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University of Georgia

1. Wu, Jianbao. Spherical splines for Hermite interpolation and surface design.

Degree: PhD, Mathematics, 2007, University of Georgia

URL: http://purl.galileo.usg.edu/uga_etd/wu_jianbao_200708_phd

The following dissertation consists of two parts. Throughout this dissertation, we assume
that the spherical triangulation could be a part of a sphere with or without holes, or the
whole sphere S2. In the first part, given a set of function values and derivatives at scattered
data locations over a spherical surface, we first use the minimal energy method to find a
Hermite interpolation on the spherical spline spaces over a spherical triangulation of the
scattered data locations. We show that the minimal energy method produces a unique spherical
Hermite interpolation spline of the given scattered data with derivatives. Also we show
that the Hermite interpolatory surface converges to a given sufficiently smooth function f in
L2 and L∞ norm if the values are obtained from this f. That is, the surface of the spherical
Hermite interpolation spline resembles the given set of scattered data values and derivatives.
Some numerical results are given to demonstrate our method. In the second part, for any
integer r ≥ 0, we first give a method of Cr hole filling by the minimal energy quasi-Hermite
interpolation method and delicate care of Cr related boundaries. Then we present a method
to deal with point cloud with Cr continuity by using the minimal energy Hermite interpolation
method or minimal energy quasi-Hermite interpolation method, and our surface can
interpolate these points and their derivatives if they are given. Several numerical experiments
are presented to show our methods.
*Advisors/Committee Members: Mingjun Lai.*

Subjects/Keywords: Approximation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Wu, J. (2007). Spherical splines for Hermite interpolation and surface design. (Doctoral Dissertation). University of Georgia. Retrieved from http://purl.galileo.usg.edu/uga_etd/wu_jianbao_200708_phd

Chicago Manual of Style (16^{th} Edition):

Wu, Jianbao. “Spherical splines for Hermite interpolation and surface design.” 2007. Doctoral Dissertation, University of Georgia. Accessed September 16, 2019. http://purl.galileo.usg.edu/uga_etd/wu_jianbao_200708_phd.

MLA Handbook (7^{th} Edition):

Wu, Jianbao. “Spherical splines for Hermite interpolation and surface design.” 2007. Web. 16 Sep 2019.

Vancouver:

Wu J. Spherical splines for Hermite interpolation and surface design. [Internet] [Doctoral dissertation]. University of Georgia; 2007. [cited 2019 Sep 16]. Available from: http://purl.galileo.usg.edu/uga_etd/wu_jianbao_200708_phd.

Council of Science Editors:

Wu J. Spherical splines for Hermite interpolation and surface design. [Doctoral Dissertation]. University of Georgia; 2007. Available from: http://purl.galileo.usg.edu/uga_etd/wu_jianbao_200708_phd