Spline: Here is a good video

• linear spline: connecting two points

• quadratic spline: two linear interpolation on 3 points, generates 2 points, and interpolate the 2 points

• qubit spline: most common, break down to 4 basis equation. Spline will pass through first and last point. Middle two points are tangent.

Continuity:

• $C_0$: position is continuous

• $C_1$: velocity is continuous

• Every points in the middle of a spline is $C^\infty$, you can construct any continuity by putting constraints on piecewise qubit splines to ensure anywhere from not continuos to $C^\infty$

Bounces: 1: light 2: direct lighting, soft shadow, specular, diffuse 3: color bleeding 4: caustics, refracted object