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 in the presence of obstacles constraining this approximation at the same time. Therefore, 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 reconstruct any apparent boundaries of the data set. Second, we define arbitrary regions the fitting must not penetrate. We discuss several numerical aspects of this constrained optimization and present experimental results for B-spline curve and surface fittings in the presence of obstacles.