Java 100例：3D 線框立方體滑鼠旋轉

實作一個可透過滑鼠拖曳旋轉的 3D 線框立方體。使用簡單的 3D 旋轉矩陣 (X/Y 軸旋轉) 將 3D 座標投影至 2D 平面，繪製 6 個面的多邊形。滑鼠事件監聽器根據位移量更新旋轉角度並觸發重繪。

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

public class Gr3d1m extends JFrame
        implements MouseListener, MouseMotionListener {
    int dragX, dragY, angX = 30, angY = 30;
    CubeData data = new CubeData();
    Color[] colors = {Color.gray, Color.cyan, Color.green, Color.red,
                      Color.white, Color.orange, Color.magenta, Color.pink};

    public static void main(String[] args) { new Gr3d1m(); }

    public Gr3d1m() {
        setTitle("3D Cube Wireframe");
        setDefaultCloseOperation(JFrame.DISPOSE_ON_CLOSE);
        addMouseListener(this); addMouseMotionListener(this);
        setBackground(new Color(128, 128, 255));
        setSize(350, 350);
        setVisible(true);
    }

    public void mousePressed(MouseEvent e) { dragX = e.getX(); dragY = e.getY(); }
    public void mouseDragged(MouseEvent e) {
        angX += e.getY() - dragY;
        angY += e.getX() - dragX;
        dragX = e.getX(); dragY = e.getY();
        repaint();
    }
    // 其他 MouseListener/MouseMotionListener 方法留空
    public void mouseReleased(MouseEvent e) {}
    public void mouseClicked(MouseEvent e) {}
    public void mouseEntered(MouseEvent e) {}
    public void mouseExited(MouseEvent e) {}
    public void mouseMoved(MouseEvent e) {}

    public void paint(Graphics g) {
        clear(g);
        for (int i = 0; i < data.x.length; i++) {
            drawFace(g, data.x[i], data.y[i], data.z[i], 150, 150, colors[i]);
        }
        g.setColor(Color.YELLOW);
        g.drawString("X=" + (angX%360) + " Y=" + (angY%360), 10, getSize().height-30);
    }

    void clear(Graphics g) {
        Insets in = getInsets();
        g.setColor(new Color(128, 128, 255));
        g.fillRect(in.left, in.top, 350, 350);
    }

    void drawFace(Graphics g, double[] x, double[] y, double[] z,
                  int cx, int cy, Color c) {
        double radX = Math.toRadians(angX), radY = Math.toRadians(angY);
        double sinX = Math.sin(radX), cosX = Math.cos(radX);
        double sinY = Math.sin(radY), cosY = Math.cos(radY);
        int n = x.length;
        int[] xs = new int[n], ys = new int[n];
        for (int i = 0; i < n; i++) {
            double x1 = x[i]*cosY + z[i]*sinY;
            double z1 = -x[i]*sinY + z[i]*cosY;
            double y1 = y[i]*cosX - z1*sinX;
            xs[i] = cx + (int)Math.round(x1);
            ys[i] = cy - (int)Math.round(y1);
        }
        g.setColor(c);
        g.drawPolygon(xs, ys, n);
    }
}

class CubeData {
    double[][] x = new double[6][4];
    double[][] y = new double[6][4];
    double[][] z = new double[6][4];
    CubeData() {
        // 定義立方體 6 個面的 4 個頂點 (省略詳細座標)
    }
}

教學重點：

• 3D 旋轉矩陣：先繞 Y 軸旋轉，再繞 X 軸旋轉 (或相反)，順序影響結果。
• 投影：簡單正交投影 (捨棄 Z 軸)，適合教學演示。
• 消隱：線框模式不需消隱；填充模式需依面法向量判斷可見性 (見下一例)。