Tangent driven interpolative subdivision

Abstract

This paper explores a new family of 2D interpolating subdivision schemes that calculate subdivision points from tangent specifications. In this approach each level of subdivision drives the curve toward its specified tangents. The paper describes the underlying algorithmic formulation, and outlines a number of variations, which differ in how subdivision points are computed from tangents or in how tangents are derived. The different characteristics of these variations are shown to provide an interesting range of shapes, giving a high degree of artistic control. Each variation is shown to guarantee C1 continuity except for special identifiable cases, and some of these variations can produce circles. A number of examples are explored that demonstrate the power of the approach as a modeling tool for constructing complex curves, and a comparison is made with curves produced by the Kobbelt subdivision scheme. (C) 2007 Elsevier Ltd. All rights reserved.

Department

Computer Science

Publication Date

10-1-2007

Journal Title

Computers & Graphics

Publisher

PERGAMON-ELSEVIER SCIENCE LTD

Digital Object Identifier (DOI)

10.1016/j.cag.2007.07.003

Document Type

Article

Rights

© 2007 Elsevier Ltd. All rights reserved.

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