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Presentation Transcript

Overview (Part 1)

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

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

Examples of Selective Refinement

uniform high resolution

uniform low resolution

high resolution just in the legs

high resolution just in the head

Examples of Spatial Selection

Some meshes describing details of the bunny

Level-Of-Detail

- 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

Examples of LOD Criteria

- 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)

Examples of LOD Criteria on a Terrain

Uniform LODs

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

Variable LOD on the domain (lower left angle)

Selective Refinement Query

Given a multiresolution mesh M and a LOD criterion t

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

Spatial Selection Query

- 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

Examples of ROIs

Window and range queries at different resolutions on a terrain

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