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Part I: PerspectivesStateoftheArt in Volume GraphicsArie E. KaufmanAn increasing trend in volume graphics focuses on the use of modelling data, that is, the use of discrete voxel representation for a variety of geometrybased applications. These applications include CAD, simulation, and animation, as well as those that intermix geometric objects with 3D sampled or computed datasets. In these applications, the inherently continuous 3D geometric model is discretised employing voxelisation (3D scan conversion) algorithms, which generate a volume buffer (3D raster) of voxels. In order to render these volumetric models and other volumetric data sets in realtime a specialpurpose volume engine, such as Cube4, is imperative. Currently, Mitsubishi Electric and Japan Radio Corp. are fabricating chips and boards using the Cube4 technology. These trends in volume graphics have th potential to revolutionise the field of computer graphics by offering an alternative to the existing surface graphics approach. This chapter provides an overview of volume graphics, the Cube volume rendering engine, and volume graphics applications. For relevant information, images and animation, please visitVolume ModellingGregory M. NielsonThis chapter presents a stateoftheart report on volume modelling research. A volume model is a mathematical means of modelling volume data. Volume data consists of a collection of positions in 3D space with an associated measure of "density" at each location. This can be denoted as (x_{i}, y_{i}, z_{i}: D_{i}), i = 1, ..., N, where the D_{i} is the measured or simulated quantity as position (x_{i}, y_{i}, z_{i}). A volume model is a mathematical function, F(x, y, z) which represents the relationship implied by the volume data. The methods and techniques used to represent the volume model, F(x, y, z), constitute the focus of volume modelling research. To date, there has been considerable research on the development of techniques for visualising volume data, but very little on modelling volume data. This is somewhat surprising since the potential benefits of volume models are tremendous. This situation is somewhat explained by the fact that volume data is relatively new and researchers have spent their efforts in figuring out ways to "look" at the data and have not been able to afford the resources needed to develop methods for modelling volume data. In addition to providing a means for visualising volume data, some of the benefits of a volume model are the generation of hierarchical and multiresolution models which are extremely useful for the efficient analysis, visualisation, transmission, and archiving of volume data. Also, the volume model can serve as the mathematical foundation for subsequent engineering simulations and analysis required for design and fabrication. This chapter surveys some of the recent research in volume modelling with particular emphasis on noisy, redundant, scattered data associated with some of the newer scanning devices. 
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