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The Weierstrass representation for minimal surfaces in $\mathbb{R}^3$provides a flexible method for constructing minimal surfaces of arbitrarygenus. The topological limitations of minimal surfaces interfere with thisproviding a more general geometric modeling tool. Minimal surfaces lie in thelarger class of harmonic surfaces, which in general don't have the sametopological limitations of minimal surfaces and can have complicated embeddedends. In this paper we demonstrate the flexibility of using the Weierstrassrepresentation for harmonic surfaces to combine embedded harmonic ends togetherto construct embedded harmonic surfaces of arbitrary genus.

Harmonic parametrization of surfaces of arbitrary genus