Podnoid


Podnoid


Starnoid


Starnoid


Trinoid


Trinoid

 Noid

Noid is a Java software package to compute n-noids, constant mean curvature (CMC) genus-zero surfaces with asymptotically Delaunay ends.

Noid, developed by Nick Schmitt, is a component of ongoing research in the geometry of CMC and related surfaces and development of scientific numerics and visualization tools at the GANG and SFB288 research groups.

Noid computes three classes of n-noids:

  • Trinoids have three Delaunay ends of unduloid or nodoid type.
  • Starnoids have ends radiating from the center like a wheel.
  • Podnoids have non-coplanar end axes.
The images on the left, generated with Noid and the iSight scientific visualization software, show a variety of examples of each type.

Noid uses the Dorfmeister-Pedit-Wu algorithm for the construction of CMC surface. Software components of Noid:

  • The calculation starts with a DPW loop algebra valued Potential.
  • The Unitarizer computes the dressing loop which closes the ends by unitarizing the monodromy representation.
  • The Bubbler optionally computes a dressing loop which changes the central bulge to a central neck.
  • The Domain component computes a grid domain of curvature lines and associated texture coordinates via the Hopf differential.
  • The DPW Engine performs loop-group integration and Birkhoff and Iwasawa loop group factorizations.
  • The Sym Formula computes the CMC surface from the output of the DPW Engine.
  • The Delaunay Ends component glues Delaunay ends to the base n-noid to produce arbitrarily long ends.
  • The 2D Viewer displays the monodromy curves and the surface domain in R2.
  • The 3D Viewer displays the surface in R3.
Extensions to Noid currently under development:
  • Generalize the Sym Formula to produce CMC surfaces in S3 and H3 spaceforms.
  • Generalize the Bubbler to add bubbles to n-noids via Bäcklund transforms.
  • Generalize the Potential component to allow arbitrary text-based coefficient functions via a parser.
  • Extend file reading and writing capabilities to allow manipulation and transfer of general DPW input data and surface output in standard formats.
Noid Applet

Try the applet demonstration of the Noid package.

Noid Application
Acknowledgements and References
  • Research supported by SFB288.
  • Thanks to Markus Schmies for converting the C++ version of the GANG CMCLab DPW engine to Java.
  • Jtem - Java scientific computational and visualization library.
  • JavaView - Java 3D geometry viewer
  • Oorange - Java programming environment for interactively creating and manipulating networks of Java objects.
  • iSight - OpenGL scientific visualization package.
  • CMCLab - C++ package on which the base components of Noid are based.