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 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.
curve fitting squared distance minimization constrained optimization b b -spline curve b b b b b geometric constraints damped gaussnewton method shape approximation free-form curves splines on manifolds constrained curve design