Abstract: The exact reconsctruction of sharp features is a difficult problem concerned by reverse engineering, computer aided design and manufacture. To optimize the α-shape algorithm, our algorithm uses approximation of the topological neighbors of a sample point as the surface local sample, which makes α-shape scale thresholds reflect density of the points better, then the validity of the surface reconstruction is improved. Gaining the approximation of the topological neighbors of a sample point is essentially to achieve gain optimization for the Euclidean neighbors of the point, which extends the latter toward the sparse region of the sampled data so that it decreeses dropping of the topological neighbors caused by non-uniform points. Based on the approximation of the topological neighbors of points and prior knowledge of surface reconstruction, an α-shape scale threshold corresponding to an triangular face could be calculated, so that the scale thresholds used in surface reconstruction could be adjusted by itself adaptively. The tests show that this algorithm can reconstruct non-uniform point set with few holes and edge hollows, better maintain the accuracy of form and position, and reduce non-manifold facets, meanwhile, its efficiency is comparable with mainstream algorithms.

Key words: α-shape, gain optimization, local sample, sharp feature, surface reconstruction