fineStarTriangulation -- refine a triangulation to a fine star triangulation by coning over a center

• Usage:

  star = fineStarTriangulation(A, tri)

• Inputs:
  • A, a matrix, whose columns are the boundary points of a polytope (and possibly an interior cone center)
  • tri, a list, a triangulation of the columns of $A$, typically a triangulation of the boundary
• Optional inputs:
  • ConeIndex => an integer, default value null, the column index to use as the cone center; if null (default), uses numColumns A, treating the cone center as a new point to be appended
• Outputs:
  • a list, a list of simplices forming a star triangulation centered at the chosen index: each maximal simplex of tri, intersected with each facet of $\mathrm{conv}(A)$, is appended with the cone index

i1 : A = transpose matrix {{1,1},{-1,1},{-1,-1},{1,-1}}

o1 = | 1 -1 -1 1  |
     | 1 1  -1 -1 |

              2       4
o1 : Matrix ZZ  <-- ZZ

i2 : tri = topcomRegularFineTriangulation A

o2 = {{0, 1, 2}, {0, 2, 3}}

o2 : List

i3 : fineStarTriangulation(A, tri)

o3 = {{0, 1, 4}, {0, 3, 4}, {1, 2, 4}, {2, 3, 4}}

o3 : List