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International Journal on Interactive Design and Manufacturing (IJIDeM)
Published in: International Journal on Interactive Design and Manufacturing (IJIDeM) 1/2021

19-10-2020 | Short Original Paper

Point Inversion for triparametric NURBS

Authors: Leonardo Orazi, Barbara Reggiani

Published in: International Journal on Interactive Design and Manufacturing (IJIDeM) | Issue 1/2021

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Abstract

In this paper a Point Inversion algorithm for NURBS volumes is presented. This algorithm is an extension to 3D of the classic Newton–Raphson iteration, thus implying the calculation of the NURBS volume partial derivatives. Explicit formulas for the derivatives are deduced and reported, in turn requiring the evaluation of the corresponding derivatives of the rational basis functions. Also these derivatives are inferred and shown together with some examples of applications. The method, applicable to any free-form shape NURBS volume is moreover compared with Fast Mapping, a novel approach presented here that, once applied to simple NURBS boxes give performance 20–50 times higher.
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Metadata
Title
Point Inversion for triparametric NURBS
Authors
Leonardo Orazi
Barbara Reggiani
Publication date
19-10-2020
Publisher
Springer Paris
Published in
International Journal on Interactive Design and Manufacturing (IJIDeM) / Issue 1/2021
Print ISSN: 1955-2513
Electronic ISSN: 1955-2505
DOI
https://doi.org/10.1007/s12008-020-00719-z

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