Graphics: Visual and Interactive Computing
Constructive Volume Geometry
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Constructive solid geometry (CSG) is one of the most important modeling methods in computer graphics and computer aided design (CAD). It allows complicated objects to be built as various ordered "union", "intersection" and "difference" of simpler objects, which may be bounded primitives or half-spaces. It is supported by the Boolean algebra and a set of well-understood regularized set operations. Constructive volume geometry (CVG) is a major generalization of CSG. Unlike CSG, CVG does not limit itself to geometrical operations only, and it can also be employed to manipulate physical properties that are associated with objects. Its combinational operations, mostly defined in the real domain, can be used to model complex interior structures of objects and amorphous phenomena in a constructive manner. In CVG, combinational operators are defined upon unbounded spatial objects, and are constructed from simple arithmetic operations on scalars through a series of operational decomposition. The operations on scalars are normally defined in the real domain. The basic CVG operators include union, intersection, difference, and blending. With the flexibility and accuracy of the real domain, complex operators, such as those for data filtering and volume deformation, can easily be specified. A spatial object can be specified as a set of scalar fields, F1(p), F2(p), ..., Fk(p), that define the geometrical and physical properties of the object at every point p in three-dimensional space. Scalar fields are typically defined by using mathematical, discrete (e.g. volume datasets) and procedural specifications. Considering different applications may define spatial objects with different attributes. CVG utilizes an algebraic concept called signature to describe the algebraic structure of a particular graphics model in a consistent manner. Although conceptually it is not necessary, CVG also allows the specification of additional geometry fields to suit the needs of some applications. In comparison with CSG, CVG offers a comprehensive algebraic framework for a variety of volume graphics models. In fact, it has been shown that the CSG model based on union, intersection and difference '-' is embedded in a simple CVG model, that is, the Boolean opacity only model based on the corresponding volume operations. CVG operates on the interior as well as the exterior of objects, and therefore preserves the main geometrical properties in volumetric datasets such as volume density and multiple iso-surfaces. Physical properties such as colours are defined and manipulated in the same way as geometry. It accommodates objects that are defined mathematically by scalar fields as well as those built from digitized volumetric datasets. Images and videos can be naturally integrated into a scene as a volumetric object. Scenes specified in CVG can be rendered directly by a sophisticated volume rendering engine, or may be voxelized into volume buffers as the input to general-purpose volume rendering systems. One of the main obstacles in the development of volume-based applications has been the size of volume datasets -- important building blocks of many spatial objects. However, the problem is becoming alleviative due to the rapid reduction in the costs of computer hardware. This very much reminds us an old scenario in image space where the development of raster graphics superseded that of vector graphics. It is now feasible to model and render a complex graphics scene composed of multiple volume datasets, for which TROVE is one of the first such modelling schemes. TROVE introduces several of new concepts for volume-based modelling, including channels and transformations between three coordinate systems, WC, NVC and VC. TROVE is also supported by a rendering engine based ray casting. Further developments have been made in multi-volume modelling and rendering to incorporate CVG objects into the scene. In particular, a new volume graphics library, vlib, will provides programmers with a powerful tool for developing advanced volume graphics and volume visualisation applications.Main References
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