How can I visualize a minimal surface of this library?

As an example we explain how to visualize Costa's surface.

  1. Start GRAPE by typing "grape".
  2. Add project amandus by clicking button "add project"
  3. In the project list doubleclick "amandus".
  4. Click button ""amandus" Amandus" .
  5. Click button "read st" (read in the position of the surface).
  6. Find button "costa.st" on the appearing browser and doubleclick.
  7. Click button "opts" (go to the Options-menue).
  8. Click button "read *.in"
  9. Find button "costa.am" on the appearing browser and doubleclick. This file contains specifications of the parameter domain in the complex plane and its triangulation. (Note that the Weierstrass functions for the library are contained in a different file, namely the source file g_arg_weier.c.)
  10. To compute the fundamental domain of the surface click button "compute". Other examples in the library are in fact families; you compute them by pressing "-video" and can use the arrow buttons next to "Frame */*" to move around the family.
  11. You can now use the "reflect" button to reflect the fundamental domain step by step to a complete surface. Use the mouse in the "GrapeOutput" window to mark the curves you want to reflect at. Leave the mouse in that window and follow the instructions at the bottom of the "grapeControl" window.
  12. Under "manager", "switches" you can toggle "to grid" and "to patch". Moreover "manager", "display method", "../(Explicit)", "lines" gives a grid output without triangle diagonals. The tools of "trans" let you rotate and move the surface. Under "light" and "surf" you can change the appearance of the surface. Finally, "manager", "I/O", "PostScript" produces postscript output (you may need to adjust the appearance).

For further information see the GRAPE Manual.


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grape@iam.uni-bonn.de - revised 1/99 Karsten Grosse-Brauckmann