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Overview (Part 1)

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- Background notions
- A reference framework for multiresolution meshes
- Classification of multiresolution meshes
- An introduction to LOD queries

- 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

uniform high resolution

uniform low resolution

high resolution just in the legs

high resolution just in the head

Some meshes describing details of the bunny

- LOD criteriont: Boolean function defined over the n-cells of a multiresolution mesh
- t(g) =True if g satisfies the LOD requirements

- A mesh satisfies a given LOD criteriont iff t(g)= True for all n-cells g of G
- 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

- Uniform LOD:
- t(g)= True if the error associated with g is less or equal to a constant threshold e

- Variable LOD:
- t(g)= True if the error associated with g is less or equal to the maximum over g of a threshold function f defined at each point of the domain (e.g., a view-dependent function)

- Special case of variable LOD for scalar fields:
- the threshold function f depends on the value of the field at each point of the domain (e.g, f(p) small at a set of interesting field values, large otherwise)

Uniform LODs

Variable LOD on the field range (top of the mountain)

Variable LOD on the domain (lower left angle)

Given a multiresolution mesh M and a LOD criterion t

- extract from M the mesh of minimum size GS satisfying t

- Given a multiresolution mesh M, a Region Of Interest (ROI) R in space, and a LOD criterion t, extract from M a mesh G of minimum size such that
- G satisfies t
- G 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

Window and range queries at different resolutions on a terrain