36-Issue 5

Permanent URI for this collection

https://diglib.eg.org/handle/10.2312/2631654

Browse

Browsing 36-Issue 5 by Subject "Curve"

Now showing 1 - 3 of 3
  • No Thumbnail Available
    Item
    A Constrained Resampling Strategy for Mesh Improvement
    (The Eurographics Association and John Wiley & Sons Ltd., 2017) Abdelkader, Ahmed; Mahmoud, Ahmed H.; Rushdi, Ahmad A.; Mitchell, Scott A.; Owens, John D.; Ebeida, Mohamed S.; Bærentzen, Jakob Andreas and Hildebrandt, Klaus
    In many geometry processing applications, it is required to improve an initial mesh in terms of multiple quality objectives. Despite the availability of several mesh generation algorithms with provable guarantees, such generated meshes may only satisfy a subset of the objectives. The conflicting nature of such objectives makes it challenging to establish similar guarantees for each combination, e.g., angle bounds and vertex count. In this paper, we describe a versatile strategy for mesh improvement by interpreting quality objectives as spatial constraints on resampling and develop a toolbox of local operators to improve the mesh while preserving desirable properties. Our strategy judiciously combines smoothing and transformation techniques allowing increased flexibility to practically achieve multiple objectives simultaneously. We apply our strategy to both planar and surface meshes demonstrating how to simplify Delaunay meshes while preserving element quality, eliminate all obtuse angles in a complex mesh, and maximize the shortest edge length in a Voronoi tessellation far better than the state-of-the-art.
  • No Thumbnail Available
    Item
    Fast and Memory-Efficient Voronoi Diagram Construction on Triangle Meshes
    (The Eurographics Association and John Wiley & Sons Ltd., 2017) Qin, Yipeng; Yu, Hongchuan; Zhang, Jiangjun; Bærentzen, Jakob Andreas and Hildebrandt, Klaus
    Geodesic based Voronoi diagrams play an important role in many applications of computer graphics. Constructing such Voronoi diagrams usually resorts to exact geodesics. However, exact geodesic computation always consumes lots of time and memory, which has become the bottleneck of constructing geodesic based Voronoi diagrams. In this paper, we propose the window-VTP algorithm, which can effectively reduce redundant computation and save memory. As a result, constructing Voronoi diagrams using the proposed window-VTP algorithm runs 3-8 times faster than Liu et al.'s method [LCT11], 1.2 times faster than its FWP-MMP variant and more importantly uses 10-70 times less memory than both of them.
  • No Thumbnail Available
    Item
    Ternary Sparse Matrix Representation for Volumetric Mesh Subdivision and Processing on GPUs
    (The Eurographics Association and John Wiley & Sons Ltd., 2017) Mueller-Roemer, Johannes Sebastian; Altenhofen, Christian; Stork, André; Bærentzen, Jakob Andreas and Hildebrandt, Klaus
    In this paper, we present a novel volumetric mesh representation suited for parallel computing on modern GPU architectures. The data structure is based on a compact, ternary sparse matrix storage of boundary operators. Boundary operators correspond to the first-order top-down relations of k-faces to their (k-1)-face facets. The compact, ternary matrix storage format is based on compressed sparse row matrices with signed indices and allows for efficient parallel computation of indirect and bottomup relations. This representation is then used in the implementation of several parallel volumetric mesh algorithms including Laplacian smoothing and volumetric Catmull-Clark subdivision. We compare these algorithms with their counterparts based on OpenVolumeMesh and achieve speedups from 3x to 531x, for sufficiently large meshes, while reducing memory consumption by up to 36%.