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In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths. More formally, let and be open subsets of . A function is called conformal (or angle-preserving) at a point if it preserves angles between directed curves through , as well as preserving orientation.
數學上，共形變換（英語： Conformal map ）或稱保角變換，來自於流體力學和幾何學的概念，是一個保持角度不變的映射。 更正式的說，一個映射 w = f ( z ) {\displaystyle w=f(z)\,}
数学上，共形变换（英語： Conformal map ）或稱保角变换，來自於流体力学和几何学的概念，是一个保持角度不变的映射。 更正式的说，一个映射 w = f ( z ) {\displaystyle w=f(z)\,}
As we’ve seen, once we have flows or harmonic functions on one region, we can use conformal maps to map them to other regions. In this section we will offer a number of conformal maps between various regions. By chaining these together along with scaling
6 天前 · A conformal mapping, also called a conformal map, conformal transformation, angle-preserving transformation, or biholomorphic map, is a transformation w=f(z) that preserves local angles. An analytic function is conformal at any point where it has a nonzero derivative.
Informal Definition: Conformal Maps Conformal maps are functions on \(C\) that preserve the angles between curves. More precisely: Suppose \(f(z)\) is differentiable at \(z_0\) and \(\gamma (t)\) is a smooth curve through \(z_0\). To be concrete, let's suppose
A mapping that preserves the magnitude of the angle between two smooth curves but not necessarily the sense is called an isogonal mapping. Example 3: The mapping w = z ― is a reflection in the real axis. This mapping is isogonal but not conformal. Consider for example the curves C 1 and C 2 given by.
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