Precursors of Isogeometric Analysis pp 255-314 | Cite as

# BEZIER Interpolation and Relevant Isoparametric Elements

## 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.

## Keywords

BEZIER interpolation Bézier curve Casteljau algorithm Lagrange versus Bézier polynomials Bézierian macroelements Equivalency P-method Rational Bézier element Bézier triangle Test cases## References

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