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Ternary sparse matrix representation for volumetric mesh subdivision and processing on GPUs

: Mueller-Roemer, Johannes; Altenhofen, Christian; Stork, André

Volltext urn:nbn:de:0011-n-4591194 (4.6 MByte PDF)
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This is the accepted version of the following article: Mueller‐Roemer, J. S., C. Altenhofen, and A. Stork. "Ternary Sparse Matrix Representation for Volumetric Mesh Subdivision and Processing on GPUs." Computer Graphics Forum 36, no. 5 (2017): 59-69, which has been published in final form at This article may be used for non-commercial purposes in accordance with the Wiley Self-Archiving Policy []
Erstellt am: 18.8.2018

Computer graphics forum 36 (2017), Nr.5, S.59-69
ISSN: 0167-7055
ISSN: 1467-8659
Symposium on Geometry Processing (SGP) <15, 2017, London>
European Commission EC
Horizon 2020-H2020-FoF-2015; 680448; CAxMan
Zeitschriftenaufsatz, Konferenzbeitrag, Elektronische Publikation
Fraunhofer IGD ()
concurrent programming; parallel programming; computational geometry; object modeling; object representation; Guiding Theme: Digitized Work; Research Area: Computer graphics (CG); Research Area: (Interactive) simulation (SIM); Research Area: Modeling (MOD)

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 bottom-up 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%.