Alpha-shapes and flow shapes are homotopy equivalent

Authors:
Tamal K. Dey;Joachim Giesen;Matthias John
Affiliations:
The Ohio State University, USA;ETH Zürich, Switzerland;ETH Zürich, Switzerland
Venue:
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Year:
2003

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Abstract

In this paper we establish a topological similarity between two apparently different shape constructors from a set of points. Shape constructors are geometric structures that transform finite point sets into continuous shapes. Due to their immense practical importance in geometric modeling various shape constructors have been proposed recently. Understanding the relations among them often leads to new insights that are potentially helpful in applications. Here we discover a topological equivalence among two such geometric structures, namely α shapes and flow shapes. Both shapes found applications in surface reconstruction and molecular modelin.