shader编程-三维场景下SDF建模，对模型进行扭曲、弯曲、裁剪、掏空操作（WebGL-Shader开发基础12）_综合

对模型进行扭曲、弯曲、裁剪、掏空操作

1. demo效果
2. 实现要点
- 2.1 模型扭曲
- 2.2 模型弯曲
- 2.3 模型裁剪与掏空
- - 2.3.1 球体裁剪与掏空
  - 2.3.2 圆柱裁剪与掏空
  - 2.3.3 甜圈圈裁剪与掏空
3. demo代码

1. demo效果

在这里插入图片描述

如上图所示，第一张是对方形圆柱进行扭曲操作的效果图，第二张图是对扁平立方体面进行弯曲操作的效果图，第三张图是从内到外依次是原物体，裁剪后的物体，裁剪后掏空物体的效果，从左到右依次对圆柱、球体、甜圈圈进行同样变换的效果

2. 实现要点

先回顾一下之前学习的SDF建模相关的一些操作，首先学习了基本变换旋转、缩放、平移，之后学习了通过布尔运算(交集、并集、差集)组合模型，进而拓展了平滑布尔运算组合模型，今天解锁一点点新的技能，对模型进行扭曲、弯曲、裁剪、掏空操作

2.1 模型扭曲

通过前面的demo效果展示知道，我们首先绘制了一个长条状的立方体，然后又绘制了一个以同样立方体扭曲后的物体，实现的核心思想就是变换用来绘制扭曲立方体的坐标，即依据y分量的变化使x分量和z分量转圈圈，具体代码如下

vec3 opTwistY( in vec3 p ,float k)
{
    float c = cos(k*p.y);float s = sin(k*p.y);mat2  m = mat2(c,-s,s,c);p.xz *=m;return p;
}

如果你想物体绕z轴或x轴扭曲，两种办法，一是先按y轴扭曲然后将物体旋转，二是将上面的函数中的分量替换为对应的坐标轴

扭曲的坐标处理完接着就是像之前一样绘制图形，为了方便使用我们将绘制过程封装成了一个函数，具体如下

vec2 twistBox (vec4 pos){
    //绘制原立方体pos.x += 2.5; float box1 = sdBox(pos.xyz,vec3(0.4,1.2,0.4),0.06);//方块vec2 mBox1 = vec2(box1,1.0);//绘制扭曲立方体pos.x -= 5.0; pos.xyz=opTwistY(pos.xyz,3.0);//扭曲float box2 = sdBox(pos.xyz,vec3(0.4,1.2,0.4),0.06);//方块vec2 mBox2 = vec2(box2,1.0);vec2 res = opU(mBox1,mBox2);return res;
}

调用过程如下

vec2 res =  vec2(p.y,0.0);//地面vec3 pos = p-vec3(0,2,5);//确定模型的中心
vec4 oriPos = vec4(pos,1.0);//转为其次坐标//扭曲
vec2 twistBox = twistBox(oriPos);res = opU(res,twistBox);//扭曲立方体

2.2 模型弯曲

弯曲也是同样的思想，通过改变绘制弯曲模型的坐标来实现，返回弯曲坐标的函数如下

vec3 opCheapBend(in vec3 p ,float k)
{
    float c = cos(k*p.x);float s = sin(k*p.x);mat2  m = mat2(c,-s,s,c);vec3  q = vec3(m*p.xy,p.z);return q;
}

像上一次一样，使用处理好的坐标绘制图形即可，这次也将绘制过程封装成了一个函数，具体如下

vec2 cheapBendBox (vec4 pos){
    //绘制原立方体面pos.x += 2.5; float box1 = sdBox(pos.xyz,vec3(1.0,0.2,0.6),0.06);//方块vec2 mBox1 = vec2(box1,1.0);//绘制弯曲立方体面pos.x -= 5.0; pos.xyz=opCheapBend(pos.xyz,0.5);//弯曲float box2 = sdBox(pos.xyz,vec3(1.0,0.2,0.6),0.06);//方块vec2 mBox2 = vec2(box2,1.0);vec2 res = opU(mBox1,mBox2);return res;
}

调用过程如下

vec2 res =  vec2(p.y,0.0);//地面vec3 pos = p-vec3(0,2,5);//确定模型的中心
vec4 oriPos = vec4(pos,1.0);//转为其次坐标//扭曲
vec2 twistBox = twistBox(oriPos);//弯曲
vec2 cheapBendBox = cheapBendBox(oriPos);
//res = opU(res,twistBox);//扭曲立方体
res = opU(res,cheapBendBox); //弯曲立方体

2.3 模型裁剪与掏空

2.3.1 球体裁剪与掏空

掏空函数

//掏空
float opOnion(float sdf, in float thickness )
{
    return abs(sdf)-thickness;
}

绘制过程是，我们首先绘制了一个完整的球体，然后绘制了一个裁剪的球体，最后绘制一个掏空且裁剪的球体，之所以也裁剪是因为不裁剪的画我们看不到内部结构，具体如下

vec2 onionSphere (vec4 pos){
    //绘制球体vec4 pos1 = pos;pos1.z -= 6.0; float sphere1 = sdSphere(pos1.xyz,0.6);vec2 mSphere1 = vec2(sphere1,2.0);//绘制裁剪球体vec4 pos2 = pos;pos2.z -= 2.5; float sphere2 = sdSphere(pos2.xyz,0.6);sphere2 = max( sphere2, pos2.y );//裁剪vec2 mSphere2 = vec2(sphere2,2.0);//绘制裁剪掏空球体vec4 pos3 = pos;float sphere3 = sdSphere(pos3.xyz,0.6);sphere3 = opOnion(sphere3,0.01);//掏空sphere3 = max( sphere3, pos3.y );//裁剪vec2 mSphere3 = vec2(sphere3,2.0);vec2 res = opU(mSphere1,mSphere2);res = opU(res,mSphere3);return res;
}

关于裁剪，不知你有没有联想到，这里的裁剪效果是裁掉了y轴大于0 的部分，如果想裁掉x轴或z上的大于0的部分，只需把max( sphere3, pos3.y );//裁剪此处的分量y替换,如果你想要留下y轴上部分，即demo中裁掉和留下的部分互换，那么在y分量前添加负号即可，max( sphere3, -pos3.y );//裁剪，其他轴中的裁剪同理

2.3.2 圆柱裁剪与掏空

圆柱的实现与球体的思路一样，只不过把球体换成圆柱，如下

vec2 onionCylinder (vec4 pos){
    //绘制圆柱vec4 pos1 = pos;pos1.z -= 6.0; float cylinder1 = sdCylinder(pos1.xyz,0.4,0.6);vec2 mCylinder1 = vec2(cylinder1,1.0);//绘制裁剪圆柱vec4 pos2 = pos;pos2.z -= 2.5; float cylinder2 = sdCylinder(pos2.xyz,0.4,0.6);cylinder2 = max( cylinder2, pos2.y );//裁剪vec2 mCylinder2 = vec2(cylinder2,1.0);//绘制裁剪掏空圆柱vec4 pos3 = pos;float cylinder3 = sdCylinder(pos3.xyz,0.4,0.6);cylinder3 = opOnion(cylinder3,0.01);//掏空cylinder3 = max( cylinder3, pos3.y );//裁剪vec2 mCylinder3 = vec2(cylinder3,1.0);vec2 res = opU(mCylinder1,mCylinder2);res = opU(res,mCylinder3);return res;
}

2.3.3 甜圈圈裁剪与掏空

甜圈圈裁剪与掏空也是同样的思路，绘制过程如下

vec2 onionTorus (vec4 pos){
    //绘制甜圈圈vec4 pos1 = pos;pos1.z -= 6.0; float torus1 = sdTorus(pos1.xyz,vec2(0.6,0.2));vec2 mTorus1 = vec2(torus1,3.0);//绘制裁剪甜圈圈vec4 pos2 = pos;pos2.z -= 2.5; float torus2 = sdTorus(pos2.xyz,vec2(0.6,0.2));torus2 = max( torus2, pos2.y );//裁剪vec2 mTorus2 = vec2(torus2,3.0);//绘制裁剪掏空甜圈圈vec4 pos3 = pos;float torus3 = sdTorus(pos3.xyz,vec2(0.6,0.2));torus3 = opOnion(torus3,0.01);//掏空torus3 = max( torus3, pos3.y );//裁剪vec2 mTorus3 = vec2(torus3,3.0);vec2 res = opU(mTorus1,mTorus2);res = opU(res,mTorus3);return res;
}

3. demo代码

继续，可直接跑起来的代码

<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_ESprecision mediump float;#endifuniform 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;}//掏空float opOnion(float sdf, in float thickness ){return abs(sdf)-thickness;}//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;}//圆柱float sdCylinder( vec3 p, float h, float r ){vec2 d = abs(vec2(length(p.xz),p.y)) - vec2(r,h);return min(max(d.x,d.y),0.0) + length(max(d,0.0));}//甜圈圈float sdTorus( vec3 p, vec2 t ){vec2 q = vec2(length(p.xz)-t.x,p.y);return length(q)-t.y;}vec3 opTwistY( in vec3 p ,float k){float c = cos(k*p.y);float s = sin(k*p.y);mat2 m = mat2(c,-s,s,c);p.xz *=m;return p;}vec3 opCheapBend(in vec3 p ,float k){float c = cos(k*p.x);float s = sin(k*p.x);mat2 m = mat2(c,-s,s,c);vec3 q = vec3(m*p.xy,p.z);return q;}vec2 twistBox (vec4 pos){//绘制原立方体pos.x += 2.5; float box1 = sdBox(pos.xyz,vec3(0.4,1.2,0.4),0.06);//方块vec2 mBox1 = vec2(box1,1.0);//绘制扭曲立方体pos.x -= 5.0; pos.xyz=opTwistY(pos.xyz,3.0);//扭曲float box2 = sdBox(pos.xyz,vec3(0.4,1.2,0.4),0.06);//方块vec2 mBox2 = vec2(box2,1.0);vec2 res = opU(mBox1,mBox2);return res;}vec2 onionCylinder (vec4 pos){//绘制圆柱vec4 pos1 = pos;pos1.z -= 6.0; float cylinder1 = sdCylinder(pos1.xyz,0.4,0.6);vec2 mCylinder1 = vec2(cylinder1,1.0);//绘制裁剪圆柱vec4 pos2 = pos;pos2.z -= 2.5; float cylinder2 = sdCylinder(pos2.xyz,0.4,0.6);cylinder2 = max( cylinder2, pos2.y );//裁剪vec2 mCylinder2 = vec2(cylinder2,1.0);//绘制裁剪掏空圆柱vec4 pos3 = pos;float cylinder3 = sdCylinder(pos3.xyz,0.4,0.6);cylinder3 = opOnion(cylinder3,0.01);//掏空cylinder3 = max( cylinder3, pos3.y );//裁剪vec2 mCylinder3 = vec2(cylinder3,1.0);vec2 res = opU(mCylinder1,mCylinder2);res = opU(res,mCylinder3);return res;}vec2 onionSphere (vec4 pos){//绘制球体vec4 pos1 = pos;pos1.z -= 6.0; float sphere1 = sdSphere(pos1.xyz,0.6);vec2 mSphere1 = vec2(sphere1,2.0);//绘制裁剪球体vec4 pos2 = pos;pos2.z -= 2.5; float sphere2 = sdSphere(pos2.xyz,0.6);sphere2 = max( sphere2, pos2.y );//裁剪vec2 mSphere2 = vec2(sphere2,2.0);//绘制裁剪掏空球体vec4 pos3 = pos;float sphere3 = sdSphere(pos3.xyz,0.6);sphere3 = opOnion(sphere3,0.01);//掏空sphere3 = max( sphere3, pos3.y );//裁剪vec2 mSphere3 = vec2(sphere3,2.0);vec2 res = opU(mSphere1,mSphere2);res = opU(res,mSphere3);return res;}vec2 onionTorus (vec4 pos){//绘制甜圈圈vec4 pos1 = pos;pos1.z -= 6.0; float torus1 = sdTorus(pos1.xyz,vec2(0.6,0.2));vec2 mTorus1 = vec2(torus1,3.0);//绘制裁剪甜圈圈vec4 pos2 = pos;pos2.z -= 2.5; float torus2 = sdTorus(pos2.xyz,vec2(0.6,0.2));torus2 = max( torus2, pos2.y );//裁剪vec2 mTorus2 = vec2(torus2,3.0);//绘制裁剪掏空甜圈圈vec4 pos3 = pos;float torus3 = sdTorus(pos3.xyz,vec2(0.6,0.2));torus3 = opOnion(torus3,0.01);//掏空torus3 = max( torus3, pos3.y );//裁剪vec2 mTorus3 = vec2(torus3,3.0);vec2 res = opU(mTorus1,mTorus2);res = opU(res,mTorus3);return res;}vec2 cheapBendBox (vec4 pos){//绘制原立方体面pos.x += 2.5; float box1 = sdBox(pos.xyz,vec3(1.0,0.2,0.6),0.06);//方块vec2 mBox1 = vec2(box1,1.0);//绘制弯曲立方体面pos.x -= 5.0; pos.xyz=opCheapBend(pos.xyz,0.5);//弯曲float box2 = sdBox(pos.xyz,vec3(1.0,0.2,0.6),0.06);//方块vec2 mBox2 = vec2(box2,1.0);vec2 res = opU(mBox1,mBox2);return res;}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 oriPos = vec4(pos,1.0);//转为其次坐标//扭曲vec2 twistBox = twistBox(oriPos);//弯曲vec2 cheapBendBox = cheapBendBox(oriPos);//裁剪掏空vec2 onionSphere = onionSphere(oriPos);vec2 onionCylinder = onionCylinder(oriPos+vec4(2.0,0.0,0.0,1.0));vec2 onionTorus = onionTorus(oriPos-vec4(2.0,0.0,0.0,1.0));//res = opU(res,twistBox);//扭曲立方体//res = opU(res,cheapBendBox); //弯曲立方体res = opU(res,onionSphere);//裁剪掏空球体res = opU(res,onionCylinder);//裁剪掏空圆柱res = opU(res,onionTorus);//裁剪掏空甜圈圈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0~1vec3 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(0.0,4.0,0.0);//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IDfloat d = res.x;//物体与视点的距离float m = res.y;//材质IDvec3 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: {
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    type: "v2",value: new THREE.Vector2()},u_mouse: {
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    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.pageXuniforms.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>