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Point Inversion for triparametric NURBS
https://orcid.org/http://orcid.org/0000-0002-4507-0518
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
https://orcid.org/http://orcid.org/0000-0002-4507-0518
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
https://orcid.org/http://orcid.org/0000-0002-4507-0518
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
Int J Interact Des Manuf
Orazi, Leonardo (author) / Reggiani, Barbara (author)
2021-03-01
7 pages
Article (Journal)
Electronic Resource
English
Point Inversion , triparametric NURBS , NURBS volume , NURBS derivatives , Basis functions derivatives Engineering , Engineering, general , Engineering Design , Mechanical Engineering , Computer-Aided Engineering (CAD, CAE) and Design , Electronics and Microelectronics, Instrumentation , Industrial Design
Correction to: Point Inversion for triparametric NURBS
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