A Halfedge Refinement Rule for Parallel Catmull‐Clark Subdivision

Abstract

We derive a halfedge refinement rule for Catmull-Clark subdivision. The rule is illustrated on the left: Catmull-Clark subdivision splits each halfedge into exactly 4 new ones independently from the face within which the subdivision operates (see highlighted halfedges). We leverage this rule in a novel GPU implementation that runs at state-of-the-art performances. For instance, the control mesh of this illustrated T-Rex production model consists of ∼11.5k faces and vertices. We compute its subdivision down to level 4, which produces ∼2.9M faces and vertices, in less than three milliseconds on an NVIDIA RTX 2080 GPU.

Feature‐Adaptive and Hierarchical Subdivision Gradient Meshes

“…Our implementation recomputes the meshes and fully updates the graphics buffers after each edit, whereas a better alternative would update these structures only locally. The shaders could be optimised using for example table‐driven approaches or the recent half‐edge approach of Dupuy and Vanhoey [DV21]. Computationally demanding functionality like subdivision may significantly benefit from multicore processing.…”

Edge‐Friend: Fast and Deterministic Catmull‐Clark Subdivision Surfaces

“…Subdivision requires neighbor information through suitable data structures. Existing ones suffer from a large memory foot‐print [PEO09, MWS*20, DV21]. We propose a more light‐weight data structure that allows to quickly access neighbor information.…”

“…An atomic‐operation free gathering approach. Implementations using atomic floating‐point operations [PEO09, MWS*20, DV21] come with a performance penalty and require vendor‐ and API‐specific extensions. Moreover, the non‐deterministic scheduling of atomic operations changes their order on a frame‐by‐frame basis.…”

“…A single synchronization barrier. Many existing GPU approaches [PEO09, MWS*20, DV21] need multiple dependent compute‐kernel dispatches with expensive barrier synchronizations for a single subdivision step. We require only a single dispatch, and thus a single synchronization barrier per subdivision iteration, which provides additional performance benefits.…”

“…However, our approach possesses the following limitations : Surface evaluation with hardware tessellation [NLMD12, Pix22] remains faster, but requires substantially more pre‐processing than our method. We obtain conformal, crack‐free meshes with uniform subdivision; however, like other methods [MWS*20, DV21], we do not handle crack‐free adaptive subdivision.…”