Is there a way to draw spherical objects without triangles? It seems that in all existing graphics libraries, 3D objects are always described in terms of triangles. Drawing triangles can be implemented very efficiently on video hardware and since any 3D object can be approximated with triangles, triangles are the only basic element needed. Triangles can be represented by 3-tuples and are simple to work with.

I have always wondered whether other approaches have been tried. There are certain complications when approximating spherical objects with triangles. Have there been any alternative approaches to drawing spherical objects (for example, without using polygons for approximations)? What are the problems with such approaches that make using triangles the best option?
A standard technique is to use a ray/sphere intersection test inside a pixel shader. One draws a billboard large enough cover the area the sphere could appear on the screen (or drawing a bounding cube) to reduce the number of wasted intersection tests (other geometric shapes could be used). The fragment is killed if the intersection test fails; if an intersection occurs, the appropriate depth value is calculated in the pixel shader and output for further visibility tests.