The computation and application of the medial axis have been limited because of its instability and algebraic complexity. In this paper, we use a simplification of the medial axis, the θ-SMA, that is parameterized by a separation angle formed by the vectors connecting a point on the medial axis to the closest points on the boundary. We formally characterize the degree of simplification of the θ-SMA as a function of θ. We present a fast algorithm to compute an approximation of the θ-SMA. It relies on computation of the distance field and its gradient using graphics hardware. The complexity of the algorithm varies based on resolution of the volume discretization and is a linear function of the input size. We have applied this algorithm to approximate the SMA of complex models composed of tens or hundreds of thousands of triangles. On a 2-GHz PC, its running time varies from a few seconds, for a model consisting of hundreds of triangles, to minutes for highly complex models.
Efficient Computation of A Simplified Medial Axis
Contributed by the Engineering Simulation & Visualization Committee for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received July 2003; revised manuscript received October 2003. Guest Editors: G. Shapiro and V. Elber.
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Foskey, M., Lin, M. C., and Manocha, D. (December 24, 2003). "Efficient Computation of A Simplified Medial Axis ." ASME. J. Comput. Inf. Sci. Eng. December 2003; 3(4): 274–284. https://doi.org/10.1115/1.1631582
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