We consider the problem of reconstructing a surface from noisy samples by approximating the point set with non-uniform rational B-spline surfaces. We focus on the fact that the knot sequences should also be part of the unknown variables that include the control points and the weights in order to find their optimal positions. We show how to set up the free knot problem such that constrained nonlinear optimization can be applied efficiently. We describe in detail a parallel implementation of our approach that give almost linear speedup. Finally, we provide numerical results obtained on the Chemnitzer Linux Cluster supercomputer.

This paper is concerned with approximating noisy samples by non-uniform rational B-spline curves with special emphasis on free knots. We show how to set up the problem such that nonlinear optimization methods can be applied efficiently. This involves the introduction of penalizing terms in order to avoid undesired knot positions. We report on our implementation of the nonlinear optimization and we show a way to implement the program in parallel. Parallel performance results are described. Our experiments show that our program has a linear speedup and an efficiency value close to unity. Runtime results on a parallel computer are displayed.

This paper is concerned with approximating noisy samples by non-uniform rational B-spline curves with special emphasis on free knots. We show how to set up the problem such that nonlinear optimization methods can be applied efficiently. This involves the introduction of penalizing terms in order to avoid undesired knot positions. We report on our implementation of the nonlinear optimization and we show a way to implement the program in parallel. Parallel performance results are described. Our experiments show that our program has a linear speedup and an efficiency value close to unity. Runtime results on a parallel computer are displayed.

We consider the problem of reconstructing a surface from noisy samples by approximating the point set with non-uniform rational B-spline surfaces. We focus on the fact that the knot sequences should also be part of the unknown variables that include the control points and the weights in order to find their optimal positions. We show how to set up the free knot problem such that constrained nonlinear optimization can be applied efficiently. We describe in detail a parallel implementation of our approach that give almost linear speedup. Finally, we provide numerical results obtained on the Chemnitzer Linux Cluster supercomputer.