Pointwise radial minimization: Hermite interpolation on arbitrary domains

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dc.contributor.authorFloater, M. S.en_US
dc.contributor.authorSchulz, C.en_US
dc.date.accessioned2015-02-21T17:32:37Z
dc.date.available2015-02-21T17:32:37Z
dc.date.issued2008en_US
dc.description.abstractIn this paper we propose a new kind of Hermite interpolation on arbitrary domains, matching derivative data of arbitrary order on the boundary. The basic idea stems from an interpretation of mean value interpolation as the pointwise minimization of a radial energy function involving first derivatives of linear polynomials. We generalize this and minimize over derivatives of polynomials of arbitrary odd degree. We analyze the cubic case, which assumes first derivative boundary data and show that the minimization has a unique, infinitely smooth solution with cubic precision. We have not been able to prove that the solution satisfies the Hermite interpolation conditions but numerical examples strongly indicate that it does for a wide variety of planar domains and that it behaves nicely.en_US
dc.description.number5en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume27en_US
dc.identifier.doi10.1111/j.1467-8659.2008.01291.xen_US
dc.identifier.issn1467-8659en_US
dc.identifier.pages1505-1512en_US
dc.identifier.urihttps://doi.org/10.1111/j.1467-8659.2008.01291.xen_US
dc.publisherThe Eurographics Association and Blackwell Publishing Ltden_US
dc.titlePointwise radial minimization: Hermite interpolation on arbitrary domainsen_US
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27-Issue 5
SGP08: Eurographics Symposium on Geometry Processing