A simple strategy for defining polynomial spline spaces over hierarchical T-meses
We present a new strategy for constructing spline spaces over hierarchical T-meshes with quad- and octree subdivision schemes. The proposed technique includes some simple rules for inferring local knot vectors to define -continuous cubic tensor product spline blending functions. Our conjecture is th...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2016 |
| País: | España |
| Repositorio: | accedaCRIS portal de investigación de la Universidad de las Palmas de Gran Canaria |
| OAI Identifier: | oai:accedacris.ulpgc.es:10553/16442 |
| Acceso en línea: | http://hdl.handle.net/10553/16442 |
| Access Level: | acceso abierto |
| Palabra clave: | 1204 Geometría 1206 Análisis numérico Isogeometric analysis Multivariate splines Local refinement T-mesh Nested spaces |
| Sumario: | We present a new strategy for constructing spline spaces over hierarchical T-meshes with quad- and octree subdivision schemes. The proposed technique includes some simple rules for inferring local knot vectors to define -continuous cubic tensor product spline blending functions. Our conjecture is that these rules allow to obtain, for a given T-mesh, a set of linearly independent spline functions with the property that spaces spanned by nested T-meshes are also nested, and therefore, the functions can reproduce cubic polynomials. In order to span spaces with these properties applying the proposed rules, the T-mesh should fulfill the only requirement of being a 0-balanced mesh. The straightforward implementation of the proposed strategy can make it an attractive tool for its use in geometric design and isogeometric analysis. In this paper we give a detailed description of our technique and illustrate some examples of its application in isogeometric analysis performing adaptive refinement for 2D and 3D problems. |
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