Constrained curve fitting on manifolds

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...

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Veröffentlicht in:Computer aided design 2008, Vol.40 (1), p.25-34
Hauptverfasser: Flöry, Simon, Hofer, Michael
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0010-4485
1879-2685
DOI:10.1016/j.cad.2007.01.012