Enneper-Weierstrass parameterization
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In mathematics, the Enneper-Weierstrass parameterization of minimal surfaces is a classical piece of differential geometry.
Alfred Enneper and Karl Weierstrass studied minimal surfaces as far back as 1863.
Given complex-valued functions f(z) and g(z), parameterize minimal surfaces by taking the real part of
- ∫ (f(x)(1 − g(x)2), i*f(x)(1 + g(x))2, 2f(x)g(x)).
In this way a number of different surfaces can be parameterized, including Enneper's minimal surface, Henneberg's minimal surface, Bour's minimal surface, and the trinoid.
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