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Stable Simplex Spline Bases for $$C^3$$C3 Quintics on the Powell–Sabin 12-Split
| Content Provider | Semantic Scholar |
|---|---|
| Author | Lyche, Tom Muntingh, Georg |
| Copyright Year | 2015 |
| Abstract | For the space of $$C^3$$C3 quintics on the Powell–Sabin 12-split of a triangle, we determine explicitly the six symmetric simplex spline bases that reduce to a B-spline basis on each edge and have a positive partition of unity, a Marsden identity that splits into real linear factors, and an intuitive domain mesh. The bases are stable in the $$L_\infty $$L∞ norm with a condition number independent of the geometry and have a well-conditioned Lagrange interpolant at the domain points and a quasi-interpolant with local approximation order 6. We show an $$h^2$$h2 bound for the distance between the control points and the values of a spline at the corresponding domain points. For one of these bases, we derive $$C^0$$C0, $$C^1$$C1, $$C^2$$C2, and $$C^3$$C3 conditions on the control points of two splines on adjacent macrotriangles. |
| Starting Page | 1 |
| Ending Page | 32 |
| Page Count | 32 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s00365-016-9332-8 |
| Volume Number | 45 |
| Alternate Webpage(s) | https://arxiv.org/pdf/1504.02628v2.pdf |
| Alternate Webpage(s) | https://www.duo.uio.no/bitstream/handle/10852/59769/SS532-Final3.pdf?isAllowed=y&sequence=2 |
| Alternate Webpage(s) | https://doi.org/10.1007/s00365-016-9332-8 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
