I'm a programmer trying to get my head around the math I need for a problem and was hoping it has been covered in one branch of mathematics or another.
My model is a continuously expanding space (like the inner volume of an expanding balloon) where shapes behave locally as if they are euclidean but shrink non-uniformly as they are moved toward the origin - imagine an infinite line of wire framed cubes and a camera looking straight down the tunnel they create to the vanishing point at its center, as the camera moves in or out everything measures as it should for euclidean geometry (taking into account lens magnification etc); but then change the rules so that the vanishing point is actually a true point where parallel lines converge (but for a drone camera zooming through the tunnel the point would remain infinitely far away as the drone continued to shrink).
Any papers or places to start on putting this into mathematics (well my bastardized version of mathematics called source code) or at least formulate a coherent description so I can search further on the internet?
Edit To clarify below is a grid to illustrate: the grid cells depicted here have a radial length equal to the average of the inner and outer arc lengths and the origin can be zoomed in on indefinately.
