Advertisement
Published in:
2019 | OriginalPaper | Chapter
6. BEZIER Interpolation and Relevant Isoparametric Elements
Author : Christopher G. Provatidis
Published in: Precursors of Isogeometric Analysis
Publisher: Springer International Publishing
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
Abstract
Previously, in Chap. 2 the basics of Bézier interpolation have been exposed. This chapter continues with the construction of univariate (1D) and tensor-product (2D) Bézier-based macroelements. The reader is introduced to the fact that, due to a basis change, the nonrational Bézierian elements are equivalent with Lagrangian ones, in all dimensions. The aforementioned higher-order elements are also compared with the well-known p-method. It is shown that, particularly in the 1D problem, all three approaches (Lagrange polynomials, Bernstein–Bézier polynomials, and p-method) are equivalent, in the sense that each of them includes the same monomials. The theory is supported by eleven exercises. Also, the de Casteljau algorithm in curves and the Bernstein–Bézier triangles are explained in detail through three original Appendices.