Lofting curve networks using subdivision surfaces

S. Schaefer, J. Warren, D. Zorin

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

43 Citations (Scopus)

Abstract

Lofting is a traditional technique for creating a curved shape by first specifying a network of curves that approximates the desired shape and then interpolating these curves with a smooth surface. This paper addresses the problem of lofting from the viewpoint of subdivision. First, we develop a subdivision scheme for an arbitrary network of cubic B-splines capable of being interpolated by a smooth surface. Second, we provide a quadrangulation algorithm to construct the topology of the surface control mesh. Finally, we extend the Catmull-Clark scheme to produce surfaces that interpolate the given curve network. Near the curve network, these lofted subdivision surfaces are C 2 bicubic splines, except for those points where three or more curves meet. We prove that the surface is C1 with bounded curvature at these points in the most common cases; empirical results suggest that the surface is also C1 in the general case.

Original languageEnglish
Title of host publicationSGP 2004 - Symposium on Geometry Processing
Pages103-114
Number of pages12
DOIs
Publication statusPublished - 2004
Externally publishedYes
Event2nd Symposium on Geometry Processing, SGP 2004 - Nice, France
Duration: 8 Jul 200410 Jul 2004

Publication series

NameACM International Conference Proceeding Series
Volume71

Conference

Conference2nd Symposium on Geometry Processing, SGP 2004
Country/TerritoryFrance
CityNice
Period8/07/0410/07/04

Keywords

  • I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling

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