Minimum-link paths among obstacles in the plane
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Curvature-constrained shortest paths in a convex polygon (extended abstract)
Proceedings of the fourteenth annual symposium on Computational geometry
Touring a sequence of polygons
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Curvature-bounded traversals of narrow corridors
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Link Distance and Shortest Path Problems in the Plane
AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
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Many surgical procedures could benefit from guiding a bevel-tip needle along circular arcs to multiple treatment points in a patient. At each treatment point, the needle can inject a radioactive pellet into a cancerous region or extract a tissue sample. Our main result is an algorithm to steer a bevel-tip needle through a sequence of treatment points in the plane while minimizing the number of times that the needle must be reoriented. This algorithm is related to [6] and takes quadratic time when consecutive points in the sequence are sufficiently separated. We can also guide a needle through an arbitrary sequence of points in the plane by accounting for a lack of optimal substructure.