Towards the multivariate simplotope spline

Continuity conditions in a class of mixed

Journal article (2016)

Authors

T. Visser Astrodynamics & Space Missions - Aerospace Engineering
Research Group
Astrodynamics & Space Missions (Aerospace Engineering) (TU Delft)
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Published Date

2016

Language

English

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Faculty

Aerospace Engineering

Department

Space Engineering

Research Group

Astrodynamics & Space Missions

Abstract

Smooth joins of simplex Bernstein-B'ezier polynomials have been studied extensively in the past. In this paper a new method is proposed to define continuity conditions for tensor-product Bernstein polynomials on a class of mixed grids that meets certain out-of-facet parallelism criteria. The conditions are derived by first defining a simplex around the simplotopic bases of the tensor-product polynomials. Then the continuity conditions in the multivariate simplex spline defined on the resulting simplices, are adapted to hold for the tensor-product polynomials. The two- and three-dimensional results agree with the results found in the literature. It is expected that the method can be employed in more general grids.