Name
Abstract | ||
|---|---|---|
Our interest is to characterize the spline-like integer-shift-invariant bases capable of reproducing exponential polynomial curves. We prove that any compact-support function that reproduces a subspace of the exponential polynomials can be expressed as the convolution of an exponential B-spline with a compact-support distribution. As a direct consequence of this factorization theorem, we show that the minimal-support basis functions of that subspace are linear combinations of derivatives of exponential B-splines. These minimal-support basis functions form a natural multiscale hierarchy, which we utilize to design fast multiresolution algorithms and subdivision schemes for the representation of closed geometric curves. This makes them attractive from a computational point of view. Finally, we illustrate our scheme by constructing minimal-support bases that reproduce ellipses and higher-order harmonic curves. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1016/j.cagd.2011.10.005 | Computer Aided Geometric Design |
Keywords | Field | DocType |
computational point,minimal-support base,minimal-support basis function,exponential b-splines,curve representation,compact-support distribution,exponential polynomial curve,compact-support function,exponential b-spline,exponential polynomial,exponential spline,closed geometric curve,refinement,biology,parameterization,algorithms,order,interpolation,subdivision,approximation | Spline (mathematics),Mathematical optimization,Exponential function,Shift theorem,Convolution,Exponential polynomial,Basis function,Mathematics,Double exponential function,Exponential formula | Journal |
Volume | Issue | ISSN |
29 | 2 | 0167-8396 |
Citations | PageRank | References |
6 | 0.49 | 23 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ricard Delgado-Gonzalo | 1 | 99 | 13.43 |
| P. Thévenaz | 2 | 6 | 0.49 |
| Unser, M. | 3 | 3438 | 442.40 |