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Pointwise radial minimization: Hermite interpolation on arbitrary domains
Author(s) -
Floater M. S.,
Schulz C.
Publication year - 2008
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2008.01291.x
Subject(s) - pointwise , hermite interpolation , mathematics , interpolation (computer graphics) , monotone cubic interpolation , cubic hermite spline , hermite polynomials , mathematical analysis , minification , boundary (topology) , birkhoff interpolation , pure mathematics , linear interpolation , polynomial interpolation , polynomial , bicubic interpolation , computer science , mathematical optimization , animation , computer graphics (images)
In 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.