Generalized plane offsets and rational parameterizations
In the first part of the paper a planar generalization of offset curves is introduced and some properties are derived. In particular, it is seen that these curves exhibit good regularity properties and a study on self-intersection avoidance is performed. The representation of a rational curve as the...
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| Tipo de documento: | artigo |
| Estado: | Versión enviada para evaluación y publicación |
| Data de publicação: | 2023 |
| País: | España |
| Recursos: | Basque Center for Applied Mathematics (BCAM) |
| Repositório: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/1588 |
| Acesso em linha: | http://hdl.handle.net/20.500.11824/1588 https://doi.org/10.1016/j.cagd.2023.102196 |
| Access Level: | Acesso embargado |
| Palavra-chave: | Offset curve Pythagorean-hodograph curve Rational parameterization Support function Constant width curve Zindler curve |
| Resumo: | In the first part of the paper a planar generalization of offset curves is introduced and some properties are derived. In particular, it is seen that these curves exhibit good regularity properties and a study on self-intersection avoidance is performed. The representation of a rational curve as the envelope of its tangent lines, following the approach of Pottmann, is revisited to give the explicit expression of all rational generalized offsets. Other famous shapes, such as constant width curves, bicycle tire-tracks curves and Zindler curves are related to these generalized offsets. This gives rise to the second part of the paper, where the particular case of rational parameterizations by a support function is considered and explicit families of rational constant width curves, rational bicycle tire-track curves and rational Zindler curves are generated and some examples are shown. |
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