shader编程-三维场景下SDF建模,平滑交集、平滑并集、平滑差集(WebGL-Shader开发基础11)

三维场景下SDF建模,平滑交集、平滑并集、平滑差集

1. demo效果

smooth-operate

如上所示,三个展示的模型分别为球体和立方体进行平滑交集、平滑并集、平滑差集运算的效果

2. 实现要点

2.1 平滑运算方法定义

demo用到平滑交集、平滑并集、平滑差集运算,它们的定义如下

//平滑交集
float opSmoothI( float d1, float d2, float k )
{
  float h = max(k-abs(d1-d2),0.0);
  return max(d1, d2) + h*h*0.25/k;
}

//平滑并集
float opSmoothU( float d1, float d2, float k )
{
  float h = max(k-abs(d1-d2),0.0);
  return min(d1, d2) - h*h*0.25/k;
}

//平滑差集
float opSmoothS( float d1, float d2, float k )
{
  float h = max(k-abs(-d1-d2),0.0);
  return max(-d1, d2) + h*h*0.25/k;
}

2.2 模型计算

有了之前的铺垫,今天的内容比较简单,就是将两个模型使用对应的平滑操作函数处理,然后使用处理好的结果追加上材质ID,之后把它们求并集返回即可,具体如下

vec2 res =  vec2(p.y,0.0);//地面

vec3 pos = p-vec3(0,2,5);//确定模型的中心
vec4 boxPos = vec4(pos,1.0);//转为其次坐标
boxPos*=rotX(0.6);//旋转

//平滑交集
boxPos.x += 2.5; //使模型绘制原点沿x轴左移2.5个单位
float box1 = sdBox(boxPos.xyz,vec3(1.0),0.06);//方块
float sphere1 = sdSphere(boxPos.xyz-vec3(0.0,sin(u_time)*0.25+1.2,0.0),0.6);//上下浮动的球
vec2 boxSphereSmoothI = vec2(opSmoothI(sphere1,box1,0.25),1.0);



//平滑并集
boxPos.x -= 2.5;//使模型绘制原点沿x轴右移2.5个单位
float box2 = sdBox(boxPos.xyz,vec3(1.0),0.06);//方块
float sphere2 = sdSphere(boxPos.xyz-vec3(0.0,sin(u_time)*0.25+1.2,0.0),0.6);//上下浮动的球
vec2 boxSphereSmoothU = vec2(opSmoothU(sphere2,box2,0.25),2.0);


//平滑差集
boxPos.x -= 2.5;//使模型绘制原点沿x轴右移2.5个单位
float box = sdBox(boxPos.xyz,vec3(1.0),0.06);//方块
float sphere = sdSphere(boxPos.xyz-vec3(0.0,sin(u_time)*0.25+1.2,0.0),0.6);//上下浮动的球
vec2 boxSphereSmoothS = vec2(opSmoothS(sphere,box,0.25),3.0);

res = opU(res,boxSphereSmoothI); 
res = opU(res,boxSphereSmoothU); 
res = opU(res,boxSphereSmoothS); 

return res;

3. demo代码

今天新内容不但少而且简单,只经过两步就跳到最后的代码展示了,愿天下没有难写的shader!

<body>
  <div id="container"></div>
  <script src="http://www.yanhuangxueyuan.com/versions/threejsR92/build/three.js"></script>
  <script>
    var container;
    var camera, scene, renderer;
    var uniforms;
    var vertexShader = `
      void main() {
        gl_Position = vec4( position, 1.0 );
      } 
    `
    var fragmentShader = `
    #ifdef GL_ES
    precision mediump float;
    #endif
    uniform float u_time;
    uniform vec2 u_mouse;
    uniform vec2 u_resolution;

    const int MAX_STEPS = 100;//最大步进步数
    const float MAX_DIST = 100.0;//最大步进距离
    const float SURF_DIST = 0.01;//相交检测临近表面距离

    //绕z轴旋转矩阵
    mat4 rotZ(float a) {
      return mat4(cos(a),-sin(a),0.0,0.0,
                  sin(a),cos(a),0.0,0.0,
                  0.0,0.0,1.0,0.0,
                  0.0,0.0,0.0,1.0
                  );
    }
    
    //绕x轴旋转矩阵
    mat4 rotX(float a) {
      return mat4(1.0,0.0,0.0,0.0,
                  0.0,cos(a),-sin(a),0.0,
                  0.0,sin(a),cos(a),0.0,
                  0.0,0.0,0.0,1.0
                );
    }
    
    //绕y轴旋转矩阵
    mat4 rotY(float a) {
      return mat4(cos(a),0.0,sin(a),0.0,
                  0.0,1.0,0.0,0.0,
                  -sin(a),0.0,cos(a),0.0,
                  0.0,0.0,0.0,1.0
                );
    } 

    //平滑交集
    float opSmoothI( float d1, float d2, float k )
    {
      float h = max(k-abs(d1-d2),0.0);
      return max(d1, d2) + h*h*0.25/k;
    }

    //平滑并集
    float opSmoothU( float d1, float d2, float k )
    {
      float h = max(k-abs(d1-d2),0.0);
      return min(d1, d2) - h*h*0.25/k;
    }

    //平滑差集
    float opSmoothS( float d1, float d2, float k )
    {
      float h = max(k-abs(-d1-d2),0.0);
      return max(-d1, d2) + h*h*0.25/k;
    }


    //并集
    vec2 opU( vec2 d1, vec2 d2 )
    {
      return (d1.x<d2.x) ? d1 : d2;
    }


    //球体
    float sdSphere( vec3 p, float s )
    {
      return length(p)-s;
    }

    //立方体
    float sdBox( vec3 p, vec3 b,float rad )
    {
      vec3 d = abs(p) - b;
      return min(max(d.x,max(d.y,d.z)),0.0) + length(max(d,0.0)) - rad;
    }


    vec2 getDistandMaterial(vec3 p){

      vec2 res =  vec2(p.y,0.0);//地面
 
      vec3 pos = p-vec3(0,2,5);//确定模型的中心
      vec4 boxPos = vec4(pos,1.0);//转为其次坐标
      boxPos*=rotX(0.6);//旋转

      //平滑交集
      boxPos.x += 2.5; //使模型绘制原点沿x轴左移2.5个单位
      float box1 = sdBox(boxPos.xyz,vec3(1.0),0.06);//方块
      float sphere1 = sdSphere(boxPos.xyz-vec3(0.0,sin(u_time)*0.25+1.2,0.0),0.6);//上下浮动的球
      vec2 boxSphereSmoothI = vec2(opSmoothI(sphere1,box1,0.25),1.0);


     
      //平滑并集
      boxPos.x -= 2.5;//使模型绘制原点沿x轴右移2.5个单位
      float box2 = sdBox(boxPos.xyz,vec3(1.0),0.06);//方块
      float sphere2 = sdSphere(boxPos.xyz-vec3(0.0,sin(u_time)*0.25+1.2,0.0),0.6);//上下浮动的球
      vec2 boxSphereSmoothU = vec2(opSmoothU(sphere2,box2,0.25),2.0);

      
      //平滑差集
      boxPos.x -= 2.5;//使模型绘制原点沿x轴右移2.5个单位
      float box = sdBox(boxPos.xyz,vec3(1.0),0.06);//方块
      float sphere = sdSphere(boxPos.xyz-vec3(0.0,sin(u_time)*0.25+1.2,0.0),0.6);//上下浮动的球
      vec2 boxSphereSmoothS = vec2(opSmoothS(sphere,box,0.25),3.0);
   
      res = opU(res,boxSphereSmoothI); 
      res = opU(res,boxSphereSmoothU); 
      res = opU(res,boxSphereSmoothS); 

      return res;
    }

    vec2 rayMarch(vec3 rayStart, vec3 rayDirection) {
      float depth=0.;
      float material=0.;
      for(int i=0; i<MAX_STEPS; i++) {
        vec3 p = rayStart + rayDirection*depth;//上一次步进结束后的坐标也就是这一次步进出发点

        vec2 dm = getDistandMaterial(p);
        float dist = dm.x;//获取当前步进出发点与物体相交时距离
        material = dm.y;
        depth += dist; //步进长度累加

        if(depth>MAX_DIST || dist<SURF_DIST) break;//步进距离大于最大步进距离或与物体表面距离小于最小表面距离(光线进入物体)停止前进
      }
      return vec2(depth,material);
    }

    vec3 getNormal(vec3 p){
      return normalize(vec3(
        getDistandMaterial(vec3(p.x + SURF_DIST, p.y, p.z)).x - getDistandMaterial(vec3(p.x - SURF_DIST, p.y, p.z)).x,
        getDistandMaterial(vec3(p.x, p.y + SURF_DIST, p.z)).x - getDistandMaterial(vec3(p.x, p.y - SURF_DIST, p.z)).x,
        getDistandMaterial(vec3(p.x, p.y, p.z  + SURF_DIST)).x - getDistandMaterial(vec3(p.x, p.y, p.z - SURF_DIST)).x
      ));
    }


    //Blinn-Phong模型光照计算
    vec3 calcBlinnPhongLight( vec3 materialColor, vec3 p, vec3 ro) {

      vec3 lightPos = vec3(5.0 * sin(u_time), 20.0, 10.0*cos(u_time)-18.);//光源坐标

      //计算环境光
      float k_a = 0.3;//环境光反射系数
      vec3 ambientLight = 0.6 * vec3(1.0, 1.0, 1.0);
      vec3 ambient = k_a*ambientLight;
      
      vec3 N = getNormal(p); //法线
      vec3 L = normalize(lightPos - p); //光照方向
      vec3 V = normalize(ro - p); //视线
      vec3 H = normalize(V+L); //半程向量

      float r = length(lightPos - p);


      //计算漫反射光
      float k_d = 0.6;//漫反射系数
      float dotLN = clamp(dot(L, N),0.0,1.0);//点乘,并将结果限定在0~1
      vec3 diffuse = k_d * (materialColor/r*r) * dotLN;


      //计算高光反射光
      float k_s = 0.8;//镜面反射系数
      float shininess = 160.0;
      vec3 specularColor = vec3(1.0, 1.0, 1.0);
      vec3 specular = k_s * (specularColor/r*r)* pow(clamp(dot(N, H), 0.0, 1.0), shininess);//计算高光
  
      
      //计算阴影
      vec2 res = rayMarch(p + N*SURF_DIST*2.0,L); 
      if(res.x<length(lightPos-p)-0.001){
        diffuse*=0.1;
      }
        
      //颜色 =  环境光 + 漫反射光 + 镜面反射光
      return ambient +diffuse + specular;
    }

    void main( void ) {

      //窗口坐标调整为[-1,1],坐标原点在屏幕中心
      vec2 st = (gl_FragCoord.xy * 2. - u_resolution) / u_resolution.y;


      vec3 ro = vec3(0.0,2.0,0.0);//视点
      vec3 rd = normalize(vec3(st.x,st.y,1.0));//视线方向

      vec2 res = rayMarch(ro,rd);//反向光线追踪求交点距离与材质ID

      float d = res.x;//物体与视点的距离
      float m = res.y;//材质ID
  
      vec3 p = ro + rd * d;

      vec3 materialColor = vec3(1.0, 0.0, 1.0);//默认材质色,使用差集计算出来的内壁会使用该色填充
      
      
      //为不同物体设置不同的材质颜色
      if(m==0.0){
        materialColor = vec3(.2, 0.0, 0.0);
      }
      if(m==1.0){
        materialColor = vec3(.2, 0.0, 1.0);
      }
      if(m==2.0){
        materialColor = vec3(.7, 0.2, 0.0);
      }
      if(m==3.0){
        materialColor = vec3(.8, .9, 0.0);
      }

      vec3 color = vec3(1.0,1.0,1.0);

      //使用Blinn-Phong模型计算光照
      color *= calcBlinnPhongLight( materialColor, p, ro);

      gl_FragColor = vec4(color, 1.0);

    }
    `

    init();
    animate();

    function init() {
      container = document.getElementById('container');

      camera = new THREE.Camera();
      camera.position.z = 1;

      scene = new THREE.Scene();

      var geometry = new THREE.PlaneBufferGeometry(2, 2);

      uniforms = {
        u_time: {
          type: "f",
          value: 1.0
        },
        u_resolution: {
          type: "v2",
          value: new THREE.Vector2()
        },
        u_mouse: {
          type: "v2",
          value: new THREE.Vector2()
        }
      };

      var material = new THREE.ShaderMaterial({
        uniforms: uniforms,
        vertexShader: vertexShader,
        fragmentShader: fragmentShader
      });

      var mesh = new THREE.Mesh(geometry, material);
      scene.add(mesh);

      renderer = new THREE.WebGLRenderer();
      //renderer.setPixelRatio(window.devicePixelRatio);

      container.appendChild(renderer.domElement);

      onWindowResize();
      window.addEventListener('resize', onWindowResize, false);

      document.onmousemove = function (e) {
        uniforms.u_mouse.value.x = e.pageX
        uniforms.u_mouse.value.y = e.pageY
      }
    }

    function onWindowResize(event) {
      renderer.setSize(800, 800);
      uniforms.u_resolution.value.x = renderer.domElement.width;
      uniforms.u_resolution.value.y = renderer.domElement.height;
    }

    function animate() {
      requestAnimationFrame(animate);
      render();
    }

    function render() {
      uniforms.u_time.value += 0.02;
      renderer.render(scene, camera);
    }
  </script>
</body>

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