Ternary Sparse Matrix Representation for Volumetric Mesh Subdivision and Processing on GPUs

• Published in: Computer graphics forum Vol. 36; no. 5; pp. 59 - 69
• Main Authors: Mueller‐Roemer, J. S., Altenhofen, C., Stork, A.
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.08.2017
• Subjects: Algorithms; Categories and Subject Descriptors (according to ACM CCS); D.1.3 [Programming Techniques]: Concurrent Programming—Parallel Programming; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and object representations; Matrix representation; Operators; Parallel processing; Smoothing; Sparsity
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.13245

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 3× to 531×, for sufficiently large meshes, while reducing memory consumption by up to 36%.