Chapter 4

Representing, Storing and Visualizing 3D Data

William A.P. Smith

Abstract In this chapter, we review methods for storing, modeling and visualizing 3D data. We focus in particular on representations for raw 3D data, surfacebased and solid-based models. We describe and compare the various data structures available for representing triangular meshes and formats for mesh storage. We also provide details on three different subdivision schemes and explain how differential surface properties can be computed from different surface representations. In the context of data compression, we describe in detail the Quadric Error Metric algorithm for mesh simplification. Finally, we suggest areas for future work in this area and provide some concluding remarks.

4.1 Introduction

There is a wide range of 3D acquisition technologies and applications for 3D data. Perhaps not surprisingly, there are an equally wide number of systems for 3D data representation, compression, storage, search, manipulation and visualization. 3D data representations serve as an intermediary between the data acquisition and the application, with constraints imposed from both sides.

In many cases, the method of acquisition dictates a specific native representation format. For example, classical stereo vision recovers disparity and hence depth values at each pixel and so usually is represented as a range image. On the other hand, the target application also imposes constraints on the method of representation. For example, certain operations are more efficient when a particular 3D representation is used. For this reason, it may be necessary to convert between representations, perhaps involving some level of approximation.

Examples of common 3D datasets range from the very small (molecules, microscopic tissue structures, 3D microstructures in materials science), to the human scale (3D human heart, 3D face, 3D body scans) to the large (3D modeling of buildings and landscapes) and beyond (3D modeling of astrophysical data). It is the scale, res-