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
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- 「已注销」 2023-03-03 07:24关注
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; } }
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