Computational Geometry 14 (1999) 1–3 Editorial Multi-Resolution Modeling and 3D Geometry Compression André Guéziec, Gabriel Taubin This special issue addresses some of the problems involved in manipulating multi-resolution three-dimensional polygonal models and sharing and delivering polygonal models across networked environments. Techniques for compressing meshes of arbitrary connectivity and topology and for developing multi- resolution representations have matured considerably in recent years, justifying their inclusion in international standards such as MPEG-4, as well as in commercial software and hardware. The papers presented here illustrate some of the most recent approaches and results, and show how multi-resolution modeling and compression are intimately related. Three-dimensional (3D) computer graphics exert a powerful attraction, that has revolutionized the computer gaming industry. Until recently, 3D graphics have met limited success on the Internet, partly because bandwith limitations have impeded the transmission of three-dimensional models. Exploiting the results presented here, or equivalent 3D compression and progressive transmission technologies, 3D graphics may play a more important role in the future of the Internet. 1. Contents of the issue The first four papers center on methods for generating and editing multi-resolution mesh representa- tions, while the last four papers focus on mesh compression issues. Kobbelt et al. develop a framework for multi-resolution modeling exploiting general edge collapse operations, generalizing previous work using subdivision-surface hierarchies. Gioia extends methods for applying wavelet techniques to arbitrary surfaces by introducing a new mesh partitioning technique that allows to define a higher quality base mesh. Mesh simplification techniques have been used to generate multi-resolution models. Heckbert and Garland study the theoretical behavior of their mesh simplification method and provide results on triangle aspect ratios. Gopi and Manocha address the issue of simplifying curved surface meshes consisting of triangular Bezier patches. Their approach may also be used for representing polygonal models using triangular Bezier patches. King and Rossignac’s paper studies the appropriate combination between mesh simplification and vertex quantization level when encoding a shape. It is thus an appropriate transition paper between 0925-7721/99/$ – see front matter  1999 Published by Elsevier Science B.V. All rights reserved. PII:S0925-7721(99)00033-4