How to recalculate the normals of projected sphere?

Is there a way I can ensure that the projected sphere on the left, made of planes has the correct normals as the sphere on the right? This way, I can achieve a lighting effect such as Phong lighting similar to the sphere on the right.

example code

Screenshot 2023-12-20 13035812123

Normal of sphere surfaces are quite nice and simple in that terms - normal of any vertex / point on a sphere is just a normalized position.

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Okay, I see what you mean. Normalizing the position will give this.
Screenshot 2023-12-20 163717

I guess this is where I have to calculate the tangents myself to get the normals for each face to align.

so i figured out how to get the normals align. At least that’s a win :tada:
Screenshot 2023-12-20 205717

But lighting calculation is off