Catmull-Rom spline

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

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 (http://www.mvps.org/directx/articles/catmull/), MVPs.org