3D, step 2: is a point inside the sphere?

A point along the ray is ro + rd * t, where t is "how far along". t = 0 is the camera, t = 3 is three units out.

A sphere of radius 1 at the origin is simple to test: a point is inside it when its distance from the origin is less than 1: length(pos) < 1.0. (It is the circle test from the 2D lessons, with one more dimension.)

Test just one point per pixel, 3 units along its ray. The camera is at z = -3, so that point is about at z = 0, the middle of the sphere. Pixels whose point is inside the sphere get the sphere colour:

float2 p = (uv - 0.5) * float2(aspect, 1.0) * 2.0;
float3 ro = float3(0.0, 0.0, -3.0);
float3 rd = normalize(float3(p, 1.5));
float3 pos = ro + rd * 3.0;                // a point 3 units along the ray
float inside = step(length(pos), 1.0);     // 1 if it is inside the sphere

You will see a disc. Why only a disc and not a ball? We only tested one point per ray, so we found the sphere's silhouette, not its surface. Next step fixes that by walking along the ray.