Is it not possible to do some sort of multivariate taylory thing to get a polynomial representation?
Is it even computationally useful to do something like that?
Shell
Could you do something where you split up the more complex shapes into smaller surfaces and then somehow combine the equations together? Kind of like functions, where if you apply g(x) to f(x) then you can get a graph that looks like a combination of the two graphs?
L100magikarp
@Shell I guess combining smaller, locally-polynomial surfaces into more complex ones is the intuition of the B-splines except that you combine them piecewise rather than as compositions of functions (f(g(x)).
kallico
Assume a spherical cow in a vacuum. QED
keenan
@ceviri You can fit polynomials to surfaces, just takes some serious optimization (and often isn't guaranteed to work). More generally there are lots of techniques for constructing implicit surfaces from polygon soup, like this paper: https://people.engr.tamu.edu/schaefer/teaching/689_Fall2006/Shen-2004-IAI.pdf
Is it not possible to do some sort of multivariate taylory thing to get a polynomial representation?
Is it even computationally useful to do something like that?
Could you do something where you split up the more complex shapes into smaller surfaces and then somehow combine the equations together? Kind of like functions, where if you apply g(x) to f(x) then you can get a graph that looks like a combination of the two graphs?
@Shell I guess combining smaller, locally-polynomial surfaces into more complex ones is the intuition of the B-splines except that you combine them piecewise rather than as compositions of functions (f(g(x)).
Assume a spherical cow in a vacuum. QED
@ceviri You can fit polynomials to surfaces, just takes some serious optimization (and often isn't guaranteed to work). More generally there are lots of techniques for constructing implicit surfaces from polygon soup, like this paper: https://people.engr.tamu.edu/schaefer/teaching/689_Fall2006/Shen-2004-IAI.pdf