Discrete harmonic maps and their conjugates are used to minimize surface area.

**Find:** Minimal surface bounded by a given curve G

**Algorithm:** Use initial surface M_{0} and
construct sequence of surfaces M_{i+1} by finding
(Laplace-Beltrami) harmonic maps F_{i} with

F_{i} : M_{i} --> M_{i+1}
with boundary(M_{i+1}) = G.

Limit surface is a minimal surfaces under certain conditions.

During minimization boundary vertices are retained. Pick and
drag vertices with the left mouse button by holding key "p"
pressed to modify the initial surface. Set the number of
iteration loops for the minimization algorithm by typing into
the textfield "Num Loops".

By the checkboxes "Tangential"
and "Normal" you define, in which directions the minimizer is
allowed to move vertices. The Checkboxes "Update Normals" and
"Update Domain" appoint, if surface normals and domain are
recomputed in every minimization step.

The Button "Step"
invokes one minimization step, the button "Minimize" starts as
many minimizing iterations as are specified in the "Num Loops"
textfield. By the "Resume" button you can stop and continue the
iteration.