Space complexity of exact discrete geodesic algorithms on regular triangulations

Abstract Computing geodesic distances on 2-manifold meshes is a fundamental problem in computational geometry. To date, two notable classes of exact algorithms, namely, the Mitchell–Mount–Papadimitriou (MMP) algorithm and the Chen–Han (CH) algorithm, have been widely studied. For an arbitrary triangle mesh with n vertices, these algorithms have space complexity of O ( n 2 ) . In this paper, we prove that both algorithms have Θ ( n 1.5 ) space complexity on a completely regular triangulation (i.e., all triangles are equilateral).

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