3D object class.

[ThomasJohnsen]

The reason for dividing 3D objects into triangles (or similar) is to make the calculations simple even for very complex objects.

Using equations to generate objects is implementable, and is commonly used for quadrics. But the second you need more complex objects (ie. objects that may intersect any given line more than twice), you're moving into areas, where you have to solve n-degree polynomials, in order to generate effect such as light/shadow etc.
Consider for instance an ellipsoid. It is easy to generate by the common equation. Now if we were to bend this ellipsoid, our equation would suddenly become extremely complex. Whereas bending an object consisting of triangles would be easy to implement.
Add to this gravity, lightmaps, transparency, materials etc., and you get something impossible to generate using formulae.

But very interesting results within the field of ray-tracing have been constructed using nothing more than quadrics and boolean operations upon them. Also chemical models use mainly spheres and cylinders to illustrate structures. But as a general application, using formulae to generate objects isn't feasible IMO.

Tom


#EDIT: There are also models called spatial-occupancy in which objects are divide into socalled voxels (similar to a picture and pixels). They are not used as much today - probably mainly in fields of weather-studies and similar. Most applications, I know of use triangle representations.