Lofting curve networks using subdivision surfaces Conference Paper uri icon

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. The Eurographics Association 2004.

name of conference

  • the 2004 Eurographics/ACM SIGGRAPH symposium

published proceedings

  • Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing - SGP '04

author list (cited authors)

  • Schaefer, S., Warren, J., & Zorin, D.

citation count

  • 48

complete list of authors

  • Schaefer, S||Warren, J||Zorin, D

publication date

  • January 2004