Surface Evolver Newsletter no. 4

		      Surface Evolver Newsletter Number 4
			      May 28, 1993

                    Editor: Ken Brakke, brakke@geom.umn.edu

Contents:

New features
Bibliography

Version 1.91 now available. New features:

      The two sides of a facets can have different colors. 'COLOR'
      applies to both sides, 'FRONTCOLOR' and 'BACKCOLOR'
      to different sides, according to the orientation inherited
      from the datafile. Example:
	"set facet backcolor red"

      Attributes of individual named elements can be set inside
      loops, i.e. "foreach facet ff do set ff color red"
      does the same as "set facet color red".

      To reduce need for explicit line-splicing on long commands,
      the parser now keeps track of depth of brace and parenthesis
      nesting, and will call for more input if a line ends inside nest.
      So if you want to type a multiline command, start with '{'
      and end with '}' many lines later.  Also does auto line-splicing 
      if certain tokens are last token in line (such as '+'), but it
      is wiser to enclose with braces rather than count on this.  

      Queries can run through edges and facets adjacent to
      a vertex, and facets of a body, as in "list vertices vv
      where max(vv.facet,color==red) > 0".

      New attributes: Valence attribute has been extended to vertices
      and bodies.  Vertex valence is the number of edges on
      a vertex.  Body valence is the number of facets on the
      body (edges in the string model). Example:
      "list vertices where valence == 4"

      Surface area can be minimized by minimizing Dirichlet integral,
      according to a scheme of Polthier and Pinkall.  Command 'dirichlet'.
      Not a replacement for other evolutions.

      Using a command from the history list now echoes it.

      Improved NeXT terminal interface.  -u option for no graphics,
      -t for terminal and graphics.

      Command assignment fixed to assign only one command.
      so "ggg := g; g" will be the same as "{ggg := g}; g"
      and not "ggg := {g;g}".

      Every time a command changed a global variable, the surface
      was being recalculated.  This slowed down scripts immensely.
      So now the only variables that cause recalculation are
      1) adjustable parameters defined in the datafile
      2) quantity moduli and parameters
      You can turn off even this with "autorecalc off".

      "view_4d" command to toggle sending full 4D coordinates
      to geomview.  Default is OFF.


Bibliography:

      Alice Underwood, "Constructing barriers to minimal surfaces from
      polyhedral data," Ph.D. thesis, Princeton, 1993.

         When the Evolver reaches a minimum area for a given triangulation
      of a surface, can you guarantee that there is a smooth minimal
      surface nearby?  This thesis proves some sufficient conditions.
      You have to be able to "blow" on the surface and still have it
      stable.  The triangulation must be well-behaved.  Unfortunately,
      the estimates are far from the best possible (I hope!), and one
      needs on the order of 10^7 to apply the proof.

      Ken Brakke, "Stability of a toroidal bubble in a rotating tank."

	 This is the final report of an Evolver project I did for Lockheed.
      A tank of liquid helium is rotating in weightlessness.  The tank
      has a rod along the axis of rotation.  The tank is partially full,
      and the bubble is supposed to form an axisymmetric torus so the center
      of mass is on the axis.  The questions are: what is the rotation rate
      needed to force a spherical bubble to form a torus, and what is the
      minimum rotation rate at which the torus is stable against breaking 
      up into a sphere?  This is not an official publication of anybody,
      but copies are available to anybody interested.

      Hans Mittelmann, "Symmetric Capillary Surfaces in a Cube",
      Math. Comp. Simul. 35 (1993), 139-152.  (reference update)


End of Evolver Newsletter 4