在IDEA实现正四面体的透视投影动态隐线算法java

正四面体是一个四面体，每个面都是一个等边三角形。要实现正四面体的透视投影动态隐线算法，可以按照以下步骤进行：

1. 定义正四面体的顶点坐标和面的顶点索引。

double[][] vertices = {{-1, -1, -1}, {-1, -1, 1}, {-1, 1, -1}, {1, -1, -1}};
int[][] faces = {{0, 1, 2}, {1, 3, 2}, {0, 2, 3}, {0, 3, 1}};

2. 对正四面体进行透视投影。

double f = 1.5; // 焦距
double[][] projected = new double[4][2];
for (int i = 0; i < 4; i++) {
    double x = vertices[i][0];
    double y = vertices[i][1];
    double z = vertices[i][2];
    projected[i][0] = f * x / (f - z);
    projected[i][1] = f * y / (f - z);
}

3. 根据面的顶点索引，绘制正四面体的各个面。

for (int i = 0; i < 4; i++) {
    int[] face = faces[i];
    double[] p1 = projected[face[0]];
    double[] p2 = projected[face[1]];
    double[] p3 = projected[face[2]];
    // 绘制三角形面
    // ...
}

4. 实现动态隐线算法。

动态隐线算法是指在绘制立体物体时，根据视点的位置和物体的几何形状，动态地确定哪些线段是可见的，哪些是被遮挡的。实现动态隐线算法需要使用 Z 缓冲算法。

// 初始化 Z 缓冲区
double[][] zBuffer = new double[width][height];
for (int i = 0; i < width; i++) {
    for (int j = 0; j < height; j++) {
        zBuffer[i][j] = Double.NEGATIVE_INFINITY;
    }
}
// 绘制三角形面并更新 Z 缓冲区
for (int i = 0; i < 4; i++) {
    int[] face = faces[i];
    double[] p1 = projected[face[0]];
    double[] p2 = projected[face[1]];
    double[] p3 = projected[face[2]];
    // 计算三角形面的法向量
    double[] normal = {0, 0, 0};
    // ...
    // 判断是否可见
    boolean visible = normal[2] > 0;
    if (visible) {
        // 对三角形面进行裁剪
        // ...
        // 计算三角形面的重心坐标
        double alpha = 0.5, beta = 0.5, gamma = 0.5;
        // ...
        // 计算三角形面的深度值
        double z = alpha * p1[2] + beta * p2[2] + gamma * p3[2];
        // 更新 Z 缓冲区
        if (z > zBuffer[i][j]) {
            zBuffer[i][j] = z;
            // 绘制三角形面
            // ...
        }
    }
}

这样就可以实现正四面体的透视投影动态隐线算法了。完整代码如下：

import javax.swing.*;
import java.awt.*;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;

public class Tetrahedron extends JPanel implements ActionListener {
    private static final int WIDTH = 600;
    private static final int HEIGHT = 600;
    private static final double[][] VERTICES = {{-1, -1, -1}, {-1, -1, 1}, {-1, 1, -1}, {1, -1, -1}};
    private static final int[][] FACES = {{0, 1, 2}, {1, 3, 2}, {0, 2, 3}, {0, 3, 1}};
    private static final double F = 1.5;
    private static final double[][] PROJECTED = new double[4][2];
    private static final double[][] Z_BUFFER = new double[WIDTH][HEIGHT];
    private static final Color[] COLORS = {Color.RED, Color.GREEN, Color.BLUE, Color.YELLOW};

    private Timer timer;
    private double angle;

    public Tetrahedron() {
        setPreferredSize(new Dimension(WIDTH, HEIGHT));
        timer = new Timer(10, this);
        timer.start();
    }

    @Override
    protected void paintComponent(Graphics g) {
        super.paintComponent(g);

        // 绘制正四面体
        for (int i = 0; i < 4; i++) {
            double x = VERTICES[i][0];
            double y = VERTICES[i][1];
            double z = VERTICES[i][2];
            PROJECTED[i][0] = F * x / (F - z) + WIDTH / 2;
            PROJECTED[i][1] = F * y / (F - z) + HEIGHT / 2;
        }
        for (int i = 0; i < 4; i++) {
            int[] face = FACES[i];
            double[] p1 = PROJECTED[face[0]];
            double[] p2 = PROJECTED[face[1]];
            double[] p3 = PROJECTED[face[2]];
            double[] normal = getNormal(p1, p2, p3);
            boolean visible = normal[2] > 0;
            if (visible) {
                double alpha = 0.5, beta = 0.5, gamma = 0.5;
                double z = alpha * VERTICES[face[0]][2] + beta * VERTICES[face[1]][2] + gamma * VERTICES[face[2]][2];
                if (z > Z_BUFFER[(int) p1[0]][(int) p1[1]]) {
                    Z_BUFFER[(int) p1[0]][(int) p1[1]] = z;
                    g.setColor(COLORS[i]);
                    g.fillPolygon(new int[]{(int) p1[0], (int) p2[0], (int) p3[0]}, new int[]{(int) p1[1], (int) p2[1], (int) p3[1]}, 3);
                }
            }
        }
    }

    private double[] getNormal(double[] p1, double[] p2, double[] p3) {
        double[] v1 = {p2[0] - p1[0], p2[1] - p1[1], 0};
        double[] v2 = {p3[0] - p1[0], p3[1] - p1[1], 0};
        double[] normal = {v1[1] * v2[2] - v1[2] * v2[1], v1[2] * v2[0] - v1[0] * v2[2], v1[0] * v2[1] - v1[1] * v2[0]};
        double len = Math.sqrt(normal[0] * normal[0] + normal[1] * normal[1] + normal[2] * normal[2]);
        normal[0] /= len;
        normal[1] /= len;
        normal[2] /= len;
        return normal;
    }

    @Override
    public void actionPerformed(ActionEvent e) {
        angle += 0.01;
        double[][] rotateX = {{1, 0, 0}, {0, Math.cos(angle), -Math.sin(angle)}, {0, Math.sin(angle), Math.cos(angle)}};
        double[][] rotateY = {{Math.cos(angle), 0, Math.sin(angle)}, {0, 1, 0}, {-Math.sin(angle), 0, Math.cos(angle)}};
        double[][] rotateZ = {{Math.cos(angle), -Math.sin(angle), 0}, {Math.sin(angle), Math.cos(angle), 0}, {0, 0, 1}};

        // 旋转正四面体
        for (int i = 0; i < 4; i++) {
            double x = VERTICES[i][0];
            double y = VERTICES[i][1];
            double z = VERTICES[i][2];
            double[][] p = {{x}, {y}, {z}};
            p = matrixMultiply(rotateX, p);
            p = matrixMultiply(rotateY, p);
            p = matrixMultiply(rotateZ, p);
            VERTICES[i][0] = p[0][0];
            VERTICES[i][1] = p[1][0];
            VERTICES[i][2] = p[2][0];
        }

        // 清空 Z 缓冲区
        for (int i = 0; i < WIDTH; i++) {
            for (int j = 0; j < HEIGHT; j++) {
                Z_BUFFER[i][j] = Double.NEGATIVE_INFINITY;
            }
        }

        repaint();
    }

    private double[][] matrixMultiply(double[][] m1, double[][] m2) {
        int row1 = m1.length;
        int col1 = m1[0].length;
        int col2 = m2[0].length;
        double[][] result = new double[row1][col2];
        for (int i = 0; i < row1; i++) {
            for (int j = 0; j < col2; j++) {
                for (int k = 0; k < col1; k++) {
                    result[i][j] += m1[i][k] * m2[k][j];
                }
            }
        }
        return result;
    }

    public static void main(String[] args) {
        JFrame frame = new JFrame("Tetrahedron");
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        frame.getContentPane().add(new Tetrahedron());
        frame.pack();
        frame.setLocationRelativeTo(null);
        frame.setVisible(true);
    }
}