How should geometry work in an ideal programming language

How should geometry work in an ideal programming language

We should explore whether it is feasible to build geometrical objects that are pixel perfect at any scale or size. Imagine a circle or a fractal consisting of dimension-less points that glow. As one zooms in on an increasing small portion of the object the screen pixels are computed accurately. At extreme scales such as a googol-fold expansion the system may begin to slow down as the exact rational or real arithmetic may become relatively expensive. Turtle geometry could also be implemented using exact real arithmetic (or an approximation so long as no artifact can be observed).

It needs to be investigated as to whether exact 3D geometry can be rendered using existing 3D graphics engines, especially those that rely upon hardware acceleration.

Such an implementation would make "real" and "concrete" the idealizations of geometry.