Blends of canal surfaces from polyhedral medial transform representations

Authors:
Bohumír Bastl;Bert Jüttler;Miroslav Lávička;Tino Schulz
Affiliations:
University of West Bohemia, Department of Mathematics, Plzeň, Czech Republic;Johannes Kepler University of Linz, Institute of Applied Geometry, Austria;University of West Bohemia, Department of Mathematics, Plzeň, Czech Republic;Johannes Kepler University of Linz, Institute of Applied Geometry, Austria
Venue:
Computer-Aided Design
Year:
2011

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Abstract

We present a new method for constructing G^1 blending surfaces between an arbitrary number of canal surfaces. The topological relation of the canal surfaces is specified via a convex polyhedron and the design technique is based on a generalization of the medial surface transform. The resulting blend surface consists of trimmed envelopes of one- and two-parameter families of spheres. Blending the medial surface transform instead of the surface itself is shown to be a powerful and elegant approach for blend surface generation. The performance of our approach is demonstrated by several examples.