Floriani, L. DeHui, A.Gershon Elber and Nicholas Patrikalakis and Pere Brunet2016-02-172016-02-1720043-905673-55-X1811-7783https://doi.org/10.2312/sm.20041387We address the problem of updating non-manifold mixed-dimensional objects, described by three-dimensional simplicial complexes embedded in 3D Euclidean space. We consider two local update operations, edge collapse and vertex split, which are the most common operations performed for simplifying a simplicial complex. We examine the effect of such operations on a 3D simplicial complex, and we describe algorithms for edge collapse and vertex split on a compact representation of a 3D simplicial complex, that we call the Non-Manifold Indexed data structure with Adjacencies (NMIA). We also discuss how to encode the information needed for performing a vertex split and an edge collapse on a 3D simplicial complex. The encoding of such information together with the algorithms for updating the NMIA data structure form the basis for de ning progressive as well as multi-resolution representations for objects described by 3D simplicial complexes and for extracting variable-resolution object descriptions.I.3.5 [Computer Graphics]Computational Geometry and Object ModelingCurvesurfacesolid and object representations10.2312/sm.20041387169-180