A Fourier nodal surface is the zero level set of a real function of three variables represented by a Fourier series. It is a nodal set; wherever the function is smooth and its gradient is nonzero, the zero level set is a regular surface by the implicit function theorem. Finite sums of trigonometric terms give convenient implicit equations for periodic surfaces (von Schnering and Nesper 1991).
For example,
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gives a nodal approximation to the Schwarz P surface. It resembles the triply periodic minimal surface, but its mean curvature does not vanish everywhere. Thus a Fourier nodal approximation and the exact minimal surface must be distinguished.
