Lofting curve networks using subdivision surfaces

S. Schaefer, J. Warren, D. Zorin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 (US)
Title of host publicationSGP 2004 - Symposium on Geometry Processing
Pages103-114
Number of pages12
DOIs
StatePublished - 2004
Event2nd Symposium on Geometry Processing, SGP 2004 - Nice, France
Duration: Jul 8 2004Jul 10 2004

Publication series

NameACM International Conference Proceeding Series
Volume71

Other

Other2nd Symposium on Geometry Processing, SGP 2004
CountryFrance
CityNice
Period7/8/047/10/04

Keywords

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

ASJC Scopus subject areas

  • Software
  • Human-Computer Interaction
  • Computer Vision and Pattern Recognition
  • Computer Networks and Communications

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  • Cite this

    Schaefer, S., Warren, J., & Zorin, D. (2004). Lofting curve networks using subdivision surfaces. In SGP 2004 - Symposium on Geometry Processing (pp. 103-114). (ACM International Conference Proceeding Series; Vol. 71). https://doi.org/10.1145/1057432.1057447