Hierarchical Decomposition of Datasets on Irregular Surface Meshes

In this paper we introduce multiresolution analysis (MRA) algorithmsintendedto be used in scientific visualization,and basedon a non-nestedset ofapproximatingspaces. The need for non nested spaces arises from the fact that the required scaling functionsdo not fulfillany refinement equation. Therefore we introduce in the first part the concept of approximated refinement equation, that allows to generalize the filter bank and exact reconstruction algorithms. The second partshows howthis concept enables to define a MRA scheme for piecewise constant data defined on an arbitrary planaror spherical triangularmesh. The abilityto deal with arbitrary triangularmeshes, withoutsubdivision connectivity, can be achieved only through the use of non nested approximating spaces, as introduced in the first part.

• Type: Conference
• Year: 1998
• Where: CGI
• Authors: Georges-Pierre Bonneau, Alexandre Gerussi
• Keywords: CGI 1998, Computer Graphics, Fulfillany Refinement Equation, Non Nested Spaces, Refinement Equation