Why are simple shapes like spheres built using polygons? I was wondering what is the reason to implement shapes like spheres with triangles instead of a mathematical equation? This could allow perfectly round spheres and not kind of spherical with some levels of subdivision surface. Not to mention the significant boost in rendering time.
Creating an "equation" for rendering non-simple objects, such as a tank model, for instance, is much more difficult, especially when it comes to ray-tracing and shading. While for instance a sphere from an equation would be very simple, a sphere next to a complex object would be difficult, and its better to build complicated meshes out of polygons. The reason you can't have math-based meshes next to polygon-based meshes together is because they use different ways of rendering, as well as to keep everything consistent. This is my understanding of it, anyways, and people can correct me if I am mistaken.