Curves and Surfaces for CAGD, 5th Edition

9

Constructing Spline Curves

A spline is a flexible rod of wood or plastic. It has its origins in shipbuilding, where splines were used to draft the curves (ribs) that define a ship body. Early uses go back to the 1600s, and are documented in [450]. Although mechanical splines are used less frequently now, the underlying principle still gives rise to new algorithms.

9.1 Greville Interpolation

In Chapter 7, we saw how to pass a polynomial curve of degree n through n + 1 data points p₀, …, p_n with parameter values t₀, …, t_n. The key to the solvability of the problem was simple: the number of knowns (the data points with parameter values) had to equal the number of unknowns (the polynomial coefficients).

Something quite analogous happens in a ...