Catmull-Rom Splines
With Hermite splines, the designer must arrange for consecutive tangents to be collinear, to get C1 continuity. Similar for Bezier. This gets tedious.
Catmull-Rom: an interpolating cubic spline with built-in C1 continuity.
Compared to Hermite/Bezier: fewer control points required, but less freedom.
Given n control points in 3-D: p1, p2, …, pn,
- Tangent at pi given by s(pi+1 – pi-1) for i=2..n-1, for some s
- What about endpoint tangents? (several good answers: extrapolate, or use extra control points p0, pn+1)
- Now we have positions and tangents at each knot – a Hermite specification.
- Curve between pi and pi+1 is determined by pi-1, pi, pi+1, pi+2