TRIANGULATION(1)       Mathematica package       TRIANGULATION(1)



NAME
     Triangulation, faces, edges, alledges, vertices, allver-
     tices, corners, glue, ne, nv, nc, euler, vN, eN

SYNOPSIS
     <<Triangulation`

     Triangulation[faces, glue]

     faces[tri]
     edges[tri]
     alledges[tri]
     vertices[tri]
     allvertices[tri]
     corners[tri]
     glue[tri]

     nv[tri]
     ne[tri]
     nc[tri]
     euler[tri]

     vN[tri, v]
     eN[tri, {v1, v2}]


DESCRIPTION
     The following Mathematica functions are defined by the Tri-
     angulation package.

     tri = Triangulation[faces, glue]
         faces is a list of faces in the form {{v1, v2, v3}, ...}
         and glue is a list of pairs of edges to be identified,
         given in the form {{{v1, v2}, {v3, v4}}, ...}. Each vi
         represents a vertex and must be an integer.

     This creates a triangulation object and assigns it to tri.
     The v's must be integers representing vertices of the tri-
     angulation. Faces of the triangulation are triples of ver-
     tices. Edges of the triangulation will be identified if they
     join the same two vertices or if they are specified in the
     glue parameter.

     The following functions apply to Triangulations.

     faces[tri]
         gives the original list of faces.

     edges[tri]
         gives a list of edges after identified edges have been
         deleted.  Each edge is given as a pair of vertices {v1,
         v2}.

     alledges[tri]
         gives the full list of edges without deleting identified
         edges. This will be the same as edges[tri] if and only
         if glue is empty.

     vertices[tri]
         gives a list of vertices after identified vertices have
         been removed. This is simply a list of integers {v1,
         ...}.

     allvertices[tri]
         gives the full list of vertices with which the triangu-
         lation was originally specified. Ie. The union of all
         integers appearing in the faces argument of Triangula-
         tion.

     corners[tri]
         gives a list of the corners of faces in tri.  The corner
         at v2 of {v1, v2, v3} is given as {v2, v3, v1}.

     glue[tri]
         gives the list of identifications as supplied to Tri-
         angulation.

     nv[tri], ne[tri], nc[tri]
         give the number of vertices, edges and corners respec-
         tively in tri after performing identifications.

     euler[tri]
         gives the Euler characteristic of the triangulation.

     vN[tri, v]
         returns a number in the range 1-nv[tri]. If v appears in
         the list vertices[tri] then vN[tri, v] returns the posi-
         tion of v in that list. vN[tri, v] returns the same
         value for all vertices identified with v.

     eN[tri, {v1, v2}]
         returns a number in the range 1-ne[tri] assuming that
         {v1, v2} is an edge of tri. If Sort[{v1, v2}] appears in
         edges[tri] then eN[tri, {v1, v2}] returns its position
         in that list. eN[tri, {v1, v2}] returns the same value
         for all edges identified with {v1, v2}.

SEE ALSO
     CIRCLEPACK - a Mathematica package for finding circle pack-
     ings on a given triangulated surface.

BUGS
     Triangulation, vN and eN do not check their arguments.