incompPolyhedra -- returns the pairs of incompatible polyhedra

Synopsis

• Usage:

  Lpairs = incompPolyhedra L

  Lpairs = incompPolyhedra(X,PC)

  Lpairs = incompPolyhedra(PC,X)

• Inputs:
  • L, a list
  • PC, an instance of the type PolyhedralComplex
  • X, Polyhedron or PolyhedralComplex
• Outputs:
  • Lpairs, a list

Description

If incompPolyhedra is applied to a list of polyhedra and polyhedral complexes, then it returns the pairs of elements whose intersection is not a face of each. For a Polyhedron P and a PolyhedralComplex PC in the list this means there is at least one generating Polyhedron of PC whose intersection with P is not a face of each. For two polyhedral complexes in the list this means there is at least one generating polyhedron each such that their intersection is not a face of each. If applied to a pair consisting of a polyhedron and a polyhedral complex or two polyhedral complexes, then it returns the pairs of polyhedra that do not share a common face.

i1 : P1 = convexHull matrix {{1,0,0},{1,1,0}};

i2 : P2 = convexHull matrix {{1,0,0},{0,-1,0}};

i3 : P3 = convexHull matrix {{-1,0,0},{0,1,0}};

i4 : P4 = convexHull matrix {{1,1,0},{0,1,0}};

i5 : P5 = convexHull matrix {{1,2,0},{2,1,0}};

i6 : L = {P1,P2,P3,P4,P5};

i7 : Lpairs = incompPolyhedra L

o7 = {(P1, P5), (P4, P5)}

o7 : List

i8 : Lpairs == {(P1,P4),(P1,P5)}

o8 = false