| Abstract | Multiresolution meshes are a common basis for building representationsof a geometric shape at different levels of detail. The use of the term multiresolu-
tion depends on the remark that the accuracy (or, level of detail) of a mesh in
approximating a shape is related to the mesh resolution, i.e., to the density (size
and number) of its cells. A multiresolution mesh provides several alternative mesh-
based approximations of a spatial object (e.g., a surface describing the boundary
of a solid object, or the graph of a scalar field).
A multiresolution mesh is a collection of mesh fragments, describing usually
small portions of a spatial object with different accuracies, plus suitable relations
that allow selecting a subset of fragments (according to user-defined accuracy crite-
ria), and combining them into a mesh covering the whole object, or an object part.
Existing multiresolution models differ in the type of mesh fragments they consider
and in the way they define relations among such fragments.
In this chapter, we introduce a framework for multiresolution meshes in order
to analyze and compare existing models proposed in the literature on a common
basis. We have identified two sets of basic queries on a multiresolution meshes, that
we call selective refinement and spatial selection. We describe two approaches for
answering such queries, and discuss the primitives involved in them, which must be
efficiently supported by any data structure implementing a multiresolution mesh.
We then describe and analyze data structures proposed in the literature for encoding
multiresolution meshes.
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