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

Mueller-Roemer, Johannes Sebastian; Altenhofen, Christian; Sourander, André

doi:10.1111/cgf.13245

Cited by 14 publications

(7 citation statements)

References 30 publications

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“…For example, Mueller‐Roemer et al . [MAS17] use sparse matrices to describe meshes. They encode the sign of a ternary matrix in the column index of CSR matrices.…”

Section: Resultsmentioning

confidence: 99%

Analysis of Schedule and Layout Tuning for Sparse Matrices With Compound Entries on GPUs

Mueller-Roemer

Sourander

Fellner

2020

Computer Graphics Forum

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Large sparse matrices with compound entries, i.e. complex and quaternionic matrices as well as matrices with dense blocks, are a core component of many algorithms in geometry processing, physically based animation and other areas of computer graphics. We generalize several matrix layouts and apply joint schedule and layout autotuning to improve the performance of the sparse matrix‐vector product on massively parallel graphics processing units. Compared to schedule tuning without layout tuning, we achieve speedups of up to 5.5 × . In comparison to cuSPARSE, we achieve speedups of up to 4.7 × .

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“…For example, Mueller‐Roemer et al . [MAS17] use sparse matrices to describe meshes. They encode the sign of a ternary matrix in the column index of CSR matrices.…”

Section: Resultsmentioning

confidence: 99%

Analysis of Schedule and Layout Tuning for Sparse Matrices With Compound Entries on GPUs

Mueller-Roemer

Sourander

Fellner

2020

Computer Graphics Forum

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“…The LAR representation is the basis of recent work that targets mesh processing on the GPU, e.g., Mesh Matrix [Zayer et al 2017] and the ternary sparse matrix representation [Mueller-Roemer et al 2017] for volumetric meshes. Mesh Matrix represents surface meshes by encoding the relation between 2-faces (triangles) and 0-faces (vertices), limiting it to applications that do not require explicit edge representations.…”

Section: Mesh As a Matrixmentioning

confidence: 99%

RXMesh

2021

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We propose a new static high-performance mesh data structure for triangle surface meshes on the GPU. Our data structure is carefully designed for parallel execution while capturing mesh locality and confining data access, as much as possible, within the GPU's fast "shared memory." We achieve this by subdividing the mesh into patches and representing these patches compactly using a matrix-based representation. Our patching technique is decorated with ribbons , thin mesh strips around patches that eliminate the need to communicate between different computation thread blocks, resulting in consistent high throughput. We call our data structure RXMesh : Ribbon-matriX Mesh. We hide the complexity of our data structure behind a flexible but powerful programming model that helps deliver high performance by inducing load balance even in highly irregular input meshes. We show the efficacy of our programming model on common geometry processing applications---mesh smoothing and filtering, geodesic distance, and vertex normal computation. For evaluation, we benchmark our data structure against well-optimized GPU and (single and multi-core) CPU data structures and show significant speedups.

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“…Using matrix algebra for subdivision was attempted before. The effort by Mueller‐Roemer et al [MRAS17] for volumetric subdivision uses boundary operators to boost performance on the GPU. While these differential forms have been used earlier [CRW05], their storage cost and redundancies continue to limit their practical scope.…”

Section: Related Workmentioning

confidence: 99%

Subdivision‐Specialized Linear Algebra Kernels for Static and Dynamic Mesh Connectivity on the GPU

Mlakar

Winter

Stadlbauer

et al. 2020

Computer Graphics Forum

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Subdivision surfaces have become an invaluable asset in production environments. While progress over the last years has allowed the use of graphics hardware to meet performance demands during animation and rendering, high‐performance is limited to immutable mesh connectivity scenarios. Motivated by recent progress in mesh data structures, we show how the complete Catmull‐Clark subdivision scheme can be abstracted in the language of linear algebra. While this high‐level formulation allows for a fully parallel implementation with significant performance gains, the underlying algebraic operations require further specialization for modern parallel hardware. Integrating domain knowledge about the mesh matrix data structure, we replace costly general linear algebra operations like matrix‐matrix multiplication by specialized kernels. By further considering innate properties of Catmull‐Clark subdivision, like the quad‐only structure after refinement, we achieve an additional order of magnitude in performance and significantly reduce memory footprints. Our approach can be adapted seamlessly for different use cases, such as regular subdivision of dynamic meshes, fast evaluation for immutable topology and feature‐adaptive subdivision for efficient rendering of animated models. In this way, patchwork solutions are avoided in favor of a streamlined solution with consistent performance gains throughout the production pipeline. The versatility of the sparse matrix linear algebra abstraction underlying our work is further demonstrated by extension to other schemes such as and Loop subdivision.

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

Cited by 14 publications

References 30 publications

Analysis of Schedule and Layout Tuning for Sparse Matrices With Compound Entries on GPUs

Analysis of Schedule and Layout Tuning for Sparse Matrices With Compound Entries on GPUs

RXMesh

Subdivision‐Specialized Linear Algebra Kernels for Static and Dynamic Mesh Connectivity on the GPU

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