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Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/Dynlift/dynamic_lifting_functions.ads, Revision 1.1

1.1     ! maekawa     1: with Standard_Integer_Vectors;           use Standard_Integer_Vectors;
        !             2: with Simplices,Triangulations;           use Simplices,Triangulations;
        !             3:
        !             4: package Dynamic_Lifting_Functions is
        !             5:
        !             6: -- DESCRIPTION :
        !             7: --   This package contains operations to control the lifting function
        !             8: --   in order to obtain triangulations either by placing or by pulling.
        !             9:
        !            10:   function Lift_to_Place ( s : Simplex; x : Vector ) return integer;
        !            11:   function Lift_to_Place ( t : Triangulation; x : Vector ) return integer;
        !            12:
        !            13:   -- DESCRIPTION :
        !            14:   --   Determines the next value of the lifting function for the given
        !            15:   --   point x w.r.t. each simplex s, such that the product of the inner
        !            16:   --   normal of s with x is higher than the product with any point in s.
        !            17:
        !            18:   -- REQUIRED :
        !            19:   --   x(x'last) provides a lower bound for the lifting function.
        !            20:   --   To obtain an optimal lifting, x(x'last) can be set equal to 1.
        !            21:
        !            22:   function Lift_to_Pull ( s : Simplex; x : Vector ) return integer;
        !            23:   function Lift_to_Pull ( t : Triangulation; x : Vector ) return integer;
        !            24:
        !            25:   -- DESCRIPTION :
        !            26:   --   Determines the lifting value of x such that the product of the inner
        !            27:   --   normal of each simplex s with x is strictly lower than the product
        !            28:   --   with any point of s.
        !            29:   --   The lifting value such that x can be pulled in s will be returned.
        !            30:
        !            31:   -- REQUIRED :
        !            32:   --   x(x'last) contains already a lower bound on the lifting for x.
        !            33:   --   To obtain an optimal lifting, x(x'last) can be set equal to -1.
        !            34:
        !            35:   function Degenerate ( t : Triangulation; x : Vector ) return boolean;
        !            36:
        !            37:   -- DESCRIPTION :
        !            38:   --   Returns true if there exists a cell in t, such that the lifted point
        !            39:   --   x lies in the same hyperplane as the corresponding simplex on the
        !            40:   --   lower hull.
        !            41:
        !            42:   function Lift_to_Pull ( t1,t2 : Triangulation; x : Vector ) return integer;
        !            43:
        !            44:   -- DESCRIPTION :
        !            45:   --   Determines the lifting value of x such that for all cells in t1,
        !            46:   --   the inner product of the inner normal with x is strictly lower
        !            47:   --   than the inner product with any point of that cell.
        !            48:   --   The triangulation t2 is used to be guarantee that the lifting does
        !            49:   --   not induce a degeneracy in the lower hull.
        !            50:   --   The lifting value such that x can be pulled in t will be returned.
        !            51:
        !            52:   -- REQUIRED :
        !            53:   --   x(x'last) contains already a lower bound on the lifting for x.
        !            54:   --   To obtain an optimal lifting, x(x'last) can be set equal to -1.
        !            55:
        !            56: end Dynamic_Lifting_Functions;