Conformal map

In mathematics, a conformal map is a function which preserves angles.

Related Topics:
Mathematics - Function

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More formally, a map

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:w = f(z)

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is called conformal (or angle-preserving) at z0, if it preserves oriented angles between curves through z0, as well as their orientation, i.e. direction. Conformal maps preserve both angles and the shapes of infinitesimally small figures, but not necessarily their size.

Related Topics:
Angle - Curve - Orientation

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The conformal property may be described in terms of the Jacobian derivative matrix of a coordinate transformation. If the Jacobian matrix of the transformation is everywhere a scalar times a rotation matrix, then the transformation is conformal.

Related Topics:
Jacobian - Coordinate transformation

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