3D splines, reference text

[Trenthan]

Hey guys girls and thanks in advance
(Sorry if this post is in the wrong area)

Ive been working with splines in 2D for a little while now and am fluent with the mathematics behind them. I now need to use 3D splines but cannot come across a good reference material to reconstruct them ... I'm using matlab, however the student version does not contain the splines toolbox so i have to do the crunching myself/coding. Which is okay, i would rather know how it works than let a function do it for me anyways.

Ive been searching the web and mathematics books in the library without much luck. All the texts seem to cover 2D splines that I've come across.

Just wondering if anyone knows a good reference text off the top of their heads or the mathematics area i should be looking at more specifically to help with my searching.

Cheers Trent

 

[jvicens]

Hello Trent, thank you for reaching out to the community for help with your research on 3D splines. It's great to see that you are fluent with the mathematics behind 2D splines and are now looking to expand your knowledge to 3D splines.

First of all, it's important to understand that 3D splines are essentially an extension of 2D splines, so the mathematics behind them will be similar. However, there are some additional concepts and techniques that you will need to learn in order to work with 3D splines.

One good reference text that I would recommend for learning about 3D splines is "The NURBS Book" by Les Piegl and Wayne Tiller. This book covers the mathematics and algorithms behind Non-Uniform Rational B-Splines (NURBS), which are commonly used in 3D modeling and computer graphics. It also includes code examples in C++ and Fortran, which you may find useful for implementing your own 3D spline functions in Matlab.

Another good resource is the "Handbook of Computer Aided Geometric Design" by Gerald Farin. This book covers a wide range of topics related to geometric modeling, including 3D splines and their applications. It also includes code examples in Matlab, which may be helpful for your specific needs.

In terms of specific mathematical areas to focus on, I would recommend looking into vector calculus, as it plays a key role in understanding and working with 3D splines. Specifically, you may want to brush up on concepts such as vector operations, derivatives, and integrals, as well as vector functions and curves.

I hope this helps guide you in your search for reference material on 3D splines. Best of luck with your research!