mirror of
https://github.com/TheAlgorithms/Java.git
synced 2025-12-19 07:00:35 +08:00
2da0465fe0
* feat(geometry): add Bentley-Ottmann line segment intersection algorithm - Implement sweep-line algorithm for finding all intersection points - Time complexity: O((n + k) log n) where n is segments, k is intersections - Uses event queue (PriorityQueue) and status structure (TreeSet) - Handles vertical/horizontal segments, collinear overlaps, and touching endpoints - Includes comprehensive Javadoc with examples and references * test(geometry): add comprehensive tests for Bentley-Ottmann algorithm - 19 test cases covering typical, edge, and degenerate cases - Tests include: single/multiple intersections, parallel segments, grid patterns - Performance test with 100 random segments - All tests validate correctness of intersection detection * style(geometry): fix code style * test(geometry): Achieve 100% test coverage for BentleyOttmann * style(geometry): fix code style again * fix: correct import order in BentleyOttmann * fix(geometry): Resolve SpotBugs and PMD static analysis warnings * Reorder import statements in BentleyOttmannTest --------- Co-authored-by: Deniz Altunkapan <deniz.altunkapan@outlook.com>
424 lines
15 KiB
Java
424 lines
15 KiB
Java
package com.thealgorithms.geometry;
|
||
|
||
import java.awt.geom.Point2D;
|
||
import java.util.ArrayList;
|
||
import java.util.Comparator;
|
||
import java.util.HashMap;
|
||
import java.util.HashSet;
|
||
import java.util.List;
|
||
import java.util.Map;
|
||
import java.util.NavigableSet;
|
||
import java.util.Objects;
|
||
import java.util.PriorityQueue;
|
||
import java.util.Set;
|
||
import java.util.SortedSet;
|
||
import java.util.TreeSet;
|
||
|
||
/**
|
||
* Implementation of the Bentley–Ottmann algorithm for finding all intersection
|
||
* points among a set of line segments in O((n + k) log n) time.
|
||
*
|
||
* <p>Uses a sweep-line approach with an event queue and status structure to
|
||
* efficiently detect intersections in 2D plane geometry.</p>
|
||
*
|
||
* @see <a href="https://en.wikipedia.org/wiki/Bentley%E2%80%93Ottmann_algorithm">
|
||
* Bentley–Ottmann algorithm</a>
|
||
*/
|
||
public final class BentleyOttmann {
|
||
|
||
private BentleyOttmann() {
|
||
}
|
||
|
||
private static final double EPS = 1e-9;
|
||
private static double currentSweepX;
|
||
|
||
/**
|
||
* Represents a line segment with two endpoints.
|
||
*/
|
||
public static class Segment {
|
||
final Point2D.Double p1;
|
||
final Point2D.Double p2;
|
||
final int id; // Unique identifier for each segment
|
||
|
||
Segment(Point2D.Double p1, Point2D.Double p2) {
|
||
this.p1 = p1;
|
||
this.p2 = p2;
|
||
this.id = segmentCounter++;
|
||
}
|
||
|
||
private static int segmentCounter = 0;
|
||
|
||
/**
|
||
* Computes the y-coordinate of this segment at a given x value.
|
||
*/
|
||
double getY(double x) {
|
||
if (Math.abs(p2.x - p1.x) < EPS) {
|
||
// Vertical segment: return midpoint y
|
||
return (p1.y + p2.y) / 2.0;
|
||
}
|
||
double t = (x - p1.x) / (p2.x - p1.x);
|
||
return p1.y + t * (p2.y - p1.y);
|
||
}
|
||
|
||
Point2D.Double leftPoint() {
|
||
return p1.x < p2.x ? p1 : p1.x > p2.x ? p2 : p1.y < p2.y ? p1 : p2;
|
||
}
|
||
|
||
Point2D.Double rightPoint() {
|
||
return p1.x > p2.x ? p1 : p1.x < p2.x ? p2 : p1.y > p2.y ? p1 : p2;
|
||
}
|
||
|
||
@Override
|
||
public String toString() {
|
||
return String.format("S%d[(%.2f, %.2f), (%.2f, %.2f)]", id, p1.x, p1.y, p2.x, p2.y);
|
||
}
|
||
}
|
||
|
||
/**
|
||
* Event types for the sweep line algorithm.
|
||
*/
|
||
private enum EventType { START, END, INTERSECTION }
|
||
|
||
/**
|
||
* Represents an event in the event queue.
|
||
*/
|
||
private static class Event implements Comparable<Event> {
|
||
final Point2D.Double point;
|
||
final EventType type;
|
||
final Set<Segment> segments; // Segments involved in this event
|
||
|
||
Event(Point2D.Double point, EventType type) {
|
||
this.point = point;
|
||
this.type = type;
|
||
this.segments = new HashSet<>();
|
||
}
|
||
|
||
void addSegment(Segment s) {
|
||
segments.add(s);
|
||
}
|
||
|
||
@Override
|
||
public int compareTo(Event other) {
|
||
// Sort by x-coordinate, then by y-coordinate
|
||
int cmp = Double.compare(this.point.x, other.point.x);
|
||
if (cmp == 0) {
|
||
cmp = Double.compare(this.point.y, other.point.y);
|
||
}
|
||
if (cmp == 0) {
|
||
// Process END events before START events at same point
|
||
cmp = this.type.compareTo(other.type);
|
||
}
|
||
return cmp;
|
||
}
|
||
|
||
@Override
|
||
public boolean equals(Object o) {
|
||
if (!(o instanceof Event e)) {
|
||
return false;
|
||
}
|
||
return pointsEqual(this.point, e.point);
|
||
}
|
||
|
||
@Override
|
||
public int hashCode() {
|
||
return Objects.hash(Math.round(point.x * 1e6), Math.round(point.y * 1e6));
|
||
}
|
||
}
|
||
|
||
/**
|
||
* Comparator for segments in the status structure (sweep line).
|
||
* Orders segments by their y-coordinate at the current sweep line position.
|
||
*/
|
||
private static final class StatusComparator implements Comparator<Segment> {
|
||
@Override
|
||
public int compare(Segment s1, Segment s2) {
|
||
if (s1.id == s2.id) {
|
||
return 0;
|
||
}
|
||
|
||
double y1 = s1.getY(currentSweepX);
|
||
double y2 = s2.getY(currentSweepX);
|
||
|
||
int cmp = Double.compare(y1, y2);
|
||
if (Math.abs(y1 - y2) < EPS) {
|
||
// If y-coordinates are equal, use segment id for consistency
|
||
return Integer.compare(s1.id, s2.id);
|
||
}
|
||
return cmp;
|
||
}
|
||
}
|
||
|
||
/**
|
||
* Finds all intersection points among a set of line segments.
|
||
*
|
||
* <p>An intersection point is reported when two or more segments cross or touch.
|
||
* For overlapping segments, only actual crossing/touching points are reported,
|
||
* not all points along the overlap.</p>
|
||
*
|
||
* @param segments list of line segments represented as pairs of points
|
||
* @return a set of intersection points where segments meet or cross
|
||
* @throws IllegalArgumentException if the list is null or contains null points
|
||
*/
|
||
public static Set<Point2D.Double> findIntersections(List<Segment> segments) {
|
||
if (segments == null) {
|
||
throw new IllegalArgumentException("Segment list must not be null");
|
||
}
|
||
|
||
Segment.segmentCounter = 0; // Reset counter
|
||
Set<Point2D.Double> intersections = new HashSet<>();
|
||
PriorityQueue<Event> eventQueue = new PriorityQueue<>();
|
||
TreeSet<Segment> status = new TreeSet<>(new StatusComparator());
|
||
Map<Point2D.Double, Event> eventMap = new HashMap<>();
|
||
|
||
// Initialize event queue with segment start and end points
|
||
for (Segment s : segments) {
|
||
Point2D.Double left = s.leftPoint();
|
||
Point2D.Double right = s.rightPoint();
|
||
|
||
Event startEvent = getOrCreateEvent(eventMap, left, EventType.START);
|
||
startEvent.addSegment(s);
|
||
|
||
Event endEvent = getOrCreateEvent(eventMap, right, EventType.END);
|
||
endEvent.addSegment(s);
|
||
}
|
||
|
||
// Add all unique events to the queue
|
||
for (Event e : eventMap.values()) {
|
||
if (!e.segments.isEmpty()) {
|
||
eventQueue.add(e);
|
||
}
|
||
}
|
||
|
||
// Process events
|
||
while (!eventQueue.isEmpty()) {
|
||
Event event = eventQueue.poll();
|
||
currentSweepX = event.point.x;
|
||
|
||
handleEvent(event, status, eventQueue, eventMap, intersections);
|
||
}
|
||
|
||
return intersections;
|
||
}
|
||
|
||
private static Event getOrCreateEvent(Map<Point2D.Double, Event> eventMap, Point2D.Double point, EventType type) {
|
||
// Find existing event at this point
|
||
for (Map.Entry<Point2D.Double, Event> entry : eventMap.entrySet()) {
|
||
if (pointsEqual(entry.getKey(), point)) {
|
||
return entry.getValue();
|
||
}
|
||
}
|
||
// Create new event
|
||
Event event = new Event(point, type);
|
||
eventMap.put(point, event);
|
||
return event;
|
||
}
|
||
|
||
private static void handleEvent(Event event, TreeSet<Segment> status, PriorityQueue<Event> eventQueue, Map<Point2D.Double, Event> eventMap, Set<Point2D.Double> intersections) {
|
||
Point2D.Double p = event.point;
|
||
Set<Segment> segmentsAtPoint = new HashSet<>(event.segments);
|
||
|
||
// Check segments in status structure (much smaller than allSegments)
|
||
for (Segment s : status) {
|
||
if (pointsEqual(s.p1, p) || pointsEqual(s.p2, p) || (onSegment(s, p) && !pointsEqual(s.p1, p) && !pointsEqual(s.p2, p))) {
|
||
segmentsAtPoint.add(s);
|
||
}
|
||
}
|
||
|
||
// If 2 or more segments meet at this point, it's an intersection
|
||
if (segmentsAtPoint.size() >= 2) {
|
||
intersections.add(p);
|
||
}
|
||
|
||
// Categorize segments
|
||
Set<Segment> upperSegs = new HashSet<>(); // Segments starting at p
|
||
Set<Segment> lowerSegs = new HashSet<>(); // Segments ending at p
|
||
Set<Segment> containingSegs = new HashSet<>(); // Segments containing p in interior
|
||
|
||
for (Segment s : segmentsAtPoint) {
|
||
if (pointsEqual(s.leftPoint(), p)) {
|
||
upperSegs.add(s);
|
||
} else if (pointsEqual(s.rightPoint(), p)) {
|
||
lowerSegs.add(s);
|
||
} else {
|
||
containingSegs.add(s);
|
||
}
|
||
}
|
||
|
||
// Remove ending segments and segments containing p from status
|
||
status.removeAll(lowerSegs);
|
||
status.removeAll(containingSegs);
|
||
|
||
// Update sweep line position slightly past the event
|
||
currentSweepX = p.x + EPS;
|
||
|
||
// Add starting segments and re-add containing segments
|
||
status.addAll(upperSegs);
|
||
status.addAll(containingSegs);
|
||
|
||
if (upperSegs.isEmpty() && containingSegs.isEmpty()) {
|
||
// Find neighbors and check for new intersections
|
||
Segment sl = getNeighbor(status, lowerSegs, true);
|
||
Segment sr = getNeighbor(status, lowerSegs, false);
|
||
if (sl != null && sr != null) {
|
||
findNewEvent(sl, sr, p, eventQueue, eventMap);
|
||
}
|
||
} else {
|
||
Set<Segment> unionSegs = new HashSet<>(upperSegs);
|
||
unionSegs.addAll(containingSegs);
|
||
|
||
Segment leftmost = getLeftmost(unionSegs, status);
|
||
Segment rightmost = getRightmost(unionSegs, status);
|
||
|
||
if (leftmost != null) {
|
||
Segment sl = status.lower(leftmost);
|
||
if (sl != null) {
|
||
findNewEvent(sl, leftmost, p, eventQueue, eventMap);
|
||
}
|
||
}
|
||
|
||
if (rightmost != null) {
|
||
Segment sr = status.higher(rightmost);
|
||
if (sr != null) {
|
||
findNewEvent(rightmost, sr, p, eventQueue, eventMap);
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
private static Segment getNeighbor(NavigableSet<Segment> status, Set<Segment> removed, boolean lower) {
|
||
if (removed.isEmpty()) {
|
||
return null;
|
||
}
|
||
Segment ref = removed.iterator().next();
|
||
return lower ? status.lower(ref) : status.higher(ref);
|
||
}
|
||
|
||
private static Segment getLeftmost(Set<Segment> segments, SortedSet<Segment> status) {
|
||
Segment leftmost = null;
|
||
for (Segment s : segments) {
|
||
if (leftmost == null || Objects.requireNonNull(status.comparator()).compare(s, leftmost) < 0) {
|
||
leftmost = s;
|
||
}
|
||
}
|
||
return leftmost;
|
||
}
|
||
|
||
private static Segment getRightmost(Set<Segment> segments, SortedSet<Segment> status) {
|
||
Segment rightmost = null;
|
||
for (Segment s : segments) {
|
||
if (status.comparator() != null && (rightmost == null || status.comparator().compare(s, rightmost) > 0)) {
|
||
rightmost = s;
|
||
}
|
||
}
|
||
return rightmost;
|
||
}
|
||
|
||
private static void findNewEvent(Segment s1, Segment s2, Point2D.Double currentPoint, PriorityQueue<Event> eventQueue, Map<Point2D.Double, Event> eventMap) {
|
||
Point2D.Double intersection = getIntersection(s1, s2);
|
||
|
||
if (intersection != null && intersection.x > currentPoint.x - EPS && !pointsEqual(intersection, currentPoint)) {
|
||
|
||
// Check if event already exists
|
||
boolean exists = false;
|
||
for (Map.Entry<Point2D.Double, Event> entry : eventMap.entrySet()) {
|
||
if (pointsEqual(entry.getKey(), intersection)) {
|
||
exists = true;
|
||
Event existingEvent = entry.getValue();
|
||
existingEvent.addSegment(s1);
|
||
existingEvent.addSegment(s2);
|
||
break;
|
||
}
|
||
}
|
||
|
||
if (!exists) {
|
||
Event newEvent = new Event(intersection, EventType.INTERSECTION);
|
||
newEvent.addSegment(s1);
|
||
newEvent.addSegment(s2);
|
||
eventMap.put(intersection, newEvent);
|
||
eventQueue.add(newEvent);
|
||
}
|
||
}
|
||
}
|
||
|
||
private static Point2D.Double getIntersection(Segment s1, Segment s2) {
|
||
double x1 = s1.p1.x;
|
||
double y1 = s1.p1.y;
|
||
double x2 = s1.p2.x;
|
||
double y2 = s1.p2.y;
|
||
double x3 = s2.p1.x;
|
||
double y3 = s2.p1.y;
|
||
double x4 = s2.p2.x;
|
||
double y4 = s2.p2.y;
|
||
|
||
double denom = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4);
|
||
|
||
if (Math.abs(denom) < EPS) {
|
||
// Parallel or collinear
|
||
if (areCollinear(s1, s2)) {
|
||
// For collinear segments, check if they overlap
|
||
// Return any overlapping point
|
||
List<Point2D.Double> overlapPoints = new ArrayList<>();
|
||
|
||
if (onSegment(s1, s2.p1)) {
|
||
overlapPoints.add(s2.p1);
|
||
}
|
||
if (onSegment(s1, s2.p2)) {
|
||
overlapPoints.add(s2.p2);
|
||
}
|
||
if (onSegment(s2, s1.p1)) {
|
||
overlapPoints.add(s1.p1);
|
||
}
|
||
if (onSegment(s2, s1.p2)) {
|
||
overlapPoints.add(s1.p2);
|
||
}
|
||
|
||
// Remove duplicates and return the first point
|
||
if (!overlapPoints.isEmpty()) {
|
||
// Find the point that's not an endpoint of both segments
|
||
for (Point2D.Double pt : overlapPoints) {
|
||
boolean isS1Endpoint = pointsEqual(pt, s1.p1) || pointsEqual(pt, s1.p2);
|
||
boolean isS2Endpoint = pointsEqual(pt, s2.p1) || pointsEqual(pt, s2.p2);
|
||
|
||
// If it's an endpoint of both, it's a touching point
|
||
if (isS1Endpoint && isS2Endpoint) {
|
||
return pt;
|
||
}
|
||
}
|
||
// Return the first overlap point
|
||
return overlapPoints.getFirst();
|
||
}
|
||
}
|
||
return null;
|
||
}
|
||
|
||
double t = ((x1 - x3) * (y3 - y4) - (y1 - y3) * (x3 - x4)) / denom;
|
||
double u = -((x1 - x2) * (y1 - y3) - (y1 - y2) * (x1 - x3)) / denom;
|
||
|
||
if (t >= -EPS && t <= 1 + EPS && u >= -EPS && u <= 1 + EPS) {
|
||
double px = x1 + t * (x2 - x1);
|
||
double py = y1 + t * (y2 - y1);
|
||
return new Point2D.Double(px, py);
|
||
}
|
||
|
||
return null;
|
||
}
|
||
|
||
private static boolean areCollinear(Segment s1, Segment s2) {
|
||
double cross1 = crossProduct(s1.p1, s1.p2, s2.p1);
|
||
double cross2 = crossProduct(s1.p1, s1.p2, s2.p2);
|
||
return Math.abs(cross1) < EPS && Math.abs(cross2) < EPS;
|
||
}
|
||
|
||
private static double crossProduct(Point2D.Double a, Point2D.Double b, Point2D.Double c) {
|
||
return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);
|
||
}
|
||
|
||
private static boolean onSegment(Segment s, Point2D.Double p) {
|
||
return p.x >= Math.min(s.p1.x, s.p2.x) - EPS && p.x <= Math.max(s.p1.x, s.p2.x) + EPS && p.y >= Math.min(s.p1.y, s.p2.y) - EPS && p.y <= Math.max(s.p1.y, s.p2.y) + EPS && Math.abs(crossProduct(s.p1, s.p2, p)) < EPS;
|
||
}
|
||
|
||
private static boolean pointsEqual(Point2D.Double p1, Point2D.Double p2) {
|
||
return Math.abs(p1.x - p2.x) < EPS && Math.abs(p1.y - p2.y) < EPS;
|
||
}
|
||
}
|