A Halfedge Refinement Rule for Parallel Catmull‐Clark Subdivision

We show that Catmull‐Clark subdivision induces an invariant one‐to‐four refinement rule for halfedges that reduces to simple algebraic expressions. This has two important consequences. First, it allows to refine the halfedges of the input mesh, which completely describe its topology, concurrently in...

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Bibliographic Details
Published in:Computer graphics forum Vol. 40; no. 8; pp. 57 - 70
Main Authors: Dupuy, J., Vanhoey, K.
Format: Journal Article
Language:English
Published: Oxford Blackwell Publishing Ltd 01.12.2021
Subjects:
Apexes
CCS Concepts
Computing methodologies → Massively parallel algorithms
Rendering
Topology
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary:We show that Catmull‐Clark subdivision induces an invariant one‐to‐four refinement rule for halfedges that reduces to simple algebraic expressions. This has two important consequences. First, it allows to refine the halfedges of the input mesh, which completely describe its topology, concurrently in breadth‐first order. Second, it makes the computation of the vertex points straightforward as the halfedges provide all the information that is needed. We leverage these results to derive a novel parallel implementation of Catmull‐Clark subdivision suitable for the GPU. Our implementation supports non‐quad faces, extraordinary vertices, boundaries and semi‐sharp creases seamlessly. Moreover, we show that its speed scales linearly with the number of processors, and yields state‐of‐the‐art performances on modern GPUs.
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.14381