Figure 4.

The analytical mapping from square to circle. (A) A square in 2D space $T=\left\{\overrightarrow{x}\in {ℝ}^2:\left|x\right|<1,\left|y\right|<1\right\}$. (B) Unit circle, mapped from the square using Equation (4). The lines in the square are mapped onto the curves in the circle.