Approximate Delaunay mesh reconstruction and quality estimation from point samples

• Autores: Wenyong Gong, Yong-Jin Liu, Kai Tang, Tieru Wu
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 274, Nº 1, 2015, págs. 23-34
• Idioma: inglés
• DOI: 10.1016/j.cam.2014.07.001
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• Resumen

  • Several sampling criteria had been proposed for C2 smooth surfaces such that the reconstructed meshes from point samples are homeomorphic to the original surfaces. In this paper, based on a widely used sample criterion, we present proofs that give the upper and lower bounds of mesh quality (in terms of several triangle aspect ratios) for the reconstructed mesh. To make the proposed theoretical bounds useful in practical applications with real-world point data, we propose a novel mesh reconstruction method that works in three steps: (1) approximate Delaunay mesh reconstruction; (2) point data upsampling and (3) hole filling. Finally, examples are presented, which illustrate the effectiveness of the proposed method.