A direct and local method for computing polynomial Pythagorean-normal patches with global G1 continuity. (September 2018)

• Record Type: Journal Article
• Authors: Bizzarri, Michal; Lávička, Miroslav; Vršek, Jan; Kosinka, Jiří
• Is Part Of: Computer aided design. Volume 102(2018)
• Page Start: 44
• Page End: 51
• Publication Date: 2018-09
• Subjects: Hermite interpolation -- Piece-wise polynomial PN surfaces -- Rational offsets -- Macro-elements; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2018.04.013
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: We present a direct and local construction for polynomial G 1 spline surfaces with a piece-wise Pythagorean normal (PN) vector field. A key advantage of our method is that the constructed splines possess exact piece-wise rational offsets without any need for reparametrisations, which in turn means that no trimming procedure in the parameter domain is necessary. The spline surface consists of locally constructed triangular PN macro-elements, each of which is completely local and capable of matching boundary data consisting of three points with associated normal vectors. The collection of the macro-elements forms a G 1 -continuous spline surface. The designed method is demonstrated on several examples. Highlights: We solve the challenging problem of designing a PN Hermite interpolation method which: is local, i.e., a PN macro-element is computed only from vertex and normal data of one triangle at a time is direct, i.e., it yields polynomial PN macro-elements with no need for reparametrisations yields globally G 1 -continuous PN spline surfaces