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 in | Journal of applied mathematics & computing Vol. 23; no. 1-2; pp. 73 - 86 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Dordrecht
Springer Nature B.V
01.01.2007
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1598-5865 1865-2085 |
| DOI | 10.1007/BF02831959 |
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| Abstract | 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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| AbstractList | 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 super(1) Hermite data, we construct a spatial PH curve on a sphere that is aC super(1) Hermite interpolant of the given data as follows: First, we solveC super(1) Hermite interpolation problem for the stereographically projected planar data of the given data in super(3) with planar PH curves expressed in the complex representation. Second, we construct spherical PH curves which are interpolants for the given data in super(3) using the inverse general stereographic projection. 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 spatial C1 Hermite data, we construct a spatial PH curve on a sphere that is a C1 Hermite interpolant of the given data as follows: First, we solve C1 Hermite interpolation problem for the stereographically projected planar data of the given data in R3 with planar PH curves expressed in the complex representation. Second, we construct spherical PH curves which are interpolants for the given data in R3 using the inverse general stereographic projection. 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] |
| Author | Kim, Gwang-Il Lee, Sunhong Kong, Jae-Hoon |
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| CitedBy_id | crossref_primary_10_1155_2018_5680723 crossref_primary_10_4134_BKMS_2012_49_1_175 crossref_primary_10_3390_math11143157 crossref_primary_10_1016_j_cagd_2007_11_006 crossref_primary_10_1016_j_cagd_2014_08_005 crossref_primary_10_1016_j_cam_2013_01_016 |
| Cites_doi | 10.1147/rd.345.0736 10.1016/S0167-8396(03)00095-5 10.1016/0167-8396(86)90022-1 10.1016/0010-4485(96)00030-9 10.1016/0167-8396(94)90204-6 10.1016/S0010-4485(98)00080-3 10.1016/S0167-8396(85)80002-9 10.1016/S0893-9659(02)00143-X 10.1016/0167-8396(90)90023-K 10.1016/0167-8396(95)00024-0 10.1016/S0167-8396(02)00165-6 10.1016/0010-4485(88)90005-X 10.1016/j.cam.2003.08.030 10.1090/S0025-5718-1995-1308452-6 10.1016/0010-4485(85)90249-0 10.1109/IV.1997.626490 10.1016/j.cagd.2003.06.001 10.1016/S0167-8396(99)00016-3 10.1016/S0167-8396(02)00123-1 10.1016/0167-8396(94)00008-G 10.1016/0167-8396(90)90024-L 10.1016/S0010-4485(97)00004-3 10.1023/A:1016280811626 |
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| SubjectTerms | Computational mathematics Construction Interpolation Inverse Mapping Mathematical models Projection Representations Studies |
| Title | First order hermite interpolation with spherical Pythagorean-hodograph curves |
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