Let R be a rotating, not translating, generic polyhedron in a polyhedral scene. In this paper, we consider a problem of finding an exact continuous path between two rotations of R. In a scene of complexity n with a rotating polyhedron of complexity m, a near-optimal O(n 3 m 3 log(nm)) algorithm is proposed. The algorithm is capable of constructing a complete graph describing the geometry of a configuration space. All generated features are mathematically exact. These include an exact

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... tion of edges and an exact vertex locations. This is a first implementation of an algorithm solving an exact motion planning problem involving rotations. This result can be viewed as a generalization of a some existing algorithms of this kind. Among others, there is a related work concerning a simpler rigid objects: a line segment and cigar-like object in R 3 and a general rigid body movement on a plane.