What does it do?
September 29th, 2005 by SplineGuy
I’ve very often been asked the question of what I do and when I tell someone I teach mathematics and do mathematics research, I am invariably asked what I research. For many of the things I spend my time on, I have yet to be able to communicate to someone that doesn’t speak in my jumbled mathematics tongue. Everyone once in a while, areas that my research relates to comes up in the news. Here’s a great example of an application for the surface fitting and smoothing techniques I explored in my Master’s Thesis:
Spline-Enhanced 3D Surface Visualization of the Levees Around New Orleans
Take a look, it is very fascinating. Some work I am currently doing with variable knot splines also relates, indirectly.
OK …. so … What’s a spline? Feel free to go ahead and tell me in full technical jargon ’cause I once learned all about fractals [sp] in Sunday School.
Put simply, a spline, as I refer to it, is a set of special mathematic functions which are basically made up of polynomials “spliced together,” but done so in a particularly smooth way. One of the simplest polynomials is a linear one, i.e., graphs as a line. So the easiest spline to understand is the broken line spline. If you take a series of points and connect them with straight lines (yeah, connect the dots, la la la la, for you Pee Wee Herman fans) you have formed a linear spline. Move up a degree and you can also connect them smoothly with parabolas, then cubic curves, etc. There is a method to extend the idea to three dimensional spaces (i.e., surfaces instead of curves). When its all said and done you have a very efficient modeling tool that is very smooth.