Implemented MeshTangents()

- Added Vector3OrthoNormalize() to raymath.h - not sure if it is correct
- Implemented MeshBinormals() - Mesh struct has not a place for them...
- Updated model_material_pbr example - tested but not working on my GPU
(old Intel HD), actually, it never worked on it...

examples/models/models_material_pbr.c

@@ -38,6 +38,7 @@ int main()
 
     // Load model and PBR material
     Model model = LoadModel("resources/pbr/trooper.obj");
+    MeshTangents(&model.mesh);
     model.material = LoadMaterialPBR((Color){ 255, 255, 255, 255 }, 1.0f, 1.0f);
 
     // Define lights attributes

src/models.c

@@ -2120,15 +2120,90 @@ BoundingBox MeshBoundingBox(Mesh mesh)
 }
 
 // Compute mesh tangents
+// NOTE: To calculate mesh tangents and binormals we need mesh vertex positions and texture coordinates
+// Implementation base don: https://answers.unity.com/questions/7789/calculating-tangents-vector4.html
 void MeshTangents(Mesh *mesh)
 {
-    // TODO: Compute mesh tangents
+    if (mesh->tangents == NULL) mesh->tangents = (float *)malloc(mesh->vertexCount*4*sizeof(float));
+    else TraceLog(LOG_WARNING, "Mesh tangents already exist");
+    
+    Vector3 *tan1 = (Vector3 *)malloc(mesh->vertexCount*sizeof(Vector3));
+    Vector3 *tan2 = (Vector3 *)malloc(mesh->vertexCount*sizeof(Vector3));
+
+    for (int i = 0; i < mesh->vertexCount; i += 3)
+    {
+        // Get triangle vertices
+        Vector3 v1 = { mesh->vertices[(i + 0)*3 + 0], mesh->vertices[(i + 0)*3 + 1], mesh->vertices[(i + 0)*3 + 2] };
+        Vector3 v2 = { mesh->vertices[(i + 1)*3 + 0], mesh->vertices[(i + 1)*3 + 1], mesh->vertices[(i + 1)*3 + 2] };
+        Vector3 v3 = { mesh->vertices[(i + 2)*3 + 0], mesh->vertices[(i + 2)*3 + 1], mesh->vertices[(i + 2)*3 + 2] };
+
+        // Get triangle texcoords
+        Vector2 uv1 = { mesh->texcoords[(i + 0)*2 + 0], mesh->texcoords[(i + 0)*2 + 1] };
+        Vector2 uv2 = { mesh->texcoords[(i + 1)*2 + 0], mesh->texcoords[(i + 1)*2 + 1] };
+        Vector2 uv3 = { mesh->texcoords[(i + 2)*2 + 0], mesh->texcoords[(i + 2)*2 + 1] };
+
+        float x1 = v2.x - v1.x;
+        float y1 = v2.y - v1.y;
+        float z1 = v2.z - v1.z;
+        float x2 = v3.x - v1.x;
+        float y2 = v3.y - v1.y;
+        float z2 = v3.z - v1.z;
+
+        float s1 = uv2.x - uv1.x;
+        float t1 = uv2.y - uv1.y;
+        float s2 = uv3.x - uv1.x;
+        float t2 = uv3.y - uv1.y;
+
+        float div = s1*t2 - s2*t1;
+        float r = (div == 0.0f) ? 0.0f : 1.0f/div;
+
+        Vector3 sdir = { (t2*x1 - t1*x2)*r, (t2*y1 - t1*y2)*r, (t2*z1 - t1*z2)*r };
+        Vector3 tdir = { (s1*x2 - s2*x1)*r, (s1*y2 - s2*y1)*r, (s1*z2 - s2*z1)*r };
+        
+        tan1[i + 0] = sdir;
+        tan1[i + 1] = sdir;
+        tan1[i + 2] = sdir;
+
+        tan2[i + 0] = tdir;
+        tan2[i + 1] = tdir;
+        tan2[i + 2] = tdir;
     }
 
-// Compute mesh binormals
+    // Compute tangents considering normals
+    for (int i = 0; i < mesh->vertexCount; ++i)
+    {
+        Vector3 normal = { mesh->normals[i*3 + 0], mesh->normals[i*3 + 1], mesh->normals[i*3 + 2] };
+        Vector3 tangent = tan1[i];
+
+        //Vector3 tmp = (t - n * Vector3.Dot(n, t)).normalized;
+        //tangents[i] = (Vector4){ tmp.x, tmp.y, tmp.z };
+        Vector3OrthoNormalize(&normal, &tangent);
+        
+        mesh->tangents[i*4 + 0] = tangent.x;
+        mesh->tangents[i*4 + 1] = tangent.y;
+        mesh->tangents[i*4 + 2] = tangent.z;
+        mesh->tangents[i*4 + 3] = (Vector3DotProduct(Vector3CrossProduct(normal, tangent), tan2[i]) < 0.0f) ? -1.0f : 1.0f;
+    }
+    
+    free(tan1);
+    free(tan2);
+    
+    TraceLog(LOG_INFO, "Tangents computed for mesh");
+}
+
+// Compute mesh binormals (aka bitangent)
 void MeshBinormals(Mesh *mesh)
 {
-    // TODO: Compute mesh binormals
+    for (int i = 0; i < mesh->vertexCount; i++)
+    {
+        Vector3 normal = { mesh->normals[i*3 + 0], mesh->normals[i*3 + 1], mesh->normals[i*3 + 2] };
+        Vector3 tangent = { mesh->tangents[i*4 + 0], mesh->tangents[i*4 + 1], mesh->tangents[i*4 + 2] };
+        float tangentW = mesh->tangents[i*4 + 3];
+    
+        Vector3 binormal = Vector3Multiply(Vector3CrossProduct(normal, tangent), tangentW);
+        
+        // TODO: Register computed binormal in mesh->binormal ?
+    }
 }
 
 //----------------------------------------------------------------------------------

src/raymath.h

@@ -372,6 +372,17 @@ RMDEF Vector3 Vector3Normalize(Vector3 v)
     return result;
 }
 
+// Orthonormalize provided vectors
+// Makes vectors normalized and orthogonal to each other
+// Gram-Schmidt function implementation
+RMDEF void Vector3OrthoNormalize(Vector3 *v1, Vector3 *v2)
+{
+    *v1 = Vector3Normalize(*v1);
+    Vector3 vn = Vector3CrossProduct(*v1, *v2);
+    vn = Vector3Normalize(vn);
+    *v2 = Vector3CrossProduct(vn, *v1);
+}
+
 // Transforms a Vector3 by a given Matrix
 RMDEF Vector3 Vector3Transform(Vector3 v, Matrix mat)
 {