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...

• Type: Journal
• Year: 2006
• Where: CGF
• Authors: Cristina Neacsu, Karen Daniels
• Keywords: CGF 2006, Polygonal, Spline Curve, Translational Spline