7 Splines
This chapter covers
- Making interpolating functions from points and from differential and integral conditions
- Understanding and composing Bézier splines
- Understanding and composing NURBS
In mathematics, a spline is a compound function, often continuous and smooth, made out of other simpler functions. You can stick two parabolas together and make yourself a quadratic polynomial spline. It’s as simple as that (figure 7.1).
Figure 7.1 For x < 0, y = - 0.2x2 + 2; for x ≥ 0, y = 0.3x2 + 2. This is already a spline function.
In the real world, you can see splines everywhere—not only in graphic design tools, virtual reality, computer games, ...
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