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Computing geodesic distances on triangle meshes is a fundamental problem in computational geometry and computer graphics. To date, two notable classes of algorithms, the Mitchell-Mount-Papadimitriou (MMP) algorithm and the Chen-Han (CH) algorithm, have been proposed. Although these algorithms can compute exact geodesic distances if numerical computation is(More)
Delaunay meshes (DM) are a special type of triangle mesh where the local Delaunay condition holds everywhere. We present an efficient algorithm to convert an arbitrary manifold triangle mesh <i>M</i> into a Delaunay mesh. We show that the constructed DM has <i>O</i>(<i>Kn</i>) vertices, where <i>n</i> is the number of vertices in <i>M</i> and <i>K</i> is a(More)
This paper studies the Voronoi diagrams on 2-manifold meshes based on geodesic metric (a.k.a. geodesic Voronoi diagrams or GVDs), which have polyline generators. We show that our general setting leads to situations more complicated than conventional 2D Euclidean Voronoi diagrams as well as point-source based GVDs, since a typical bisector contains line(More)
An intrinsic discrete Laplace-Beltrami operator on simplicial surfaces S proposed in [2] was established via an intrinsic Delaunay tessellation on S. Up to now, this intrinsic Delaunay tessellations can only be computed by an edge flipping algorithm without any provable complexity analysis. In the paper, we show that the intrinsic Delaunay triangulation can(More)
Computing centroidal Voronoi tessellations (CVT) has many applications in computer graphics. The existing methods, such as the Lloyd algorithm and the quasi-Newton solver, are efficient and easy to implement; however, they compute only the local optimal solutions due to the highly non-linear nature of the CVT energy. This paper presents a novel method,(More)
Intrinsic Delaunay triangulation (IDT) naturally generalizes Delaunay triangulation from R<sup>2</sup> to curved surfaces. Due to many favorable properties, the IDT whose vertex set includes all mesh vertices is of particular interest in polygonal mesh processing. To date, the only way for constructing such IDT is the edge-flipping algorithm, which(More)
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