Paper Info
Title
Transfinite surface interpolation over irregular n-sided domains
Abstract
Transfinite surface interpolation is a classic topic of computer-aided geometric design (CAGD), and many non-quadrilateral schemes are known. Surfaces defined solely by means of their boundary curves and cross-tangent functions are needed, for example, in three-dimensional curve network-based design, and to fill complex irregular holes such as in vertex blending. This paper deals with interpolating so-called tangential ribbons. Former schemes are enhanced and extended in order to minimize shape artifacts and to provide a more natural patch interior. The proposed representation is based on irregular convex domains that correspond to the lengths and orientations of the boundary curves. The mapping of the individual ribbons within the n-sided domain is calculated by focused parameterization methods that ensure a balanced orientation related to the center of the domain and avoid parametric shearing. Distance-based blending functions ensure that modifying or inserting a small edge will have only a local effect over the n-sided patch. Constructions to create one-sided or two-sided patches are also presented. Examples and open research topics conclude the paper.
Year
DOI
Venue
2011
10.1016/j.cad.2011.08.028
Computer-Aided Design
Keywords
Field
DocType
network-based design,n-sided patch,computer-aided geometric design,complex irregular hole,paper deal,natural patch interior,irregular convex domain,irregular n-sided domain,n-sided domain,boundary curve,distance-based blending function,transfinite surface interpolation,computer aided design,n,three dimensional
Topology,Mathematical optimization,Polygon,Vertex (geometry),Parametrization,Interpolation,Regular polygon,Geometric design,Parametric statistics,Transfinite number,Mathematics
Journal
Volume
Issue
ISSN
43
11
0010-4485
Citations 
PageRank 
References 
15
0.97
19
Authors
3
Name
Order
Citations
PageRank
Tamás Várady152938.87
Alyn Rockwood2950179.19
PéTer Salvi3284.58