1 Overview (Part 1) Background notions A reference framework for multiresolution meshes Classification of multiresolution meshes An introduction to LOD queries

2 Level-Of-Detail Queries on a Multiresolution Mesh Extract from a multiresolution model a mesh satisfying some application-dependent requirement based on LOD Selective refinement queries: Result: a mesh covering the whole spatial object Multiresolution mesh as a virtual simplification tool Spatial selection queries: Result: a mesh describing the portion of the object which interferes in space with a given query entity Multiresolution mesh as a spatial index

3 Examples of Selective Refinement uniform high resolution uniform low resolution high resolution just in the legs high resolution just in the head

4 Examples of Spatial Selection Some meshes describing details of the bunny

5 Level-Of-Detail LOD criterion  : Boolean function defined over the n-cells of a multiresolution mesh  (  ) =True if  satisfies the LOD requirements A mesh satisfies a given LOD criterion  iff  (  )= True for all n-cells  of  An approximation error is usually associated with the n- cells of a multiresolution mesh: distance, according to some norm, with respect to a reference surface or hypersurface

6 Examples of LOD Criteria Uniform LOD: –  (  )= True if the error associated with  is less or equal to a constant threshold  Variable LOD: –  (  )= True if the error associated with  is less or equal to the maximum over  of a threshold function  defined at each point of the domain (e.g., a view-dependent function) Special case of variable LOD for scalar fields: –the threshold function  depends on the value of the field at each point of the domain (e.g,  (p) small at a set of interesting field values, large otherwise)

7 Examples of LOD Criteria on a Terrain Variable LOD on the field range (top of the mountain) Uniform LODs Variable LOD on the domain (lower left angle)

8 Selective Refinement Query Given a multiresolution mesh M and a LOD criterion  extract from M the mesh of minimum size  S satisfying 

9 Spatial Selection Query Given a multiresolution mesh M, a Region Of Interest (ROI) R in space, and a LOD criterion , extract from M a mesh  of minimum size such that –  satisfies  –  covers the part of the domain of M that interferes with R Examples of ROIs: –An n-dimensional axis-aligned box: window query –An n-dimensional ball: range query

10 Examples of ROIs Window and range queries at different resolutions on a terrain