Fake 3D: normals & light

Before real 3D, let's fake it — and learn the thing that makes all 3D look 3D: lighting.

A normal is a unit vector pointing straight out of a surface. How bright a surface is depends on how much its normal faces the light: diffuse = max(dot(normal, lightDir), 0.0). (Dot product of two unit vectors = cosine of the angle between them: 1 facing the light, 0 sideways, negative facing away.)

For a sphere of radius R centered at the origin, a point at (x, y) on screen sits at height z = sqrt(R² − x² − y²). The normal at that point is simply normalize(float3(x, y, z)). Pixels outside the sphere get a mask of 0.