Catmull-Rom spline

From Free net encyclopedia

In mathematics, a Catmull-Rom spline is a cardinal spline with a tension of 0.5.

In computer graphics, Catmull-Rom splines are frequently used to to get smooth interpolated motion between key-frames. For example, most camera path animations generated from discreet key-frames are handled using Catmull-Rom splines. They are popular mainly for being relatively easy to compute, guaranteeing that each key-frame position will be hit exactly, and also guaranteeing that the tangents of the generated curve are continuous over multiple segments.

Explanation

Given n+1 points

p₀, ..., p_n,

to be interpolated with n cubic Hermite curve segments, for each curve we have a starting point p_i and an ending point p_i+1 with starting tangent m_i and ending tangent m_i+1 with the tangents defined by

<math> \mathbf{m}_i = \frac{1}{2}(\mathbf{p}_{i+1}-\mathbf{p}_{i-1}) </math>.

with the first and last tangent given.

External links

• Introduction to Catmull-Rom Splines, MVPs.org