ABSTRACT
To render a scene, we need a mathematical description of the geometry in that scene. Several different methods are available to us. This entry focuses on the one most important for real-time rendering: the triangle mesh. But first, let us mention a few alternatives to get some context. Constructive solid geometry (CSG) is a system for describing an object’s shape using Boolean operators (union, intersection, subtraction) on primitives. Within video games, CSG can be especially useful for rapid prototyping tools, with the Unreal engine being a notable example. Another technique that works by modeling volumes rather than their surfaces is metaballs, sometimes used to model organic shapes and fluids. CSG, metaballs, and other volumetric descriptions are very useful in particular realms, but for rendering (especially real-time rendering), we are interested in a description of the surface of the object, and seldom need to determine whether a given point is inside or outside this surface. Indeed, the surface need not be closed or even define a coherent volume.
