关于normal,binormal,tangent的计算

normal：

          三角面normal:

                    v0,v1,v2三个顶点

                   vN = normal((v1-v0)corss(v2-v1));叉乘的顺序决定了vN的z

          定点normal:
　　　　　　 v1 = normalize(a-b);
　　　　　　 v2 = normalize(a-c);
　　　　　　 normalWeight = acos(dot(v1,v2)); 
　　　　　 　normal = 0,0,0
　　　　　 　totalWeight = 0
　　　　　 　for:所有共定点的面的法线和
 　　　　　　normal += trangleNormal * normalWeight;
 　　　　　　totalWeight += normalWeight
　　　　　　 finalNormal = normal/totalWeight;

binormal abd tangent:

                来自OGRE的函数

               

 Vector3 Math::calculateTangentSpaceVector(
        const Vector3& position1, const Vector3& position2, const Vector3& position3,
        Real u1, Real v1, Real u2, Real v2, Real u3, Real v3)
    {
        //side0 is the vector along one side of the triangle of vertices passed in, 
        //and side1 is the vector along another side. Taking the cross product of these returns the normal.
        Vector3 side0 = position1 - position2;
        Vector3 side1 = position3 - position1;
        //Calculate face normal
        Vector3 normal = side1.crossProduct(side0);
        normal.normalise();
        //Now we use a formula to calculate the tangent. 
        Real deltaV0 = v1 - v2;
        Real deltaV1 = v3 - v1;
        Vector3 tangent = deltaV1 * side0 - deltaV0 * side1;
        tangent.normalise();
        //Calculate binormal
        Real deltaU0 = u1 - u2;
        Real deltaU1 = u3 - u1;
        Vector3 binormal = deltaU1 * side0 - deltaU0 * side1;
        binormal.normalise();
        //Now, we take the cross product of the tangents to get a vector which 
        //should point in the same direction as our normal calculated above. 
        //If it points in the opposite direction (the dot product between the normals is less than zero), 
        //then we need to reverse the s and t tangents. 
        //This is because the triangle has been mirrored when going from tangent space to object space.
        //reverse tangents if necessary
        Vector3 tangentCross = tangent.crossProduct(binormal);
        if (tangentCross.dotProduct(normal) < 0.0f)
        {
            tangent = -tangent;
            binormal = -binormal;
        }

        return tangent;

    }