Technical SectionMultiresolution modeling of arbitrary polygonal surfaces: a characterization
Introduction
Technological advances have provided extensive data bases of highly detailed objects. For example, the acquisition of data via satellite, laser scanners or medical image devices are methods that, thanks to their high precision, allow for the creation of large three-dimensional (3D) data sets. In turn, there are many applications that take advantage of the availability of this type of objects. Fields such as cartography, computer-aided design, computer graphics, computer vision, analysis of finite elements and scientific visualization, apply them to terrain representation, virtual reality, flight simulators, analysis of structures, etc. Normally, these objects are represented by means of polygonal surfaces [1]. Nowadays, this type of representation is the most frequently used in the field of interactive computer graphics. This is due to various reasons such as the high availability of polygonal surface data, the fact that they are used by most visualization software, and that graphic systems accelerate the visualization of polygons. However, the costs of visualization, storage or transmission of these surfaces increase considerably when they are formed by tens of millions of polygons.
Multiresolution modeling [2] has been successfully presented as a solution to the problem of efficient manipulation of highly detailed polygonal surfaces. It consists of representing an object by means of multiple approximations or levels of detail (LoDs) where each approximation or LoD represents the original object using a different number of polygons (see Fig. 1). The development of the multiresolution modeling was probably stimulated in the main by the need to achieve the interactive visualization of these objects. Of course, other techniques such as occlusion culling or image-based rendering have been proposed as satisfactory solutions to this problem. However, other applications of multiresolution modeling have gained equal importance as this one and have notably contributed to its development. We specifically refer to the progressive transmission of 3D data sets through a communication line and to the storage in a compressed form.
In this paper, we present a characterization of multiresolution schemes. In general, the idea of multiresolution modeling is not new. The first studies appeared 20 years ago [3] and they were mainly applied to terrain meshes in flight simulators. However, multiresolution modeling of arbitrary polygonal surfaces is relatively recent and this is the focal point of this study. Multiresolution schemes presented in the literature are diverse and the aim of this paper is to bring together the most interesting ones and, by means of a series of characteristics commonly used in multiresolution modeling, to make the existing similarities and differences between them visible in a simple way. These characteristics are classified into three groups:
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Input data: They refer to the input data of a multiresolution scheme, such as the type of polygonal surface that it can manage.
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Application: They refer to the suitability of a multiresolution scheme for application to interactive visualization, progressive transmission or geometry compression.
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Operation: They refer to the internal operation of the multiresolution scheme, such as the way data is stored or retrieved, and they inform on special functionalities.
Some valuable studies on multiresolution modeling have been presented in the literature. Puppo and Scopigno [4] present a study beginning with the origins of multiresolution modeling that includes geometry simplification, multiresolution modeling and even commercial applications. Garland [5] presents a review of multiresolution modeling taking the initial problem—the simplification of polygonal surfaces—as a starting point, and finally presenting a classification and explanation of several basic multiresolution representation schemes. Although both studies are very thorough, they do not show the differences between multiresolution schemes, which is the aim of this paper.
Section snippets
Multiresolution modeling
Multiresolution modeling consists of representing an object by means of a set of approximations of several levels of detail and allows any of them to be recovered on demand. The first multiresolution schemes managed a relatively small number of LoDs [6] (normally, between 5 and 10) and they were developed with the main objective of accelerating the visualization of the scene. Later, multiresolution schemes that manage a continuous range of approximations appeared. They allow the level of detail
Discrete multiresolution modeling
The simplest way to create a multiresolution representation is to generate a set of independent approximations where each one represents the original object with a different level of detail. If we can obtain these approximations, we have a discrete multiresolution representation. This technique began to be used with the main aim of increasing the performance of the graphic system and this was accomplished in applications such as walkthroughs in virtual environments as proposed by Funkhouser and
Continuous multiresolution modeling
Continuous multiresolution modeling has come about to solve the problems presented by discrete multiresolution modeling. A continuous multiresolution representation provides a wide range (virtually a continuous range [4]) of different approximations that represent the original object. The iterative application of a simplification method, starting from the original data set, M0, produces a sequence of approximations M1,M2,…,Mn−1, where Mn−1 is the approximation with the least detail. A
Characterization
Characterization has been carried out for the multiresolution schemes for arbitrary polygonal surfaces shown in Table 1. The criteria used in this characterization are classified depending on whether they refer to the applications, to the input data or to the internal operation.
Conclusions
Multiresolution modeling for arbitrary poligonal surface meshes has been developed very rapidly during the last 6 years with the aim of efficiently managing highly detailed objects. Each multiresolution scheme presented in the literature has a set of characteristics that make it different from the others. In this paper, we summarize the characteristics commonly used to define the multiresolution schemes and we classify them depending on whether they refer to the applications, to the input data
Acknowledgements
This research work has been supported by grants TIC1999-0510-C02-02 and TIC2000-1131 (CICYT, Ministerio de Educación y Ciencia, Spain). We would like to thank Michael Garland for making his code available for us; Cyberware, Inc. and the Standford Computer Graphics Laboratory for providing the 3D data sets; and the reviewers for their insightful comments which led to several improvements in the presentation of this paper.
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