Function and Space Curve Interpolation

Abstract

The first general problem we wish to consider below is how to construct an interpolatory space curve which passes, in order, through given points p₁, p ₂,…,p _n in R² or R³, perhaps along given associated directions m₁, m₂,…, m _n , with |m _i | ≠ 0 for i = 1, 2,…, n. Indeed, we could elaborate the interpretation of the direction vectors, m₁…, m _n , so that m _i = 0 would be taken to specify a sharp corner or cusp at p _i .