Multi-resolution techniques and models have been shown to be effective for the display and transmission of large static geometric object. Dynamic environments with internally deforming objects pose similar challenges in terms of time and space and need the development of similar solutions. We present the T-DAG, an adaptive multi-resolution representation for dynamic meshes with arbitrary deformations including attribute, position, connectivity and topology changes. We also provide an on-line algorithm for constructing the T-DAG, enabling the traversal and use of the multi-resolution model for partial playback while still constructing it.

Contents 1 Introduction 2 2 Map Data Modeling 4 2.1 Two-Dimensional Spatial Entities and Relationships . . . . . . . . . . . . . . . . . . . . . 4 2.2 Raster and Vector Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Subdivisions as Cell Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4 Topological Data Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 Multiresolution Data Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3 Map data processing 8 3.1 Spatial Queries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Map Overlay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 Geometric Problems in Map Generalization . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.4 Map Labeling . . . . . . . . . . . . . . . . . . . . . . . . . . .

This thesis examines two largely unrelated problems in applied algorithmics, motivated by the search for efficient geometric algorithms. In the first part of the thesis, we consider the problem of finding efficient parallel algorithms for heterogeneous parallel computers, i.e., parallel computers in which different processors have different computational potential. To this end, we define a formal computational model for heterogeneous systems and develop algorithms for commonly used communication operations. The result is that many existing parallel algorithms which use these communication operations can be adapted to our model with little or no modifications. In the second part of the thesis we consider the problem of geometric models which allow for varying levels of detail. To this end, we extend the progressive mesh representation introduced by Hoppe. The main technical contribution of this part is an efficient scheme for refining only selected regions of a progressive mesh. Using ...

Selective refinement is an operation acting on multiresolution surface models, aimed to provide a mesh approximation with a resolution variable over the surface. We address some efficiency issues related to selective refinement, and we present some results on data structures and algorithms that work on a multiresolution triangle-based model, called a MultiTriangulation.

We introduce a multiresolution representation scheme for variable levels of detail of molecular shapes (shapes synthesized as sets of balls). In particular, we consider in our model the exact boundary computation of the the basic union of balls for CPK model and solvent accessible surface as well as the more complex rolling ball solvent contact surface and molecular skin. Our decimation /refinement scheme supports the creation of a hierarchical structure which provides the flexibility to trade run-time traversal speed for storage size and adaptiveness. In our approach we also track the topology of the molecular body at any adaptive level of resolution. Moreover we are able to guarantee a consistent embedding (no self intersections) of any decimated molecular surfaces. The fast traversal version of our data-structure is a classical hierarchy that stores an explicit representation of all the triangles at all levels of resolution and a DAG of dependencies between them. The more adaptive ...

The paper deals with the problem of modeling large-size terrain data sets. To this aim, we consider multi-resolution models based on triangle meshes. We analyze and compare two multi-resolution terrain models based on regular and irregular meshes. The two models are viewed as instances of a common multi-resolution model, that we call a multiresolution triangle mesh. Our comparison takes into account the space requirements of the data structures implementing the two models as well their e#ectiveness in supporting the extraction of variable-resolution terrain representations.

. This paper introduces a dimension-independent multiresolution model of a shape, called the Multi-Complex (MC), which is based on decomposition into cells. An MC describes a shape as an initial cell complex approximating it, plus a collection of generic modification patterns to such complex arranged according to a partial order. The partial order is essential to extract variable-resolution shape descriptions in real time. We show how existing multiresolution models reduce to special cases of MCs characterized by specific modification patterns. The MC acts as a unifying framework that is also useful for comparing and evaluating the expressive power of different approaches. 1 Introduction Multiresolution geometric models support representation and processing of spatial entities at different levels of detail. Such representations have gained recently much of attention in the literature because of their potential impact on applications, such as terrain modeling in geographic information ...