Conformal map

Mathematical function that preserves angles

In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths. More formally, let U {\displaystyle U} and V {\displaystyle V} be open subsets of R n {\displaystyle \mathbb {R} ^{n}} . A function f : U → V {\displaystyle f:U\to V} is called conformal (or angle-preserving) at a point u 0 ∈ U {\displaystyle u_{0}\in U} if it preserves angles between directed curves through u 0 {\displaystyle u_{0}} , as well as preserving orientation.

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