三维场景下SDF建模，平滑交集、平滑并集、平滑差集
- 1. demo效果
- 2. 实现要点
- 2.1 平滑运算方法定义
- 2.2 模型计算
- 3. demo代码
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_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;}//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0~1vec3 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(0.0,2.0,0.0);//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() {
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