Lofting curve networks using subdivision surfaces

S. Schaefer, J. Warren, Denis 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
Volume71
DOIs
StatePublished - 2004
Event2nd Symposium on Geometry Processing, SGP 2004 - Nice, France
Duration: Jul 8 2004Jul 10 2004

Other

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

Fingerprint

Splines
Control surfaces
Topology

Keywords

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

ASJC Scopus subject areas

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

Cite this

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

Lofting curve networks using subdivision surfaces. / Schaefer, S.; Warren, J.; Zorin, Denis.

SGP 2004 - Symposium on Geometry Processing. Vol. 71 2004. p. 103-114.

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

Schaefer, S, Warren, J & Zorin, D 2004, Lofting curve networks using subdivision surfaces. in SGP 2004 - Symposium on Geometry Processing. vol. 71, pp. 103-114, 2nd Symposium on Geometry Processing, SGP 2004, Nice, France, 7/8/04. https://doi.org/10.1145/1057432.1057447
Schaefer S, Warren J, Zorin D. Lofting curve networks using subdivision surfaces. In SGP 2004 - Symposium on Geometry Processing. Vol. 71. 2004. p. 103-114 https://doi.org/10.1145/1057432.1057447
Schaefer, S. ; Warren, J. ; Zorin, Denis. / Lofting curve networks using subdivision surfaces. SGP 2004 - Symposium on Geometry Processing. Vol. 71 2004. pp. 103-114
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