原文 http://www.cnblogs.com/CGDeveloper/archive/2008/07/03/1234206.html
如果物体表面细节很多，我们可以不断的精细化物体的几何数据，但是这样会产生大量的Lighting & Transformation等计算，
为了实现丰富真实的物体表面，除了贴上一般纹理之外，往往还使用Bump mapping（凹凸纹理）技术。
Bump mapping并没有增加物体的几何复杂度，它只是在计算物体的光照效果时作了“弊”，不使用物体本身的法向量，而是
使用了经过处理的法向量。如果这样的法向量使用normal map,我们可以使用GLSL实现凹凸效果。
首先，因为没有改变对象的几何形状，所以bump mapping的实现是在FS之中进行的，因此光照计算就必须在FS之中进行。
由于normal map之中的法向量是在SURFACE_LOCAL COORDINATE SPACE，所以用于光照计算的光源的方向和视向都
必须变换到同一空间进行光照计算。也就是说，必须使用所谓TBN矩阵的逆矩阵对光源的方向和视向进行变换，转换之后的值
作为varying传入到FS之中。
对于三角形mesh而言，TBN的一种计算方法如下：
void FindInvTBN(Vertor3f Vertices[3], Vector2f TexCoords[3], Vector3f & InvNormal,
Vector3f & InvBinormal, Vector3f & InvTangent)
{
/* Calculate the vectors from the current vertex
to the two other vertices in the triangle */
Vector3f v2v1 = Vertices[0] - Vertices[2];
Vector3f v3v1 = Vertices[1] - Vertices[2];
//Calculate the “direction” of the triangle based on texture coordinates.
// Calculate c2c1_T and c2c1_B
float c2c1_T = TexCoords[0].x() - TexCoords[2].x();
float c2c1_B = TexCoords[0].y() - TexCoords[2].y();
// Calculate c3c1_T and c3c1_B
float c3c1_T = TexCoords[1].x() - TexCoords[2].x();
float c3c1_B = TexCoords[1].y() - TexCoords[2].y();
//Look at the references for more explanation for this one.
float fDenominator = c2c1_T * c3c1_B - c3c1_T * c2c1_B;
/*ROUNDOFF here is a macro that sets a value to 0.0f if the value is a very small
value, such as > -0.001f and < 0.001. */
/* EDIT by c programmer: you should NEVER perform an equality test against a floating point value, even if
your macro has set fDenominator to 0.0f. The comparison can still fail. The code needs fixed.
Instead you should check if fDenominator is within an epsilon value of 0.0f. */
if (ROUNDOFF(fDenominator) == 0.0f)
{
/* We won't risk a divide by zero, so set the tangent matrix to the
identity matrix */
InvTangent = Vector3f(1.0f, 0.0f, 0.0f);
InvBinormal = Vector3f(0.0f, 1.0f, 0.0f);
InvNormal = Vector3f(0.0f, 0.0f, 1.0f);
}
else
{
// Calculate the reciprocal value once and for all (to achieve speed)
float fScale1 = 1.0f / fDenominator;
/* Time to calculate the tangent, binormal, and normal.
Look at Søren’s article for more information. */
Vector3f T, B, N;
T = Vector3f((c3c1_B * v2v1.x() - c2c1_B * v3v1.x()) * fscale1,
(c3c1_B * v2v1.y() - c2c1_B * v3v1.y()) * fScale1,
(c3c1_B * v2v1.z() - c2c1_B * v3v1.z()) * fScale1);
B = Vector3f((-c3c1_T * v2v1.x() + c2c1_T * v3v1.x()) * fScale1, (-c3c1_T * v2v1.y() + c2c1_T * v3v1.y()) * fScale1, (-c3c1_T * v2v1.z() + c2c1_T * v3v1.z()) * fScale1); N = T%B; //Cross product! /*This is where programmers should break up the function to smooth the tangent, binormal and normal values. */ //Look at “Derivation of the Tangent Space Matrix” for more information. float fScale2 = 1.0f / ((T.x() * B.y() * N.z() - T.z() * B.y() * N.x()) + (B.x() * N.y() * T.z() - B.z() * N.y() * T.x()) + (N.x() * T.y() * B.z() - N.z() * T.y() * B.x())); InvTangent.set((B%N).x() * fScale2, ((-1.0f * N)%T).x() * fScale2, (T%B).x() * fScale2); InvTangent.normalize(); InvBinormal.set(((-1.0f *B)%N).y() * fScale2, (N%T).y() * fScale2, ((-1.0f * T)%B).y() * fScale2); InvBinormal.normalize(); InvNormal.set((B%N).z() * fScale2, ((-1.0f * N)%T).z() * fScale2, (T%B).z() * fScale2); InvNormal.normalize(); }
上述计算中可以只计算T。
相应的VS如下：
varying vec3 LightDir;
varying vec3 EyeDir; attribute vec3 Tangent; void main()
{
gl_Position = gl_ModelViewProjectionMatrix * gl_Vertex;
gl_TexCoord[0] = gl_MultiTexCoord0; // 眼坐标系下的TBN
vec3 n = normalize(gl_NormalMatrix * gl_Normal);
vec3 t = normalize(gl_NormalMatrix * Tangent);
vec3 b = cross(n, t);
mat3 TBN = mat3(t, b, n);
vec4 pos = gl_ModelViewMatrix * gl_Vertex;
vec3 epos = vec3(pos)/pos.w;
vec3 v = gl_LightSource[0].position.xyz - epos;
v = v * TBN;
LightDir = normalize(v); v = -epos * TBN;
EyeDir = normalize(v);
}
相应的FS如下：
uniform sampler2D BumpTex;
uniform sampler2D DecalTex; varying vec3 LightDir;
varying vec3 EyeDir; void main()
{
vec3 BumpNorm = vec3(texture2D(BumpTex, gl_TexCoord[0].xy));
BumpNorm = (BumpNorm -0.5) * 2.0;
vec4 DecalCol = texture2D(DecalTex, gl_TexCoord[0].xy);
float NdotL = max(dot(BumpNorm, LightDir), 0.0);
vec3 h = normalize(LightDir+EyeDir);
float NdotH = max(dot(BumpNorm, h), 0.0);
vec3 diffuse = vec3(NdotL * gl_LightSource[0].diffuse * DecalCol);
vec3 specular = vec3(pow(NdotH, 6) * gl_LightSource[0].specular);
gl_FragColor = vec4(diffuse + specular, 1.0);
}