1.ParametricGeometry自定义几何体介绍

ParametricGeometry可以创建基于等式的几何体。即可以通过自定义函数来创建自定义的几何体。创建ParametricGeometry自定义几何体时可输入以下参数：

属性	必须	描述
function	是	该参数是一个函数，以u、v值（0~1）作为参数，返回值是一个Vector3类型的对象，作为图形上的坐标
slices	是	该属性定义u值该分成多少段
stacks	是	该属性定义v值该分成多少段
useTris	否	默认是false，如果设置为true，那么几何体创建时会使用三角形面片，如果为false，将使用四边形面片

2.ParametricGeometry自定义几何体使用

2.1定义function

创建ParametricGeometry几何体时，第一个参数是一个function，拿示例中的第一个函数展示一下：

radialWave(u, v, position) {
  const r = 20

  const x = Math.sin(u) * r
  const z = Math.sin(v / 2) * 2 * r
  const y = (Math.sin(u * 4 * Math.PI) + Math.cos(v * 2 * Math.PI)) * 1.8
  position.set(x, y, z)
  return new THREE.Vector3(x, y, z)
}

2.2创建ParametricGeometry几何体对象

和其他几何体一样创建时，使用new关键字创建

//const geom = new THREE.ParametricGeometry(function, slices, stacks[,useTris])
const geom = new THREE.ParametricGeometry(this.radialWave, 120, 160)

2.3附材质创建Mesh对象并添加到场景

const geom = new THREE.ParametricGeometry(this.radialWave, 120, 160)
// 创建材质
const meshMaterial = new THREE.MeshPhongMaterial({
  color: 0x3399ff
})
meshMaterial.side = THREE.DoubleSide
// 创建网格对象
this.mesh = new THREE.Mesh(geom, meshMaterial)
this.mesh.position.set(0, 0, 0)
// 网格对象添加到场景中
this.scene.add(this.mesh)

3.demo说明

如上图所示，该示例可以通过右侧下拉选择创建自定义的四种不同的ParametricGeometry几何体

4.demo代码

<template>
  <div>
    <div id="container"></div>

    <div class="controls-box">
      <section>
        <el-row>
          <el-col :span="8" class="label-col"><label>drawFunc</label></el-col>
          <el-col :span="16">
            <el-select v-model="drawFunc" placeholder="请选择" @change="redraw">
              <el-option v-for="item in options" :key="item.value" :label="item.label" :value="item.value">
              </el-option>
            </el-select>
          </el-col>
        </el-row>
      </section>
    </div>
  </div>
</template>

<script>
import * as THREE from 'three'
import { OrbitControls } from 'three/examples/jsm/controls/OrbitControls.js'
import { SceneUtils } from 'three/examples/jsm/utils/SceneUtils.js'
export default {
  data() {
    return {
      options: [
        {
          value: 'radialWave',
          label: 'radialWave'
        },
        {
          value: 'klein',
          label: 'klein'
        },
        {
          value: 'mobius',
          label: 'mobius'
        },
        {
          value: 'mobius3d',
          label: 'mobius3d'
        }
      ],
      drawFunc: 'radialWave',
      step: 0.01,
      mesh: null,
      camera: null,
      scene: null,
      renderer: null,
      controls: null
    }
  },
  mounted() {
    this.init()
  },
  methods: {
    formatTooltip(val) {
      return val
    },
    // 初始化
    init() {
      this.createScene() // 创建场景
      this.createMesh() // 创建网格模型
      this.createLight() // 创建光源
      this.createCamera() // 创建相机
      this.createRender() // 创建渲染器
      this.createControls() // 创建控件对象
      this.render() // 渲染
    },
    // 创建场景
    createScene() {
      this.scene = new THREE.Scene()
    },
    radialWave(u, v, position) {
      const r = 20

      const x = Math.sin(u) * r
      const z = Math.sin(v / 2) * 2 * r
      const y = (Math.sin(u * 4 * Math.PI) + Math.cos(v * 2 * Math.PI)) * 1.8
      position.set(x, y, z)
      return new THREE.Vector3(x, y, z)
    },
    klein(v, u, position) {
      u *= Math.PI
      v *= 2 * Math.PI

      u = u * 2
      let x, y, z
      if (u < Math.PI) {
        x =
          3 * Math.cos(u) * (1 + Math.sin(u)) +
          2 * (1 - Math.cos(u) / 2) * Math.cos(u) * Math.cos(v)
        z =
          -8 * Math.sin(u) -
          2 * (1 - Math.cos(u) / 2) * Math.sin(u) * Math.cos(v)
      } else {
        x =
          3 * Math.cos(u) * (1 + Math.sin(u)) +
          2 * (1 - Math.cos(u) / 2) * Math.cos(v + Math.PI)
        z = -8 * Math.sin(u)
      }

      y = -2 * (1 - Math.cos(u) / 2) * Math.sin(v)

      position.set(x, y, z)
      return new THREE.Vector3(x, y, z)
    },
    mobius(u, t, position) {
      u = u - 0.5
      const v = 6 * Math.PI * t

      let x, y, z

      const a = 6
      x = Math.cos(v) * (a + u * Math.cos(v / 2))
      y = Math.sin(v) * (a + u * Math.cos(v / 2))
      z = u * Math.sin(v / 2)
      position.set(x, y, z)
      return new THREE.Vector3(x, y, z)
    },

    mobius3d(u, t, position) {
      u *= Math.PI
      t *= 10 * Math.PI

      u = u * 2
      const phi = u / 2
      const major = 8.25,
        a = 0.325,
        b = 0.65
      let x, y, z
      x = a * Math.cos(t) * Math.cos(phi) - b * Math.sin(t) * Math.sin(phi)
      z = a * Math.cos(t) * Math.sin(phi) + b * Math.sin(t) * Math.cos(phi)
      y = (major + x) * Math.sin(u)
      x = (major + x) * Math.cos(u)
      position.set(x, y, z)
      return new THREE.Vector3(x, y, z)
    },
    // 创建网格模型
    createMesh() {
      let geom = new THREE.ParametricGeometry(this.klein, 120, 120, false)
      switch (this.drawFunc) {
        case 'radialWave':
          geom = new THREE.ParametricGeometry(this.radialWave, 120, 160)
          break
        case 'klein':
          geom = new THREE.ParametricGeometry(this.klein, 120, 120, false)
          break

        case 'mobius':
          geom = new THREE.ParametricGeometry(this.mobius, 120, 100)
          break
        case 'mobius3d':
          geom = new THREE.ParametricGeometry(this.mobius3d, 120, 100)
          break
      }

      // 创建材质
      const meshMaterial = new THREE.MeshPhongMaterial({
        color: 0x3399ff
      })
      meshMaterial.side = THREE.DoubleSide
      // 创建网格对象
      this.mesh = new THREE.Mesh(geom, meshMaterial)
      this.mesh.position.set(0, 0, 0)
      // 网格对象添加到场景中
      this.scene.add(this.mesh)
    },

    // 创建光源
    createLight() {
      // 环境光
      const ambientLight = new THREE.AmbientLight(0xffffff, 0.1) // 创建环境光
      this.scene.add(ambientLight) // 将环境光添加到场景

      const spotLight = new THREE.SpotLight(0xffffff) // 创建聚光灯
      spotLight.position.set(-40, 60, -10)
      spotLight.castShadow = true
      this.scene.add(spotLight)
    },
    // 创建相机
    createCamera() {
      const element = document.getElementById('container')
      const width = element.clientWidth // 窗口宽度
      const height = element.clientHeight // 窗口高度
      const k = width / height // 窗口宽高比
      // PerspectiveCamera( fov, aspect, near, far )
      this.camera = new THREE.PerspectiveCamera(35, k, 0.1, 1000)
      this.camera.position.set(-20, 60, 40) // 设置相机位置

      this.camera.lookAt(new THREE.Vector3(10, 0, 0)) // 设置相机方向
      this.scene.add(this.camera)
    },
    // 创建渲染器
    createRender() {
      const element = document.getElementById('container')
      this.renderer = new THREE.WebGLRenderer({ antialias: true, alpha: true })
      this.renderer.setSize(element.clientWidth, element.clientHeight) // 设置渲染区域尺寸
      this.renderer.shadowMap.enabled = true // 显示阴影
      this.renderer.shadowMap.type = THREE.PCFSoftShadowMap
      this.renderer.setClearColor(0x3f3f3f, 1) // 设置背景颜色
      element.appendChild(this.renderer.domElement)
    },

    // 重新绘制
    redraw() {
      this.scene.remove(this.mesh)
      this.createMesh()
    },
    render() {
      //this.mesh.rotation.x = this.step
      this.mesh.rotation.y = this.step += 0.01
      this.renderer.render(this.scene, this.camera)
      requestAnimationFrame(this.render)
    },
    // 创建控件对象
    createControls() {
      this.controls = new OrbitControls(this.camera, this.renderer.domElement)
    }
  }
}
</script>
<style>
#container {
  position: absolute;
  width: 100%;
  height: 100%;
}
.controls-box {
  position: absolute;
  right: 5px;
  top: 5px;
  width: 300px;
  padding: 10px;
  background-color: #fff;
  border: 1px solid #c3c3c3;
}
.label-col {
  padding: 8px 5px;
}
</style>