logoalt Hacker News

sfpottertoday at 5:41 PM1 replyview on HN

One interesting and sort of unhappy artifact of CAD is the adoption of B-splines and NURBS as the primal basis for modeling. The whole point of B-splines is that they are the obvious basis for maximally continuous splines of a certain degree (i.e., degree n gives C^{n-1}). This is much more than G continuity. But in CAD, it's often the case that all you care about is just G continuity.

So you run into a weird situation where CAD software may pass around NURBS or B-splines with multiply inserted (or even fully inserted) knots, seriously reducing the need for using splines in the first place.

The problem is that splines are a really inconvenient and even unstable basis for doing numerical work... which is what all of CAD is.


Replies

tobrtoday at 6:36 PM

Curious, is there some alternative that would give you both higher order continuity and numerical stability? Or are they fundamentally at odds?

show 1 reply