Simplst possible TBN-Matrix giving weird results

Question

I'm implementing normal mapping and was trying different techniques of doing that. All seemed not to give me a correct result (e.g. the normals point in weird directions). To find the problem, I broke everything down to the simplest possible solution, but I cant find the problem.

Here is a picture of my scene outputting only the world-space normals:

And here is the scene outputting the transformed normals with the normal map:

As you can see, the normals are not pointed the way they should be (green should be to the right, for example). Here is the way I caluclate the TBN-Matrix (I know, its not the correct way of doing that, but I tried the "correct" ways too).

vec3 tangent = cross(worldspaceNormal, vec3(0,0,1));
vec3 biTangent = cross(tangent, worldspaceNormal);
mat3 tbn = mat3(tangent, biTangent, worldspaceNormal);

vec3 map = texture(normal, texCoord).rgb;
map = 2 * map - vec3(1);

outNormal = vec4(tbn * map, 0.0);

The worldspaceNormal is just the normal of the surface multiplied by the model-matrix, with w-component 0.0, of course.

Answer 1

Found the problem. The TBN apparently needs to be constructed as the following: mat3(worldspaceNormal, biTangent, tangent);. So tangent and normal need to be flipped. Don't know why, maybe a Vulkan thing.

Answer 2

The normal matrix should be the transpose inverse of the modelview matrix. You can't simply multiply with model-matrix. Hope this clears your problem.