A university assignment requires me to use the Vertex Coordinates I have to calculate the Normals and the Tangent from the Normal values so that I can create a Object Space to Texture Space Matrix.
I have the code needed to make the Matrix, and the binormal but I don't have the code for calculating the Tangent. I tried to look online, but the answers usually confuse me. Can you explain to me clearly how it works?
EDIT: I have corrected what I wrote previously as clearly I misunderstood the assignment. Thank you everyone for helping me see that.
A tangent in the mathematical sense is a property of a geometric object, not of the normalmap. In case of normalmapping, we are in addition searching for a very specific tangent (there are infinitely many in each point, basically every vector in the plane defined by the normal is a tangent).
But let's go one step back: We want a space where the u-direction of the texture is mapped on the tangent direction, the v-direction on the bitangent/binormal and the up-vector of the normalmap to the normal of the object. Thus the tangent for a triangle (v0, v1, v2) with uv-coordinates (uv1, uv2, uv3) can be calculated as:
dv1 = v1-v0
dv2 = v2-v0
duv1 = uv1-uv0
duv2 = uv2-uv0
r = 1.0f / (duv1.x * duv2.y - duv1.y * duv2.x);
tangent = (dv1 * duv2.y - dv2 * duv1.y) * r;
bitangent = (dv2 * duv1.x - dv1 * duv2.x) * r;
When having this done for all triangles, we have to smooth the tangents at shared vertices (quite similar to what happens with the normal). There are several algorithms for doing this, depending on what you need. One can, for example, weight the tangents by the surface area of the adjacent triangles or by the incident angle of them.
An implementation of this whole calculation can be found [here] along a more detailed explaination: (http://www.opengl-tutorial.org/intermediate-tutorials/tutorial-13-normal-mapping/)