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

where the first and last tangent m₀ and m_n are given and c is a constant that modifies the length of the tangent.