How to achieve smooth tangent space normals?

问题

I'm trying to add bump mapping functionality to my application but I'm getting very faceted models:

The reason it is happening is because I'm calculating tangent, binormal and normal on per face basis and completely ignoring the normals I'm getting from the model file.

The calculation currently uses two edges of the triangle and texture space vectors to get tangent and binormal, which are then used to calculate normal by cross product. It is all done on the CPU as soon as the model loads and the values are then stored as a part of model's geometry.

    vector1 = vertex2.coords - vertex1.coords;      
    vector2 = vertex3.coords - vertex1.coords;

    tuVector = vertex2.texcoords - vertex1.texcoords;
    tvVector = vertex3.texcoords - vertex1.texcoords;

    float den = 1.0f / (tuVector.x * tvVector.y - tuVector.y * tvVector.x);

    tangent.x = (tvVector.y * vector1.x - tvVector.x * vector2.x) * den;
    tangent.y = (tvVector.y * vector1.y - tvVector.x * vector2.y) * den;
    tangent.z = (tvVector.y * vector1.z - tvVector.x * vector2.z) * den;

    binormal.x = (tuVector.x * vector2.x - tuVector.y * vector1.x) * den;
    binormal.y = (tuVector.x * vector2.y - tuVector.y * vector1.y) * den;
    binormal.z = (tuVector.x * vector2.z - tuVector.y * vector1.z) * den;

    D3DXVec3Normalize(&tangent, &tangent);
    D3DXVec3Normalize(&binormal, &binormal);

    D3DXVec3Cross(&normal, &tangent, &binormal);    
    D3DXVec3Normalize(&normal, &normal);

Is there a way to either calculate these values on per vertex basis, perhaps using the normal supplied with the model or to smooth them out somehow so the model doesn't appear faceted?

回答1:

For smooth surfaces (no edges) I do it like this:

create space for per vertex
```
double N[3]; //normal
int cnt;
```
per vertex init
```
N={0.0,0.0,0.0}
cnt=0;
```
compute per face normal

normal must be normalized length=1.0 !!! add this Normal to all vertexes used in face and increment cnt to all vertexes used in face
per vertex normalize
```
N/=cnt; // N = average normal from all vertex - neighbour faces
```
be aware of cnt=0 for unused vertexes (division by zero)
per vertex N contains the Normal you want

now compute T,B vectors for TBN matrix (per vertex) as you do now
output image is smooth

My earth preview (with atmospheric scattering, bump mapping and more...) is here

hope it helps

来源：https://stackoverflow.com/questions/21766605/how-to-achieve-smooth-tangent-space-normals

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c++

math

directx

hlsl