C 1 Hermite interpolation with PH curves by boundary data modification
We show how to create a new class of infinitely many PH Hermite interpolants for a given ordinary C 1 Hermite data-set, in a way that ameliorates the rapid shape transitions in PH quintic interpolants that occurs when boundary data has poor geometric compatibility. We first interpolate a Hermite dat...
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| Published in | Journal of computational and applied mathematics Vol. 248; pp. 47 - 60 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
15.08.2013
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0377-0427 |
| DOI | 10.1016/j.cam.2013.01.016 |
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| Abstract | We show how to create a new class of infinitely many PH Hermite interpolants for a given ordinary C 1 Hermite data-set, in a way that ameliorates the rapid shape transitions in PH quintic interpolants that occurs when boundary data has poor geometric compatibility. We first interpolate a Hermite data-set using two asymmetric PH cubics, each of which satisfies the data at one boundary. Then we selectively apply one of three shape improvement techniques to the interpolant, so as to eliminate rapid shape transitions and produce C 1 PH curves with lower bending energy, at the expense of a small increase in arc-length. |
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| AbstractList | We show how to create a new class of infinitely many PH Hermite interpolants for a given ordinary C 1 Hermite data-set, in a way that ameliorates the rapid shape transitions in PH quintic interpolants that occurs when boundary data has poor geometric compatibility. We first interpolate a Hermite data-set using two asymmetric PH cubics, each of which satisfies the data at one boundary. Then we selectively apply one of three shape improvement techniques to the interpolant, so as to eliminate rapid shape transitions and produce C 1 PH curves with lower bending energy, at the expense of a small increase in arc-length. |
| Author | Kim, Gwang Il Lee, Hyun Chol Kong, Jae Hoon |
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| Cites_doi | 10.1007/BF02124754 10.1016/S0377-0427(97)00066-6 10.1016/j.cagd.2007.11.004 10.1090/S0025-5718-00-01288-6 10.1016/0167-8396(95)00047-X 10.1016/j.cagd.2007.12.007 10.1023/A:1015294029079 10.1016/j.cagd.2007.03.004 10.1090/S0025-5718-1995-1308452-6 10.1016/j.cad.2006.10.006 10.1007/s10444-003-2599-x 10.1016/0010-4485(96)00030-9 10.4134/BKMS.2012.49.1.175 10.1016/S0167-8396(99)00016-3 10.1016/0167-8396(95)00024-0 10.1016/S0890-6955(98)00018-2 10.1023/A:1016280811626 10.1016/S0010-4485(98)00020-7 10.1016/0167-8396(94)90204-6 10.1007/BF02831959 10.1147/rd.345.0736 10.1016/j.cagd.2007.11.006 |
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