Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Feature: linearity and algebra of splines #52

sixpearls opened this issue Sep 1, 2019 · 0 comments


Copy link

commented Sep 1, 2019

I'm not sure whether splines form a full algebra, but they certainly form a linear space (for the same knots and order). Could we implement the linearity and possibly an algebra?

  • "broadcast" or project splines into the same space:
    • if there is an algorithm to represent the a curve in a higher degree spline, we could use that to "broadcast" the lower degree spline to the higher
    • a knot insertion algorithm could be used to project two splines of the same degree onto the same space of splines (both splines have knots that are the union of the original two sets of knots)
  • For splines in the same linear space, linear operations can be operated on the coefficients (scalar multiplication and addition)
  • I am not sure if there is a standard algebra for splines, but it seems likely an algebra could be formed by defining a multiplication that would elevate the degree appropriately. I am not sure if this would hold for N-dimensional splines, depending on what happens to the cross-terms.
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
None yet
1 participant
You can’t perform that action at this time.