Abstract
In this paper we present a study of spaces of splines in C k(R 2) with supports the square Σ1 and the lozenge Λ1 formed respectively by four and eight triangles of the uniform four directional mesh of the plane. Such splines are called Σ1 and Λ1-splines. We first compute the dimension of the space of Σ1-splines. Then we prove the existence of a unique Σ1-spline of minimal degree for any fixed k≥0. By using this last result, we also prove the existence of a unique Σ1-spline of minimal degree. Finally, we describe algorithms allowing to compute the Bernstein–Bézier coefficients of Σ1-spline and Λ1-spline of minimal degree.
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Nouisser, O., Sbibih, D. Existence and Construction of Simple B-Splines of Class C k on a Four-Directional Mesh of the Plane. Numerical Algorithms 27, 329–358 (2001). https://doi.org/10.1023/A:1013849809199
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DOI: https://doi.org/10.1023/A:1013849809199