Dimensions of biquadratic spline spaces over T-meshes

• Autores: Jiansong Deng, Falai Chen, Liangbing Jin
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 238, Nº 1, 2013, págs. 68-94
• Idioma: inglés
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• Resumen

  • This paper discusses the dimensions of spline spaces over T-meshes of low degree.

    Two new concepts are proposed: an extension of T-meshes and spline spaces with homogeneous boundary conditions. In the dimensional analysis, the key strategy is linear space embedding with the operator of the mixed partial derivative. A lower bound on the dimension of the biquadratic spline spaces over general T-meshes is provided.

    Furthermore, by making full use of the level structure of hierarchical T-meshes, a dimension formula of biquadratic spline space over hierarchical T-meshes is proved. Additionally, a topological explanation of the dimension formula is provided.