使用 Three.js 创建对称和图案效果，展示三维对称物体的几何特性。

function createSymmetryPattern() {
    const params = {
        symmetryType: 'rotation',
        order: 4,
        pattern: 'cube',
        showAxis: true
    };

    const group = new THREE.Group();

    switch(params.pattern) {
        case 'cube':
            const cubeGeometry = new THREE.BoxGeometry(1, 1, 1);
            const cubeMaterial = new THREE.MeshStandardMaterial({ 
                color: 0x00b4d8,
                metalness: 0.3,
                roughness: 0.7
            });
            
            for(let i = 0; i < params.order; i++) {
                const cube = new THREE.Mesh(cubeGeometry, cubeMaterial);
                const angle = (i / params.order) * Math.PI * 2;
                cube.position.set(
                    Math.cos(angle) * 2,
                    0,
                    Math.sin(angle) * 2
                );
                cube.rotation.y = angle;
                group.add(cube);
            }
            break;
    }

    if(params.showAxis) {
        const axisHelper = new THREE.AxesHelper(5);
        group.add(axisHelper);
    }

    return group;
}

function createGUI() {
    const gui = new GUI();
    
    const params = {
        symmetryType: 'rotation',
        order: 4,
        pattern: 'cube',
        showAxis: true,
        regenerate: () => {
            scene.remove(symmetryPattern);
            symmetryPattern = createSymmetryPattern();
            scene.add(symmetryPattern);
        }
    };

    const symmetryFolder = gui.addFolder('对称设置');
    symmetryFolder.add(params, 'symmetryType', ['rotation', 'mirror', 'radial'])
        .name('对称类型')
        .onChange(params.regenerate);
    symmetryFolder.add(params, 'order', 2, 12, 1)
        .name('对称阶数')
        .onChange(params.regenerate);
    symmetryFolder.add(params, 'pattern', ['cube', 'sphere', 'cylinder'])
        .name('图案类型')
        .onChange(params.regenerate);
    symmetryFolder.add(params, 'showAxis')
        .name('显示对称轴')
        .onChange(params.regenerate);
    symmetryFolder.open();
}