Catmull-Rom spline

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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 get smooth interpolated motion between key-frames. For example, most camera path animations generated from discrete 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.

[edit] Explanation

For a Catmull-Rom spline, 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

.

with the first and last tangent given. See cardinal spline for the more general form of this.

[edit] External links

• Introduction to Catmull-Rom Splines, MVPs.org