Parallel implementation of curve and surface reconstructions from noisy samples

We consider the problem of reconstructing a curve or a surface from discrete noisy samples by approximating the point set with non-uniform rational B-splines. We show how to set up the free knot problem such that constrained nonlinear optimization can be applied efficiently. An approach for realizing the optimization in parallel will be described in detail. Our foremost objective in our parallel algorithm is to obtain a tangible load balancing among the different processors. We provide numerical results obtained from the Chemnitzer Linux Cluster supercomputer. From the measured runtimes on different numbers of processors, one can observe that our approach gives practically a linear speedup.