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.

Explanation

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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

$\backslash mathbf\{m\}\_i\; =\; \backslash frac\{1\}\{2\}(1-t)(\backslash mathbf\{p\}\_\{i+1\}-\backslash mathbf\{p\}\_\{i-1\})$.

with the first and last tangent given.

External links

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• Introduction to Catmull-Rom Splines, MVPs.org

Splines