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.File | Dimensione | Formato | |
---|---|---|---|
point inversion triparametric NURBS.pdf
Accesso riservato
Tipologia:
Versione pubblicata dall'editore
Dimensione
1.65 MB
Formato
Adobe PDF
|
1.65 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris