Translational Covering of Closed Planar Cubic B-Spline Curves

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Translational Covering of Closed Planar Cubic B-Spline Curves
Spline curves are useful in a variety of geometric modeling and graphics applications and covering problems abound in practical settings. This work defines a class of covering decision problems for shapes bounded by spline curves. As a first step in addressing these problems, this paper treats translational spline covering for planar, uniform, cubic B-splines. Inner and outer polygonal approximations to the spline regions are generated using enclosures that are inside two different types of piecewise-linear envelopes. Our recent polygonal covering technique is then applied to seek translations of the covering shapes that allow them to fully cover the target shape. A feasible solution to the polygonal instance provides a feasible solution to the spline instance. We use our recent proof that 2D translational polygonal covering is NP-hard to establish NP-hardness of our planar translational spline covering problem. Our polygonal approximation strategy creates approximations that are tigh...
Cristina Neacsu, Karen Daniels
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where CGF
Authors Cristina Neacsu, Karen Daniels
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