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

Computer Aided Geometric Design (CAGD) 26(2): 192-202, 2009

Abstract:

We consider the problem of tting B-spline curves and surfaces to point clouds in the
presence of obstacles constraining this approximation at the same time. Therefore,
we describe the tting 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: rst, the point cloud itself
is interpreted as obstacle, e.g. to reconstruct any apparant boundaries of the data
set. Second, we de ne arbitrary regions the tting must not penetrate. We discuss
several numerical aspects of this constrained optimization and present experimental
results for B-spline curve and surface ttings in the presence of obstacles.

Bibtex:

@article{floery-2009-fpoo,
author = {Simon Fl{\"o}ry},
title = {Fitting curves and surfaces to point clouds in the presence of obstacles},
journal = {Computer Aided Geometric Design},
volume = {26},
issue = {2},
year = {2009},
pages = {192--202},
}

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