First order hermite interpolation with spherical Pythagorean-hodograph curves

The general stereographic projection which maps a point on a sphere with arbitrary radius to a point on a plane stereographically and its inverse projection have the Pythagorean-hodograph (PH) preserving property in the sense that they map a PH curve to another PH curve. Upon this fact, for given sp...

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Published inJournal of applied mathematics & computing Vol. 23; no. 1-2; pp. 73 - 86
Main Authors Kim, Gwang-Il, Kong, Jae-Hoon, Lee, Sunhong
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Nature B.V 01.01.2007
Subjects
Computational mathematics
Construction
Interpolation
Inverse
Mapping
Mathematical models
Projection
Representations
Studies
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Summary:The general stereographic projection which maps a point on a sphere with arbitrary radius to a point on a plane stereographically and its inverse projection have the Pythagorean-hodograph (PH) preserving property in the sense that they map a PH curve to another PH curve. Upon this fact, for given spatialC^sup 1^ Hermite data, we construct a spatial PH curve on a sphere that is aC^sup 1^ Hermite interpolant of the given data as follows: First, we solveC^sup 1^ Hermite interpolation problem for the stereographically projected planar data of the given data in ^sup 3^ with planar PH curves expressed in the complex representation. Second, we construct spherical PH curves which are interpolants for the given data in ^sup 3^ using the inverse general stereographic projection.[PUBLICATION ABSTRACT]
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ISSN:1598-5865
1865-2085
DOI:10.1007/BF02831959