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We give a Weierstrass type representation for semi-discrete minimal surfacesin Euclidean 3-space. We then give explicit parametrizations of various smooth,semi-discrete and fully-discrete catenoids, determined from either variationalor integrable systems principles. Finally, we state the shared properties thatthose various catenoids have.

Weierstrass representation for semi-discrete minimal surfaces, and comparison of various discretized catenoids