Constrained Curve Fitting on Manifolds
S. Flöry, and M. Hofer.

Computer-Aided Design 40/1, 25-34, (2008).


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 at hand of several examples showing different applications.


	author = "Simon Fl{\"o}ry and Michael Hofer",
	title =  "Constrained curve fitting on manifolds",
	journal = "Computer-Aided Design",
	volume = "40",
	number = "1",
	pages = "25-34",
	year= "2008",


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