2-Dimensional Grid Square Spiral Coordinates

spiral.ipynb

One of the problems I faced while working on Plotz was how do you partion segments of a world such that the following criteria are met:

1. Plots must be near other plots. Adding extreme separation or randomness makes the world feel empty.
2. Plots arrangements should be continous. Empty plots make for an empty server.
3. A new plot should be speedy to allocate. Millions of plots may be active at any time. Referencing the x/y coordinate makes it difficult to find the next location to allocate as a plot.

These problems are solved by clamping world coordinates to a square spiral. The problem is that the conversion between x/y world coordinates and the spiral segment index is extremely difficult if not performed iteratively.

The code above defines the formulas necessary to convert x/y to index and index back to x/y.

See here for a great explaination on the math: https://math.stackexchange.com/questions/163080/on-a-two-dimensional-grid-is-there-a-formula-i-can-use-to-spiral-coordinates-in