A quick take on splines
In computer graphics, a spline is a curve, defined piecewise by polynomials. A polynomial for splines is a formula, where a single variable is used with different exponents and the results are summed up:
In the preceding formula, the first of the four base polynomials of a cubic Hermite spline is shown. Here, the t variable is used in a cubic and a squared version, and a real number is added to the polynomial.
Different spline variants use different polynomials to generate the resulting curved lines. The plots for the basic functions of the usually used spline variants – B-splines, Bezier, and Hermite splines – are drawn in Figure 7.12:
Figure 7.12: The basic functions for B-splines, Bezier, and Hermite splines
The construction of a spline can be done with numerical calculations, by solving all the polynomials for the given interpolation point between 0 and 1. Other splines can be created more easily by using...
