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Article overview
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Ellipse-preserving Hermite interpolation and subdivision | | Costanza Conti
; Lucia Romani
; Michael Unser
; | | Date: |
17 Nov 2014 | | Abstract: | We introduce a family of piecewise-exponential functions that have the
Hermite interpolation property. Our design is motivated by the search for an
effective scheme for the joint interpolation of points and associated tangents
on a curve with the ability to perfectly reproduce ellipses. We prove that the
proposed Hermite functions form a Riesz basis and that they reproduce
prescribed exponential polynomials. We present a method based on Green’s
functions to unravel their multi-resolution and approximation-theoretic
properties. Finally, we derive the corresponding vector and scalar subdivision
schemes, which lend themselves to a fast implementation. The proposed vector
scheme is interpolatory and level-dependent, but its asymptotic behaviour is
the same as the classical cubic Hermite spline algorithm. The same convergence
properties---i.e., fourth order of approximation---are hence ensured. | | Source: | arXiv, 1411.4627 | | Services: | Forum | Review | PDF | Favorites | |
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