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- Chunxu Xu, Tuanfeng Y. Wang, Yong-Jin Liu, Ligang Liu, Ying He
- IEEE Transactions on Visualization and Computer…
- 2015

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)

- Yong-Jin Liu, Chunxu Xu, Dian Fan, Ying He
- ACM Trans. Graph.
- 2015

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)

- Chunxu Xu, Yong-Jin Liu, Qian Sun, Jinyan Li, Ying He
- Comput. Graph. Forum
- 2014

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)

- Yong-Jin Liu, Chunxu Xu, Ying He, Deok-Soo Kim
- CCCG
- 2014

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)

- Yong-Jin Liu, Chunxu Xu, Ran Yi, Dian Fan, Ying He
- ACM Trans. Graph.
- 2016

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)

- Yong-Jin Liu, Dian Fan, Chunxu Xu, Ying He
- ACM Trans. Graph.
- 2017

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)

- Chunxu Xu, Yong-Jin Liu, Qian Sun, Jinyan Li, Ying He
- SGP Posters
- 2014

- Yong-Jin Liu, Dian Fan, Chunxu Xu, Ying He
- Inf. Process. Lett.
- 2017

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