Harmonic Maps on Polyhedral Surfaces

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 M0 and construct sequence of surfaces Mi+1 by finding (Laplace-Beltrami) harmonic maps Fi with

Fi : Mi --> Mi+1 with boundary(Mi+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.

© 1996-2012 Last modified: 29.10.2012 --- Konrad Polthier --- Freie Universität Berlin, Germany