Motion planning for a steering-constrained robot through moderate obstacles
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Angle-restricted tours in the plane
Computational Geometry: Theory and Applications
The Angular-Metric Traveling Salesman Problem
SIAM Journal on Computing
Optimal Covering Tours with Turn Costs
SIAM Journal on Computing
Improved upper bounds on the reflexivity of point sets
Computational Geometry: Theory and Applications
SIAM Journal on Discrete Mathematics
Drawing hamiltonian cycles with no large angles
GD'09 Proceedings of the 17th international conference on Graph Drawing
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Let @e0 and let @W be a disk of sufficiently large radius R in the plane, i.e., R=R(@e). We first show that the set of lattice points inside @W can be connected by a (possibly self-intersecting) spanning tour (Hamiltonian cycle) consisting of straight line edges such that the turning angle at each point on the tour is at most @e. This statement remains true for any large and evenly distributed point set (suitably defined) in a disk. This is the first result of this kind that suggests far-reaching generalizations to arbitrary regions with a smooth boundary. Our methods are constructive and lead to an efficient algorithm for computing such a tour. On the other hand, it is shown that such a result does not hold for convex regions without a smooth boundary.