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 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. Key words: B-spline curve, curve fitting, constrained optimization, squared distance minimization, geometric constraints, damped Gauss-Newton method, shape approximation, free-form curves, sp...

• Type: Journal
• Year: 2008
• Where: CAD
• Authors: Simon Flöry, Michael Hofer
• Keywords: B-spline Curve, CAD 2008, Curve, Fitting Curve, Theoretical Computer Science