Deforming Curves in the Plane for Tethered-Robot Motion Planning

We present an algorithm that deforms a given set of polygonal lines (polylines) defined on a set of 2n vertices into the new set of polylines that results from one of the vertices moving along a straight line to a new point in the plane, creating bends in the polylines intersected by the line of motion. The algorithm has applications in robotics, where the moving point is one of n robots in the plane and the polylines are representations of taut tethers attached to the robots. The algorithm runs in O(kn 2 ) time, where k is the maximum number of line segments a polyline may have. The algorithm makes use of work presented in [8], which requires that a triangulation of the set of polyline vertices be maintained. When the polyline vertices change, so must the triangulation. Also presented here is a new triangulation algorithm and data structure that allows for easy insertion and deletion of triangle vertices. The data structure requires O(n) space and allows vertices to be inserted in ..

Deforming Curves in the Plane for Tethered-Robot Motion Planning (Extended Abstract)

) Susan Hert y Vladimir Lumelsky z Abstract We present an algorithm that deforms a given set of polygonal lines (polylines) defined on a set of 2n vertices into the new set of polylines that results from one of the vertices moving along a straight line to a new point in the plane, creating bends in the polylines intersected by the line of motion. The algorithm has applications in robotics, where the moving point is one of n robots in the plane and the polylines are representations of taut tethers attached to the robots. The algorithm runs in O(kn 2 ) time, where k is the maximum number of line segments a polyline may have. The algorithm makes use of work presented in [8], which requires that a triangulation of the set of polyline vertices be maintained. When the polyline vertices change, so must the triangulation. Also presented here is a new triangulation algorithm and data structure that allows for easy insertion and deletion of triangle vertices. The data structure requires ..