},
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{-4, 0},
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{4, 0},
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{-4, 0},
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}));
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}
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/**
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* Tests the drawEllipse method with various parameters.
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*
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* @param centerX the x-coordinate of the center of the ellipse
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* @param centerY the y-coordinate of the center of the ellipse
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* @param a the length of the semi-major axis
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* @param b the length of the semi-minor axis
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* @param expectedPoints the expected points forming the ellipse
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*/
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@ParameterizedTest
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@MethodSource("ellipseTestProvider")
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@DisplayName("Test drawing ellipses with various parameters")
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void testDrawEllipse(int centerX, int centerY, int a, int b, int[][] expectedPoints) {
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List<int[]> points = MidpointEllipse.drawEllipse(centerX, centerY, a, b);
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// Validate the number of points and the specific points
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assertEquals(expectedPoints.length, points.size(), "Number of points should match expected.");
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for (int i = 0; i < expectedPoints.length; i++) {
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assertArrayEquals(expectedPoints[i], points.get(i), "Point mismatch at index " + i);
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}
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}
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}
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