Compression -- Recent Advances in Compression of 3D Meshes -- Shape Compression using Spherical Geometry Images -- Data Structures -- A Survey on Data Structures for Level-of-Detail Models -- An Algorithm for Decomposing Multi-dimensional Non-manifold Objects into Nearly Manifold Components -- Encoding Level-of-Detail Tetrahedral Meshes -- Multi-Scale Geographic Maps -- Modelling -- Constrained Multiresolution Geometric Modelling -- Multi-scale and Adaptive CS-RBFs for Shape Reconstruction from Clouds of Points -- Parameterization -- Surface Parameterization: a Tutorial and Survey -- Variations on Angle Based Flattening -- Subdivision -- Recent Progress in Subdivision: a Survey -- Optimising 3D Triangulations: Improving the Initial Triangulation for the Butterfly Subdivision Scheme -- Simple Computation of the Eigencomponents of a Subdivision Matrix in the Fourier Domain -- Subdivision as a Sequence of Sampled Cp Surfaces -- Reverse Subdivision -- $$\sqrt 5 $$ -subdivision -- Geometrically Controlled 4-Point Interpolatory Schemes -- Thinning -- Adaptive Thinning for Terrain Modelling and Image Compression -- Simplification of Topologically Complex Assemblies -- Topology Preserving Thinning of Vector Fields on Triangular Meshes -- Wavelets -- Periodic and Spline Multiresolution Analysis and the Lifting Scheme -- Nonstationary Sibling Wavelet Frames on Bounded Intervals: the Duality Relation -- Haar Wavelets on Spherical Triangulations.Multiresolution methods in geometric modelling are concerned with the generation, representation, and manipulation of geometric objects at several levels of detail. Applications include fast visualization and rendering as well as coding, compression, and digital transmission of 3D geometric objects. This book marks the culmination of the four-year EU-funded research project, Multiresolution in Geometric Modelling (MINGLE). The book contains seven survey papers, providing a detailed overview of recent advances in the various fields within multiresolution modelling, and sixteen additional research papers. Each of the seven parts of the book starts with a survey paper, followed by the associated research papers in that area. All papers were originally presented at the MINGLE 2003 workshop held at Emmanuel College, Cambridge, UK, 9-11 September 2003.