Conformal transformation

In mathematics, a conformal map is a function that preserves angles locally. In the most common case, the function has a domain and an image in the complex plane.

More formally, let ${\displaystyle U}$ and ${\displaystyle V}$ be subsets of ${\displaystyle \mathbb {C} ^{n}}$. A function ${\displaystyle f:U\to V}$ is called conformal (or angle-preserving) at a point ${\displaystyle u_{0}\in U}$ if it preserves oriented angles between curves through ${\displaystyle u_{0}}$ with respect to their orientation (i.e., not just the magnitude of the angle). Conformal maps preserve both angles and the shapes of infinitesimally small figures, but not necessarily their size or curvature.

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