tangent vector calculation, Lesson 6 bis

Is it possible to calculate tangent vector i using the following equations?

It's an odd math question. But it is very tempting to create such equations.

I try in my code. Sometimes, matrix A is non-invertible. And I am curious why that happens.

Thanks!

Nope, the system you are writing is degenerate. You can obtain the third line by subtracting the first line from the second one.

Provided that your model is okay (no degenerate triangles), the matrix A must be invertible, since it contains the model coordinates prior to any projection:

tinyrenderer/main.cpp

Line 41 in dbc5d92

    
           mat<3,3> AI = mat<3,3>{ {view_tri.col(1) - view_tri.col(0), view_tri.col(2) - view_tri.col(0), bn} }.invert();

Just realize it is a degenerate matrix. Thanks!