Constrained curve fitting on manifolds

Authors:
Simon Flöry;Michael Hofer
Affiliations:
Geometric Modeling and Industrial Geometry Research Group, Vienna University of Technology, Wiedner Hauptstraíe 8-10, A-1040 Wien, Austria;Geometric Modeling and Industrial Geometry Research Group, Vienna University of Technology, Wiedner Hauptstraíe 8-10, A-1040 Wien, Austria
Venue:
Computer-Aided Design
Year:
2008

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Abstract

When designing curves on surfaces the need arises to approximate a given noisy target shape by a smooth fitting shape. We discuss the problem of fitting a B-spline curve to a point cloud by squared distance minimization in the case that both the point cloud and the fitting curve are constrained to lie on a smooth manifold. The on-manifold constraint is included by using the first fundamental form of the surface for squared distance computations between the point cloud and the fitting curve. For the solution we employ a constrained optimization algorithm that allows us to include further constraints such as one-sided fitting or surface regions that have to be avoided by the fitting curve. We illustrate the effectiveness of our algorithm by means of several examples showing different applications.