Splines in 5 Minutes: Part 2 -- Catmull-Rom and Natural Cubic Splines

Equivalent to a 50 minute university lecture on Catmull-Rom and Natural Cubic Splines. Part 2 of 3 on splines.

0:00 - intro
0:16 - higher order polynomial fitting
0:49 - piece-wise cubic curves
1:32 - knots and C1 continuity
2:03 - Catmull-Rom splines
2:37 - Catmull-Rom fitting = convolution with a cubic kernel
3:00 - natural cubic spline
5:16 - C2 continuity
5:39 - natural cubic spline minimizes the squared second derivative
6:16 - local control

Graphics in 5 minutes is a series of cartoon-style videos that teach computer graphics in 10x less time. You can take the equivalent of a University level computer graphics course in just over two hours. The playlist is here:

[brunojani]

I just wanted to get some spline knowledge, a quick in and out. But you have made me stay and watch multiple videos.

Very nice, intresting and to the point.

[UzunKamis]

Thank you very much for this very explanatory video. It is the first time we are studying this with my project students. We would like to make some comments about what we get from the explanations. Please correct us if we are wrong. For NCS, we use f''[x_{k+1}]=g''[x_{k+1}] condition in the middle points together with f''[x_{1}]==0 and g''[x_{n}]==0 at the end points. While, for CRS, we use together with some derivative constraints (such as f'[x_{1}]=0 and g'[x_{n}]=-1) at the end points.

[nahuelp]

This is great, thank you very much!!!!

[existentialrap]

gang shit this was some good knowledge

[ThefamousMrcroissant]

Excellent video, but VERY VERY hard to listen to for someone with misophonia again. There are an incredible amount of wet noises coming through your microphone and they are very loud and pronounced as well.