# Analytic Representation of Three-dimensional Space

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## Abstract

In this chapter we shall discuss an exciting recent development in the representation of objects in three-dimensional space. We take a totally different approach to the definition of a scene: instead of approximating surfaces with a polygonal mesh, we define them as combinations of * primitive objects*. Each primitive object is mathematically defined in terms of an analytic function: we have already introduced this idea in the analytic representation of surfaces in chapter 6. This approach allows a very simple definition of many scenes, but the ease of definition has to be paid for with a large increase in processing overheads, although not necessarily in program complexity. To illustrate these ideas we look at two implementations. The first, the

*(Sidhu and Boute, 1972; Tanimoto, 1977; Hunter and Steiglitz, 1979; Woodwark, 1984), will be used to draw simple*

**quad-tree***composed of a grouping of spheres of arbitrary radius and position. A program, the main program of listing 7.6, which calls the SCENE routine of listing 17.1 is used to illustrate it. Secondly there is the*

**molecular models***method (Clark, 1976; Meagher, 1982): we do not give a program but outline the method and also describe the construction of a binary tree defining a scene as the union, intersection and complement of various primitives. (Such a description can also be used with ray-tracing and the quad-tree method.)*

**oct-tree**## Preview

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