This paper presents a new algorithm for computing the maximal turning state of an arbitrary mesh. This is accomplished by intersecting the mesh with a plane at even intervals along the mesh, and computing the farthest point in that plane from an axis of rotation. The algorithm will run in O(|E|*n) time and θ(n) space, where E is the list of the edges on the mesh and n is the number of intervals used. Because of this, a very high degree of accuracy can be obtained with very little computational cost. The developed algorithm has been implemented and tested on some meshed models.

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