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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