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feat: add wu's line drawing algorithm (#6695)

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* feat: add wu's line drawing algorithm

* refactor: reorganize internal class declaration

---------

Co-authored-by: a <alexanderklmn@gmail.com>
This commit is contained in:
Saahil Mahato
2025-10-08 01:27:53 +05:45
committed by GitHub
parent 3eb521b158
commit 79dc71db89
2 changed files with 325 additions and 0 deletions
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235
src/main/java/com/thealgorithms/geometry/WusLine.java Normal file
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package com.thealgorithms.geometry;
import java.awt.Point;
import java.util.ArrayList;
import java.util.List;
/**
* The {@code WusLine} class implements Xiaolin Wu's line drawing algorithm,
* which produces anti-aliased lines by varying pixel brightness
* according to the line's proximity to pixel centers.
*
* This implementation returns the pixel coordinates along with
* their associated intensity values (in range [0.0, 1.0]), allowing
* rendering systems to blend accordingly.
*
* The algorithm works by:
* - Computing a line's intersection with pixel boundaries
* - Assigning intensity values based on distance from pixel centers
* - Drawing pairs of pixels perpendicular to the line's direction
*
* Reference: Xiaolin Wu, "An Efficient Antialiasing Technique",
* Computer Graphics (SIGGRAPH '91 Proceedings).
*
*/
public final class WusLine {
private WusLine() {
// Utility class; prevent instantiation.
}
/**
* Represents a pixel and its intensity for anti-aliased rendering.
*
* The intensity value determines how bright the pixel should be drawn,
* with 1.0 being fully opaque and 0.0 being fully transparent.
*/
public static class Pixel {
/** The pixel's coordinate on the screen. */
public final Point point;
/** The pixel's intensity value, clamped to the range [0.0, 1.0]. */
public final double intensity;
/**
* Constructs a new Pixel with the given coordinates and intensity.
*
* @param x the x-coordinate of the pixel
* @param y the y-coordinate of the pixel
* @param intensity the brightness/opacity of the pixel, will be clamped to [0.0, 1.0]
*/
public Pixel(int x, int y, double intensity) {
this.point = new Point(x, y);
this.intensity = Math.clamp(intensity, 0.0, 1.0);
}
}
/**
* Internal class to hold processed endpoint data.
*/
private static class EndpointData {
final int xPixel;
final int yPixel;
final double yEnd;
final double xGap;
EndpointData(int xPixel, int yPixel, double yEnd, double xGap) {
this.xPixel = xPixel;
this.yPixel = yPixel;
this.yEnd = yEnd;
this.xGap = xGap;
}
}
/**
* Draws an anti-aliased line using Wu's algorithm.
*
* The algorithm produces smooth lines by drawing pairs of pixels at each
* x-coordinate (or y-coordinate for steep lines), with intensities based on
* the line's distance from pixel centers.
*
* @param x0 the x-coordinate of the line's start point
* @param y0 the y-coordinate of the line's start point
* @param x1 the x-coordinate of the line's end point
* @param y1 the y-coordinate of the line's end point
* @return a list of {@link Pixel} objects representing the anti-aliased line,
* ordered from start to end
*/
public static List<Pixel> drawLine(int x0, int y0, int x1, int y1) {
List<Pixel> pixels = new ArrayList<>();
// Determine if the line is steep (more vertical than horizontal)
boolean steep = Math.abs(y1 - y0) > Math.abs(x1 - x0);
if (steep) {
// For steep lines, swap x and y coordinates to iterate along y-axis
int temp = x0;
x0 = y0;
y0 = temp;
temp = x1;
x1 = y1;
y1 = temp;
}
if (x0 > x1) {
// Ensure we always draw from left to right
int temp = x0;
x0 = x1;
x1 = temp;
temp = y0;
y0 = y1;
y1 = temp;
}
// Calculate the line's slope
double deltaX = x1 - (double) x0;
double deltaY = y1 - (double) y0;
double gradient = (deltaX == 0) ? 1.0 : deltaY / deltaX;
// Process the first endpoint
EndpointData firstEndpoint = processEndpoint(x0, y0, gradient, true);
addEndpointPixels(pixels, firstEndpoint, steep);
// Process the second endpoint
EndpointData secondEndpoint = processEndpoint(x1, y1, gradient, false);
addEndpointPixels(pixels, secondEndpoint, steep);
// Draw the main line between endpoints
drawMainLine(pixels, firstEndpoint, secondEndpoint, gradient, steep);
return pixels;
}
/**
* Processes a line endpoint to determine its pixel coordinates and intensities.
*
* @param x the x-coordinate of the endpoint
* @param y the y-coordinate of the endpoint
* @param gradient the slope of the line
* @param isStart true if this is the start endpoint, false if it's the end
* @return an {@link EndpointData} object containing processed endpoint information
*/
private static EndpointData processEndpoint(double x, double y, double gradient, boolean isStart) {
double xEnd = round(x);
double yEnd = y + gradient * (xEnd - x);
double xGap = isStart ? rfpart(x + 0.5) : fpart(x + 0.5);
int xPixel = (int) xEnd;
int yPixel = (int) Math.floor(yEnd);
return new EndpointData(xPixel, yPixel, yEnd, xGap);
}
/**
* Adds the two endpoint pixels (one above, one below the line) to the pixel list.
*
* @param pixels the list to add pixels to
* @param endpoint the endpoint data containing coordinates and gaps
* @param steep true if the line is steep (coordinates should be swapped)
*/
private static void addEndpointPixels(List<Pixel> pixels, EndpointData endpoint, boolean steep) {
double fractionalY = fpart(endpoint.yEnd);
double complementFractionalY = rfpart(endpoint.yEnd);
if (steep) {
pixels.add(new Pixel(endpoint.yPixel, endpoint.xPixel, complementFractionalY * endpoint.xGap));
pixels.add(new Pixel(endpoint.yPixel + 1, endpoint.xPixel, fractionalY * endpoint.xGap));
} else {
pixels.add(new Pixel(endpoint.xPixel, endpoint.yPixel, complementFractionalY * endpoint.xGap));
pixels.add(new Pixel(endpoint.xPixel, endpoint.yPixel + 1, fractionalY * endpoint.xGap));
}
}
/**
* Draws the main portion of the line between the two endpoints.
*
* @param pixels the list to add pixels to
* @param firstEndpoint the processed start endpoint
* @param secondEndpoint the processed end endpoint
* @param gradient the slope of the line
* @param steep true if the line is steep (coordinates should be swapped)
*/
private static void drawMainLine(List<Pixel> pixels, EndpointData firstEndpoint, EndpointData secondEndpoint, double gradient, boolean steep) {
// Start y-intersection after the first endpoint
double intersectionY = firstEndpoint.yEnd + gradient;
// Iterate through x-coordinates between the endpoints
for (int x = firstEndpoint.xPixel + 1; x < secondEndpoint.xPixel; x++) {
int yFloor = (int) Math.floor(intersectionY);
double fractionalPart = fpart(intersectionY);
double complementFractionalPart = rfpart(intersectionY);
if (steep) {
pixels.add(new Pixel(yFloor, x, complementFractionalPart));
pixels.add(new Pixel(yFloor + 1, x, fractionalPart));
} else {
pixels.add(new Pixel(x, yFloor, complementFractionalPart));
pixels.add(new Pixel(x, yFloor + 1, fractionalPart));
}
intersectionY += gradient;
}
}
/**
* Returns the fractional part of a number.
*
* @param x the input number
* @return the fractional part (always in range [0.0, 1.0))
*/
private static double fpart(double x) {
return x - Math.floor(x);
}
/**
* Returns the reverse fractional part of a number (1 - fractional part).
*
* @param x the input number
* @return 1.0 minus the fractional part (always in range (0.0, 1.0])
*/
private static double rfpart(double x) {
return 1.0 - fpart(x);
}
/**
* Rounds a number to the nearest integer.
*
* @param x the input number
* @return the nearest integer value as a double
*/
private static double round(double x) {
return Math.floor(x + 0.5);
}
}

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src/test/java/com/thealgorithms/geometry/WusLineTest.java Normal file
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package com.thealgorithms.geometry;
import static org.junit.jupiter.api.Assertions.assertEquals;
import static org.junit.jupiter.api.Assertions.assertFalse;
import static org.junit.jupiter.api.Assertions.assertTrue;
import java.util.List;
import org.junit.jupiter.api.Test;
/**
* Unit tests for the {@link WusLine} class.
*/
class WusLineTest {
@Test
void testSimpleLineProducesPixels() {
List<WusLine.Pixel> pixels = WusLine.drawLine(2, 2, 6, 4);
assertFalse(pixels.isEmpty(), "Line should produce non-empty pixel list");
}
@Test
void testEndpointsIncluded() {
List<WusLine.Pixel> pixels = WusLine.drawLine(0, 0, 5, 3);
boolean hasStart = pixels.stream().anyMatch(p -> p.point.equals(new java.awt.Point(0, 0)));
boolean hasEnd = pixels.stream().anyMatch(p -> p.point.equals(new java.awt.Point(5, 3)));
assertTrue(hasStart, "Start point should be represented in the pixel list");
assertTrue(hasEnd, "End point should be represented in the pixel list");
}
@Test
void testIntensityInRange() {
List<WusLine.Pixel> pixels = WusLine.drawLine(1, 1, 8, 5);
for (WusLine.Pixel pixel : pixels) {
assertTrue(pixel.intensity >= 0.0 && pixel.intensity <= 1.0, "Intensity must be clamped between 0.0 and 1.0");
}
}
@Test
void testReversedEndpointsProducesSameLine() {
List<WusLine.Pixel> forward = WusLine.drawLine(2, 2, 10, 5);
List<WusLine.Pixel> backward = WusLine.drawLine(10, 5, 2, 2);
// They should cover same coordinates (ignoring order)
var forwardPoints = forward.stream().map(p -> p.point).collect(java.util.stream.Collectors.toSet());
var backwardPoints = backward.stream().map(p -> p.point).collect(java.util.stream.Collectors.toSet());
assertEquals(forwardPoints, backwardPoints, "Reversing endpoints should yield same line pixels");
}
@Test
void testSteepLineHasProperCoverage() {
// Steep line: Δy > Δx
List<WusLine.Pixel> pixels = WusLine.drawLine(3, 2, 5, 10);
assertFalse(pixels.isEmpty());
// Expect increasing y values
long increasing = 0;
for (int i = 1; i < pixels.size(); i++) {
if (pixels.get(i).point.y >= pixels.get(i - 1).point.y) {
increasing++;
}
}
assertTrue(increasing > pixels.size() / 2, "Steep line should have increasing y coordinates");
}
@Test
void testZeroLengthLineUsesDefaultGradient() {
// same start and end -> dx == 0 -> gradient should take the (dx == 0) ? 1.0 branch
List<WusLine.Pixel> pixels = WusLine.drawLine(3, 3, 3, 3);
// sanity checks: we produced pixels and the exact point is present
assertFalse(pixels.isEmpty(), "Zero-length line should produce at least one pixel");
assertTrue(pixels.stream().anyMatch(p -> p.point.equals(new java.awt.Point(3, 3))), "Pixel list should include the single-point coordinate (3,3)");
}
@Test
void testHorizontalLineIntensityStable() {
List<WusLine.Pixel> pixels = WusLine.drawLine(1, 5, 8, 5);
// For each x, take the max intensity among pixels with that x (the visible intensity for the column)
java.util.Map<Integer, Double> maxIntensityByX = pixels.stream()
.collect(java.util.stream.Collectors.groupingBy(p -> p.point.x, java.util.stream.Collectors.mapping(p -> p.intensity, java.util.stream.Collectors.maxBy(Double::compareTo))))
.entrySet()
.stream()
.collect(java.util.stream.Collectors.toMap(java.util.Map.Entry::getKey, e -> e.getValue().orElse(0.0)));
double avgMaxIntensity = maxIntensityByX.values().stream().mapToDouble(Double::doubleValue).average().orElse(0.0);
assertTrue(avgMaxIntensity > 0.5, "Average of the maximum per-x intensities should be > 0.5 for a horizontal line");
}
}