怎么才能用java代码实现三角网算法,通过传入的点数来绘制一个三角网
三角网算法也称为三角剖分算法,它是将一个二维平面中的点集进行三角剖分,使得任意两个三角形之间都不存在交集并且包含给定的点集。我们定义了一个 DelaunayTriangulation 类,它接收一个点集作为输入,并使用 Delaunay 三角剖分算法进行三角剖分。在 triangulate() 方法中,我们调用 Delaunay 三角剖分算法的实现代码进行三角剖分。在 paintComponent() 方法中,我们遍历所有的三角形并绘制出它们的面积。在 main() 方法中,我们创建了一个包含随机点的点集,并将 DelaunayTriangulation 添加到 JFrame 中进行绘制。
import java.awt.Graphics;
import java.awt.Point;
import java.awt.Polygon;
import java.util.ArrayList;
import java.util.List;
import javax.swing.JFrame;
import javax.swing.JPanel;
public class DelaunayTriangulation extends JPanel {
private List<Point> points;
private List<Triangle> triangles;
public DelaunayTriangulation(List<Point> points) {
this.points = points;
this.triangles = new ArrayList<>();
triangulate();
}
private void triangulate() {
// 使用 Delaunay 三角剖分算法进行三角剖分,见下面伪代码实现
}
@Override
protected void paintComponent(Graphics g) {
super.paintComponent(g);
// 绘制三角网
for (Triangle triangle : triangles) {
Polygon polygon = new Polygon();
polygon.addPoint(triangle.a.x, triangle.a.y);
polygon.addPoint(triangle.b.x, triangle.b.y);
polygon.addPoint(triangle.c.x, triangle.c.y);
g.drawPolygon(polygon);
}
}
public static void main(String[] args) {
// 创建一个包含随机点的点集
List<Point> points = new ArrayList<>();
int count = 100;
for (int i = 0; i < count; i++) {
int x = (int) (Math.random() * 500);
int y = (int) (Math.random() * 500);
points.add(new Point(x, y));
}
// 创建一个 JFrame 并将 DelaunayTriangulation 添加到其中
JFrame frame = new JFrame("Delaunay Triangulation");
frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
frame.setSize(600, 600);
frame.add(new DelaunayTriangulation(points));
frame.setVisible(true);
}
private static class Triangle {
private Point a;
private Point b;
private Point c;
// ...
}
}
使用java实现Delaunay三角剖分算法
import java.util.*;
public class Point {
public double x, y;
public Point(double x, double y) {
this.x = x;
this.y = y;
}
}
public class Edge {
public Point a, b;
public Edge(Point a, Point b) {
this.a = a;
this.b = b;
}
}
public class Triangle {
public Point a, b, c;
public Triangle(Point a, Point b, Point c) {
this.a = a;
this.b = b;
this.c = c;
}
}
public class DelaunayTriangulation {
List<Point> points;
List<Triangle> triangles;
public DelaunayTriangulation(List<Point> points) {
this.points = points;
this.triangles = new ArrayList<Triangle>();
Triangle superTriangle = createSuperTriangle();
triangles.add(superTriangle);
for (Point point : points) {
List<Triangle> badTriangles = new ArrayList<Triangle>();
for (Triangle triangle : triangles) {
if (triangleCircumcircleContains(triangle, point)) {
badTriangles.add(triangle);
}
}
Set<Edge> polygon = new HashSet<Edge>();
for (Triangle triangle : badTriangles) {
for (Edge edge : triangleEdges(triangle)) {
if (edgeSharedByTwoTriangles(edge, badTriangles)) {
polygon.remove(edge);
} else {
polygon.add(edge);
}
}
}
for (Edge edge : polygon) {
triangles.add(new Triangle(edge.a, edge.b, point));
}
triangles.removeIf(triangle -> triangleHasSuperTriangleVertex(triangle, superTriangle));
}
}
private Triangle createSuperTriangle() {
double minX = points.get(0).x;
double minY = points.get(0).y;
double maxX = minX;
double maxY = minY;
for (Point point : points) {
minX = Math.min(minX, point.x);
minY = Math.min(minY, point.y);
maxX = Math.max(maxX, point.x);
maxY = Math.max(maxY, point.y);
}
double dx = Math.max(maxX - minX, maxY - minY) * 2;
Point a = new Point(minX - dx, minY - dx);
Point b = new Point(minX - dx, maxY + dx);
Point c = new Point(maxX + dx, maxY + dx);
return new Triangle(a, b, c);
}
private boolean triangleCircumcircleContains(Triangle triangle, Point point) {
double ax = triangle.a.x - point.x;
double ay = triangle.a.y - point.y;
double bx = triangle.b.x - point.x;
double by = triangle.b.y - point.y;
double cx = triangle.c.x - point.x;
double cy = triangle.c.y - point.y;
double ab = ax * ax + ay * ay;
double bc = bx * bx + by * by;
double ca = cx * cx + cy * cy;
double det = ax * by * ca + bx * cy * ab + cx * ay * bc - ax * cy * bc - bx * ay * ca - cx * by * ab;
return det > 0;
}
private boolean edgeSharedByTwoTriangles(Edge edge, List<Triangle> triangles) {
int count = 0;
for (Triangle triangle : triangles) {
if (triangleEdges(triangle).contains(edge)) {
count++;
}
}
return count > 1;
}
private boolean triangleHasSuperTriangleVertex(Triangle triangle, Triangle superTriangle) {
return triangle.a == superTriangle.a || triangle.a == superTriangle.b || triangle.a == superTriangle.c ||
triangle.b == superTriangle.a || triangle.b == superTriangle.b || triangle.b == superTriangle.c ||
triangle.c == superTriangle.a || triangle.c == superTriangle.b || triangle.c == superTriangle.c;
}
private List<Edge> triangleEdges(Triangle triangle) {
List<Edge> edges = new ArrayList<Edge>();
edges.add(new Edge(triangle.a, triangle.b));
edges.add(new Edge(triangle.b, triangle.c));
edges.add(new Edge(triangle.c, triangle.a));
return edges;
}
}