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Annotation of OpenXM_contrib/PHC/Ada/Math_Lib/Supports/integer_face_enumerators.ads, Revision 1.1

1.1     ! maekawa     1: with Standard_Integer_Vectors;           use Standard_Integer_Vectors;
        !             2: with Standard_Integer_VecVecs;           use Standard_Integer_VecVecs;
        !             3:
        !             4: package Integer_Face_Enumerators is
        !             5:
        !             6: -- DESCRIPTION :
        !             7: --   This package contains procedures which allow the efficient
        !             8: --   enumeration of all vertices, edges and k-faces of a polytope.
        !             9: --   The polytope is spanned by a given vector of points in a general
        !            10: --   dimensional space.
        !            11: --   In addition, a procedure has been added for enumerating all
        !            12: --   facets of a certain type of the sum of a tuple of polytopes.
        !            13:
        !            14:   generic
        !            15:
        !            16:     with procedure Process ( i : in integer; cont : out boolean );
        !            17:
        !            18:   procedure Enumerate_Vertices ( pts : in VecVec );
        !            19:
        !            20:   -- DESCRIPTION :
        !            21:   --   The vector pts contains the points which span the polytope.
        !            22:   --   The candidate vertices are enumerated in order of occurrence in pts.
        !            23:   --   Each time a vertex has been found, the procedure Process is invoked,
        !            24:   --   which returns then the entry of the vertex in pts.
        !            25:   --   When cont is set to false, the enumeration stops.
        !            26:
        !            27:   generic
        !            28:
        !            29:     with procedure Process ( i,j : in integer; cont : out boolean );
        !            30:
        !            31:   procedure Enumerate_Edges ( pts : in VecVec );
        !            32:
        !            33:   -- DESCRIPTION :
        !            34:   --   The vector pts contains the points which span the polytope.
        !            35:   --   The candidate edges are enumerated in lexicographic order.
        !            36:   --   Each time an edge has been found, the procedure Process is
        !            37:   --   invoked, which returns the entries of the edge in pts.
        !            38:   --   When cont is set to be false, the enumeration stops.
        !            39:
        !            40:   generic
        !            41:
        !            42:     with procedure Process ( i,j : in integer; cont : out boolean );
        !            43:
        !            44:   procedure Enumerate_Lower_Edges ( pts : in VecVec );
        !            45:
        !            46:   -- DESCRIPTION :
        !            47:   --   Enumerates only the edges on the lower hull of the polytope.
        !            48:
        !            49:   generic
        !            50:
        !            51:     with procedure Process ( face : in Vector; cont : out boolean );
        !            52:
        !            53:     -- REQUIRED :
        !            54:     --   The range of face must be 0..k.
        !            55:
        !            56:   procedure Enumerate_Faces ( k : in natural; pts : in VecVec );
        !            57:
        !            58:   -- DESCRIPTION :
        !            59:   --   The vector pts contains the points which span the polytope.
        !            60:   --   A k-face is a face spanned by k affine linearly independent points.
        !            61:   --   The candidate k-faces are enumerated in lexicographic order.
        !            62:   --   Each time an edge has been found, the procedure Process is
        !            63:   --   invoked, which returns the entries of the k-face in pts.
        !            64:   --   When cont is set to be false, the enumeration stops.
        !            65:
        !            66:   generic
        !            67:
        !            68:     with procedure Process ( face : in Vector; cont : out boolean );
        !            69:
        !            70:     -- REQUIRED :
        !            71:     --   The range of face must be 0..k.
        !            72:
        !            73:   procedure Enumerate_Lower_Faces ( k : in natural; pts : in VecVec );
        !            74:
        !            75:   -- DESCRIPTION :
        !            76:   --   Enumerates only the k-faces on the lower hull of the polytope.
        !            77:
        !            78:   generic
        !            79:
        !            80:     with procedure Process ( faces : in VecVec; cont : out boolean );
        !            81:
        !            82:     -- DESCRIPTION :
        !            83:     --   The parameter faces has the following meaning:
        !            84:     --   faces(i) contains the entries of points in pts which span
        !            85:     --   the k-face of the ith polytope, with k = typ(i).
        !            86:     --   When cont is set to false, the enumeration stops.
        !            87:
        !            88:   procedure Enumerate_Faces_of_Sum
        !            89:                ( ind,typ : in vector; k : in natural; pts : in VecVec );
        !            90:
        !            91:   -- DESCRIPTION :
        !            92:   --   Enumerates the points which span faces of a certain type
        !            93:   --   of the polytope in lexicographic order.
        !            94:
        !            95:   -- ON ENTRY :
        !            96:   --   ind       ind(i) indicates where the points of the ith polytope
        !            97:   --             in the vector pts begin;
        !            98:   --   typ       typ(i) contains the dimension k of the k-face of the ith
        !            99:   --             polytope which spans the facet of the sum;
        !           100:   --   k         sum of the entries in typ, must be less than
        !           101:   --             or equal to the dimension of the space;
        !           102:   --   pts       contains all points of the polytopes.
        !           103:
        !           104:   -- ON RETURN :
        !           105:   --   Each time a face of the sum has been found, Process is invoked.
        !           106:
        !           107: end Integer_Face_Enumerators;