Parallel mesh simplification using embedded tree collapsing

We present a novel parallel algorithm for mesh simplification that can reduce an input triangle mesh with highly improved performance. To take full advantage of the GPU comprising many computing cores, we enable collapsing of connected edges to be processed at one time by breaking data dependency in the update of the mesh data structure. Our solution is a lazy update method, which temporarily stores edge update information in a table and then updates the mesh data with it in the next step. Thanks to the lazy update method, we can more freely choose a large number of edges in the form of small trees for collapsing. The constructed trees are split to satisfy an error constraint, prevent normal flipping, and preserve the mesh topology. In experiments performed on several test models of various scales, we found that our algorithm consistently outperformed the prior GPU algorithm of Papageorgiou and Platis (Vis Comput 31(2):235–244, 2015 ) by a factor of 10 or higher.