Thursday, September 3, 2015

Canonical space in disc-to-square mapping

In this blog, I will discuss several ways to map the circular disc to a square and vice versa.  This is the canonical mapping space:

circular domain: {(u,v) | u² + v² ≤ 1}
square range: [-1,1] x [-1,1]

The points (u,v) are in circular disc coordinates
The points (x,y) are in square coordinates

Some other relevant links:
1) also discussed the mapping and asked for the inverse.

2) Greg Cope has a nice image of a square maze converted to a circular disc.

3) Peter Shirley mentioned Dave Cline's trick to simplify his concentric map code

4) Stack exchange also has a discussion on this:

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