Fitting curves and surfaces to point clouds in the presence of obstacles

We consider the problem of fitting B-spline curves and surfaces to point clouds on taking real world obstacles into account at the same time. Therefor, we describe the fitting problem as optimization problem and employ an iterative procedure to solve it. The presence of obstacles poses constraints on this minimization process. We examine two families of obstacles: first, the point cloud itself is interpreted as obstacle, e.g. to approximate the data points’ boundaries. Second, we define arbitrary regions the fitting must not penetrate. All constrained approximations are depicted for B-spline curves as well as for surfaces.