PIMS-CSC Seminar: Numerical Construction of Multiresolutions from Subdivisions

Mesh subdivisions are used frequently to build objects and characters for computer animation, computer games, and industrial computer-aided geometric design. The design process starts with a coarse-mesh model of an object, and the mesh is refined and its geometry is transformed by local affine transformations to produce a highly detailed result. Quite separately, multiresolutions are used frequently to resolve highly detailed information into a simple, base approximation with a cascade of coarser and coarser detail information. This arrangement, also called a wavelet decomposition of the original information, is used to develop compression schemes, finds application in feature detection, and provides for efficient display of geometry at various levels of detail. Subdivisions and Multiresolutions can be built independently, but this talk will explore the construction of multiresolutions from given subdivisions. The process is intended for subdivision schemes whose refinement is local and based upon the tessilation of meshes of any dimension, and it delivers a multiresolution that is also local. The construction uses numerical linear algebra throughout, specifically the singular values decomposition. Examples will be given, results shown, and some musings about data structures will be included. (This is joint work with Faramaz Samavati at the University of Calgary.)