Constructive Volume Geometry

We present an algebraic framework, called Constructive Volume Geometry (CVG), for modelling complex spatial objects using combinational operations. By utilising scalar fields as fundamental building blocks, CVG provides high-level algebraic representations of objects that are defined mathematically or built upon sampled or simulated datasets. It models amorphous phenomena as well as solid objects, and describes the interior as well as the exterior of objects. We also describe a hierarchical representation scheme for CVG, and a direct rendering method with a new approach for consistent sampling. The work has demonstrated the feasibility of combining a variety of graphics data types in a coherent modelling scheme.