TY - GEN

T1 - Lofting curve networks using subdivision surfaces

AU - Schaefer, S.

AU - Warren, J.

AU - Zorin, D.

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=77954462999&partnerID=8YFLogxK

U2 - 10.1145/1057432.1057447

DO - 10.1145/1057432.1057447

M3 - Conference contribution

AN - SCOPUS:77954462999

SN - 3905673134

SN - 9783905673135

T3 - ACM International Conference Proceeding Series

SP - 103

EP - 114

BT - SGP 2004 - Symposium on Geometry Processing

T2 - 2nd Symposium on Geometry Processing, SGP 2004

Y2 - 8 July 2004 through 10 July 2004

ER -