Abstract
Let τ be the uniform triangulation generated by the usual three-directional mesh of the plane and let Σ1 be the unit square consisting of two triangles of τ. We study the space of piecewise polynomial functions in C k (R2) with support Σ1 having a sufficiently high degree n, which are symmetrical with respect to the first diagonal of Σ1. Such splines are called Σ1-splines. We first compute the dimension of this space in function of n and k. Then, for any fixed k≥0, we prove the existence of Σ1-splines of class C k and minimal degree. These splines are not unique. Finally, we describe an algorithm computing the Bernstein–Bezier coefficients of these splines, and we give an example.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
