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Delaunay triangulation and Voronoi diagram are widely used in computer graphics, computational geometry and other fields. Different from the planar case, Delaunay triangulation of a point set on smooth 2-manifolds does not always exist. In this paper we propose a new sampling requirement combining the maximal curvature, injectivity radius and convexity radius to guarantee the existence of Delaunay...
Design using free-form developable surfaces plays an important role in the manufacturing industry. Currently most commercial systems can only support converting free-form surfaces into approximate developable surfaces. Direct design using developable surfaces by interpolating descriptive curves is much desired in industry. In this paper, by enforcing a propagation scheme and observing its nesting...
Construction of intrinsic Delaunay triangulation (iDt for short) on 2-manifolds has attracted considerable attentions recently, due to its theoretical contributions to surface reconstruction. In this paper we analyze a 2-manifold sampling criterion based on iDt in a combinatorial way. The main contribution of this work is to establish the theoretical bounds of iDt mesh quality based on this sampling...
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