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.

Point Inversion for triparametric NURBS / Orazi, L.; Reggiani, B.. - In: INTERNATIONAL JOURNAL ON INTERACTIVE DESIGN AND MANUFACTURING. - ISSN 1955-2513. - 15:1(2021), pp. 55-61. [10.1007/s12008-020-00719-z]

Point Inversion for triparametric NURBS

Orazi L.
;
Reggiani B.
2021

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.
2021
19-ott-2020
15
1
55
61
Point Inversion for triparametric NURBS / Orazi, L.; Reggiani, B.. - In: INTERNATIONAL JOURNAL ON INTERACTIVE DESIGN AND MANUFACTURING. - ISSN 1955-2513. - 15:1(2021), pp. 55-61. [10.1007/s12008-020-00719-z]
Orazi, L.; Reggiani, B.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1223564
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