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Part III: Complex Volumetric ObjectsConstructive Representations of Volumetric EnvironmentsMin Chen, John V. Tucker and Adrian LeuAs an important subfield of computer graphics, volume graphics explores a collection of graphics techniques built upon volume data types, and has the potential to match and overtake traditional surfacebased techniques. Constructive Volume Geometry (CVG), a modelling scheme developed recently, enables complex volume objects and scenes to be constructed without involving data resampling that normally leads to quality degeneration. In this chapter, we outline the algebraic framework that supports CVG, the formulation of the CVG concepts from volume data types, and the realisation of CVG operations during rendering. In particular, through the description of a CVGbased system CROVE (Constructive Representations of Volumetric Environments), we present the methods for modelling and rendering CVG objects from a software perspective. vxt: A Class Library for Object VoxelisationMilos Sramek and Arie E. KaufmanWe describe the vxt library for filtered voxelisation of objects, being developed at SUNY Stony Brook. It provides the user with an extensible set of easytouse tools and routines for aliasfree voxelisation of analytically defined monochromatic and colour objects. Thus, resulting volumetric data represent a suitable input for both software and hardware volume rendering systems. The library provides for voxelisation of primitive objects; however, when supplemented by a suitable parser, it represents a basis for voxelisation of complex models defined in various graphics formats. 3D ScanConversion of CSG Models into Distance, ClosestPoint and Colour VolumesDavid E. Breen, Sean Mauch and Ross T. WhitakerThis chapter presents a technique for colourshading offset surfaces of CSG models. The offset surfaces are generated by first scan converting the CSG model into a distance volume. A distance volume is a volume dataset where the value stored at each voxel is the shortest distance to the surface of the object being represented by the volume. Extracting isosurfaces from the distance volume at various offset values produces the offset surfaces. The CSG model scan conversion process also produces closestpoint and colour volumes. The closestpoint volume contains at each voxel the closest point on the scan converted CSG model from that voxel location. The color volume contains at each voxel the associated color on the CSG model at the closest point. During rendering of the offset surface, the colour volume values are used to shade regions of constant colour, and the closest point values are used to supersample the surface colours of the CSG model in order to antialias regions of changing colour. For relevant information, images and animation, please visitNURBS Volume for Modelling Complex ObjectsZhongke Wu, Hock Soon Seah and Feng LinThis chapter proposes a new modelling approach for representation of both natural and artificial objects based on voxelisation of NURBS volume models. A NURBS volume is a continuous model with flexible geometric modelling ability; and a voxelised NURBS volume is a discrete model, which can represent arbitrary structure and interior of inhomogeneous objects. With the combination of NURBS and voxelisation, we are able to model complex objects. 
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