提要

在上一篇文章中，我们介绍了简单的Shading，同时提出了一个光照模型，模拟了一个点光源，但是，关于光的故事还没有结束...

今天要学习的是方向光源（Directional Light），聚光灯，per pixel shading，halfway vector。

关于光源的原理及数学描述，请参考：光线追踪(RayTracing)算法理论与实践(三)光照

方向光源

方向光源就两个参数，方向和强度。

还是简单的 ambient + diffuse + spec 光照模型。先看shader的代码。

basic.vert

#version 400
layout (location = 0) in vec3 VertexPosition;
layout (location = 1) in vec3 VertexNormal;  out vec3 LightIntensity;struct LightInfo{vec4 Direction;vec3 Intensity;
};struct MaterialInfo{vec3 Ka;vec3 Kd;vec3 Ks;float Shininess;
};uniform LightInfo Light;
uniform MaterialInfo Material;uniform mat4 ModelViewMatrix;
uniform mat3 NormalMatrix;
uniform mat4 ProjectionMatrix;
uniform mat4 MVP;void getEyeSpace(out vec3 norm, out vec4 position)
{norm =  normalize(NormalMatrix * VertexNormal);position = ModelViewMatrix * vec4(VertexPosition, 1.0);
}vec3 ads(vec4 position, vec3 norm)
{vec3 s;if(Light.Direction.w == 0.0)s = normalize(vec3(Light.Direction));elses = normalize(vec3(Light.Direction - position));vec3 v = normalize(vec3(-position));vec3 r = reflect(-s, norm);return Light.Intensity * (Material.Ka + Material.Kd*max(dot(s,norm), 0.0) + Material.Ks * pow(max(dot(r,v),0.0), Material.Shininess));
}void main()
{vec3 eyeNorm;vec4 eyePosition;getEyeSpace(eyeNorm, eyePosition);LightIntensity = ads(eyePosition, eyeNorm);gl_Position = MVP * vec4( VertexPosition, 1.0);
}

在ads函数中，首先通过nomal矩阵将顶点法向量变换到视口坐标下，（nomal矩阵其实就是model-view矩阵的左上3x3的矩阵）然后通过model-view矩阵将顶点坐标转化为视口坐标系（eye coordinates）下。

接下来的ads用来计算光照模型下顶点的颜色,分别计算三个分量，然后相加。

basic.frag

#version 400in vec3 LightIntensity;void main(void)
{gl_FragColor = vec4(LightIntensity, 1.0);//gl_FragColor = vec4(1.0,1.0,0.1, 1.0);
}

void CGL::setUniform()
{mat4 projection = glm::perspective(45.0f, 4.0f / 3.0f, 0.1f, 100.0f);mat4 mv = view * model;prog.setUniform("Material.Kd", 0.9f, 0.5f, 0.3f);prog.setUniform("Material.Ka", 0.9f, 0.5f, 0.3f);prog.setUniform("Material.Ks", 0.8f, 0.8f, 0.8f);prog.setUniform("Material.Shininess", 100.0f);prog.setUniform("Light.Direction", vec4(1.0f, 0.0f, 0.0f, 0.0f));prog.setUniform("Light.Intensity", 1.0f, 1.0f, 1.0f);prog.setUniform("ModelViewMatrix", mv);prog.setUniform("NormalMatrix",mat3( vec3(mv[0]), vec3(mv[1]), vec3(mv[2]) ));prog.setUniform("MVP", projection * mv);}

聚光灯 Spotlight

这里的采用一个最简单的聚光灯模型：

灯光的属性有：位置，强度，方向，衰减（exponent），裁剪角度。

实现起来也比较简单，在投射角内的物体，渲染方式和点光源的计算一样，投射角之外的顶点，着色的时候只有ambient。

还是采用我们比较熟悉的per vertex shading 方式。在vert中定义聚光灯：

//baisc.vert
#version 400
layout (location = 0) in vec3 VertexPosition;
layout (location = 1) in vec3 VertexNormal;  out vec3 LightIntensity;struct SpotLightInfo{vec4 position;vec3 direction;vec3 intensity;float exponent;float cutoff;
};struct MaterialInfo{vec3 Ka;vec3 Kd;vec3 Ks;float Shininess;
};uniform SpotLightInfo Spot;
uniform MaterialInfo Material;uniform mat4 ModelViewMatrix;
uniform mat3 NormalMatrix;
uniform mat4 ProjectionMatrix;
uniform mat4 MVP;void getEyeSpace(out vec3 norm, out vec4 position)
{norm =  normalize(NormalMatrix * VertexNormal);position = ModelViewMatrix * vec4(VertexPosition, 1.0);
}vec3 adsSpotLight(vec4 position, vec3 norm)
{vec3 s = normalize(vec3(Spot.position - position));float angle = acos(dot(-s, normalize(Spot.direction)));float cutoff = radians(clamp(Spot.cutoff, 0.0, 90.0));vec3 ambient = Spot.intensity * Material.Ka;if(angle < cutoff){float spotFactor = pow(dot(-s, normalize(Spot.direction)), Spot.exponent);vec3 v = normalize(vec3(-position));vec3 h = normalize(v + s);return ambient + spotFactor * Spot.intensity * (Material.Kd * max(dot(s, norm),0.0)+ Material.Ks * pow(max(dot(h,norm), 0.0),Material.Shininess)); }else{return ambient; }}void main()
{vec3 eyeNorm;vec4 eyePosition;getEyeSpace(eyeNorm, eyePosition);LightIntensity = adsSpotLight(eyePosition, eyeNorm);gl_Position = MVP * vec4( VertexPosition, 1.0);
}

几个GLSL中的内置函数在这里说明一下。

genType clamp( genType x, genType minVal, genType maxVal);

获取三个数中第二大的数。

genType radians(genType degrees);

将角度转换成弧度。

adsSpotLight是主要的函数，先计算顶点和光源方向之间的夹角，判断顶点是否在照射的区域，然后分别求得最终的颜色。

片段shader还是那样:

#version 400in vec3 LightIntensity;void main(void)
{gl_FragColor = vec4(LightIntensity, 1.0);
}

uniform变量的赋值：

void CGL::setUniform()
{//model = glm::rotate(this->model, 10.0f, vec3(0.0f,1.0f,0.0f));mat4 projection = glm::perspective(45.0f, 4.0f / 3.0f, 0.1f, 100.0f);mat4 mv = view * model;mat3 normalMatrix = mat3( vec3(view[0]), vec3(view[1]), vec3(view[2]) );prog.setUniform("Material.Kd", 0.9f, 0.5f, 0.3f);prog.setUniform("Material.Ka", 0.9f, 0.5f, 0.3f);prog.setUniform("Material.Ks", 0.8f, 0.8f, 0.8f);prog.setUniform("Material.Shininess", 100.0f);vec4 lightPos = vec4(1.0f, 5.0f, 20.0f, 1.0f);// prog.setUniform("Spot.position", lightPos);prog.setUniform("Spot.position", view * lightPos);prog.setUniform("Spot.direction", normalMatrix * vec3(-10.0,0.0,-40.0) );//prog.setUniform("Spot.direction", vec3(10.9f,10.9f,10.9f)  );prog.setUniform("Spot.intensity", vec3(0.9f,0.9f,0.9f) );prog.setUniform("Spot.exponent", 30.0f );prog.setUniform("Spot.cutoff", 15.0f );prog.setUniform("ModelViewMatrix", mv);prog.setUniform("NormalMatrix",normalMatrix);prog.setUniform("MVP", projection * mv);}

在这里给Spot.position赋值的时候不是 prog.setUniform("Spot.position", lightPos); 而是prog.setUniform("Spot.position", view * lightPos)，因为在shader中的计算都是在视口坐标下进行的，这样做是为了统一坐标。Spot.direction的赋值也是一样。也可以把坐标转换这一步放到shader中去做。

最终效果如下：

逐像素着色 per pixel shading

相对与前面将主要计算工作放在顶点shader中的 per vertex shading ，per pixel shading 指的是将计算放到片段shader中，这样可以带来更加真实可感的渲染效果。

basic2.vert

#version 400
layout (location = 0) in vec3 VertexPosition;
layout (location = 1) in vec3 VertexNormal;  out vec4 Position;
out vec3 Normal;uniform mat4 ModelViewMatrix;
uniform mat3 NormalMatrix;
uniform mat4 ProjectionMatrix;
uniform mat4 MVP;void getEyeSpace(out vec3 norm, out vec4 position)
{norm =  normalize(NormalMatrix * VertexNormal);position = ModelViewMatrix * vec4(VertexPosition, 1.0);
}void main()
{getEyeSpace(Normal, Position);gl_Position = MVP * vec4( VertexPosition, 1.0);
}

basic2.frag

#version 400in vec4 Position;
in vec3 Normal;struct SpotLightInfo{vec4 position;vec3 direction;vec3 intensity;float exponent;float cutoff;
};struct MaterialInfo{vec3 Ka;vec3 Kd;vec3 Ks;float Shininess;
};uniform SpotLightInfo Spot;
uniform MaterialInfo Material;vec3 adsSpotLight(vec4 position, vec3 norm)
{vec3 s = normalize(vec3(Spot.position - position));float angle = acos(dot(-s, normalize(Spot.direction)));float cutoff = radians(clamp(Spot.cutoff, 0.0, 90.0));vec3 ambient = Spot.intensity * Material.Ka;if(angle < cutoff){float spotFactor = pow(dot(-s, normalize(Spot.direction)), Spot.exponent);vec3 v = normalize(vec3(-position));vec3 h = normalize(v + s);return ambient + spotFactor * Spot.intensity * (Material.Kd * max(dot(s, norm),0.0)+ Material.Ks * pow(max(dot(h,norm), 0.0),Material.Shininess)); }else{return ambient; }}void main(void)
{gl_FragColor = vec4(adsSpotLight(Position, Normal), 1.0);//gl_FragColor = vec4(1.0,1.0,0.5, 1.0);
}

看一下渲染效果：

最终的效果还是有一些差别，特别是光线交界的地方。

代码下载

OpenGLPro13

参考

OpenGL 4.0 Shading Language Cookbook