This is an interesting idea. Before reading the reply i was thinking of how 2D went from bitmap to vector. And how 3D similarly went into NURB and B-spline.

Quote - With this type of program (K3DSurf itself, or something like POV-Ray) you can work with the numbers and their mathematical relationships primarily, with the resulting visualization coming in second

My first 3D Modeling software I learned is ProEngineer, an advanced AutoCAD specialized for Mechanical Engineering. There is not a single trace of vertex, polygon, or mesh. Everything is modeled from precise numerical data (like 2-5/16" or 5.1089"). At the base, you usualy start from a Sketch, which itself is a 2D vector drawing with precise data. As you said, not limited by mesh resolution, you can zoom in to infinity and get an exact render. For even more precise definition of the 3D model, you can specify mathematical relationship, like x = y^2 + 3(sin(z)). The major drawback i noticed, was how hard it is to model something when you have no numerical value.

I forgot where i going with this. Good luck with your software, im looking forward to it. (ill go at sourcefourge when i`m back home)