Cardinal spline

A cardinal spline is a cubic Hermite spline whose tangents are defined by the points and a tension parameter.

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 = (1-t)(\mathbf{p}_{i+1}-\mathbf{p}_{i-1}) <math>

where t is a constant that modifies the length of the tangent and the first and last tangent are given.