with Standard_Integer_Vectors; use Standard_Integer_Vectors;
with Simplices,Triangulations; use Simplices,Triangulations;
package Dynamic_Lifting_Functions is
-- DESCRIPTION :
-- This package contains operations to control the lifting function
-- in order to obtain triangulations either by placing or by pulling.
function Lift_to_Place ( s : Simplex; x : Vector ) return integer;
function Lift_to_Place ( t : Triangulation; x : Vector ) return integer;
-- DESCRIPTION :
-- Determines the next value of the lifting function for the given
-- point x w.r.t. each simplex s, such that the product of the inner
-- normal of s with x is higher than the product with any point in s.
-- REQUIRED :
-- x(x'last) provides a lower bound for the lifting function.
-- To obtain an optimal lifting, x(x'last) can be set equal to 1.
function Lift_to_Pull ( s : Simplex; x : Vector ) return integer;
function Lift_to_Pull ( t : Triangulation; x : Vector ) return integer;
-- DESCRIPTION :
-- Determines the lifting value of x such that the product of the inner
-- normal of each simplex s with x is strictly lower than the product
-- with any point of s.
-- The lifting value such that x can be pulled in s will be returned.
-- REQUIRED :
-- x(x'last) contains already a lower bound on the lifting for x.
-- To obtain an optimal lifting, x(x'last) can be set equal to -1.
function Degenerate ( t : Triangulation; x : Vector ) return boolean;
-- DESCRIPTION :
-- Returns true if there exists a cell in t, such that the lifted point
-- x lies in the same hyperplane as the corresponding simplex on the
-- lower hull.
function Lift_to_Pull ( t1,t2 : Triangulation; x : Vector ) return integer;
-- DESCRIPTION :
-- Determines the lifting value of x such that for all cells in t1,
-- the inner product of the inner normal with x is strictly lower
-- than the inner product with any point of that cell.
-- The triangulation t2 is used to be guarantee that the lifting does
-- not induce a degeneracy in the lower hull.
-- The lifting value such that x can be pulled in t will be returned.
-- REQUIRED :
-- x(x'last) contains already a lower bound on the lifting for x.
-- To obtain an optimal lifting, x(x'last) can be set equal to -1.
end Dynamic_Lifting_Functions;