Properties of an h‐Bernstein‐like basis and curves

Properties of an h‐Bernstein‐like basis and curves

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Article ID: iaor20134201
Volume: 63
Issue: 3
Start Page Number: 453
End Page Number: 481
Publication Date: Jul 2013
Journal: Numerical Algorithms
Authors:
Keywords: computer-aided design
Abstract:

Blossoming is a useful technique to study bases and curve representations in computer‐aided geometric design. Recently Simeonov et al. (2011) have used a blossom generalization, namely the h‐blossom, to derive new results about the h‐Bernstein basis and h‐Bézier curves that have previously been studied in approximation theory and computer‐aided geometric design. This paper introduces a basis related to the h‐Bernstein basis. There is a close relationship between this new basis and the h‐Bernstein basis, between the new basis and the h‐blossom, and between the new basis and ‘progressive’ curves. This paper explores these relationships and uses them to derive properties both of the new basis itself, and of curves represented in terms of the new basis.

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