-- File:	PrincipalProps.cdl
-- Created:	Mon Feb 17 17:50:44 1992
-- Author:	Jean Claude VAUTHIER
---Copyright:	 Matra Datavision 1992


class PrincipalProps


from GProp

---Purpose:
-- A framework to present the principal properties of
-- inertia of a system of which global properties are
-- computed by a GProp_GProps object.
-- There is always a set of axes for which the
-- products of inertia of a geometric system are equal
-- to 0; i.e. the matrix of inertia of the system is
-- diagonal. These axes are the principal axes of
-- inertia. Their origin is coincident with the center of
-- mass of the system. The associated moments are
-- called the principal moments of inertia.
-- This sort of presentation object is created, filled and
-- returned by the function PrincipalProperties for
-- any GProp_GProps object, and can be queried to access the result.
-- Note: The system whose principal properties of
-- inertia are returned by this framework is referred to
-- as the current system. The current system,
-- however, is retained neither by this presentation
-- framework nor by the GProp_GProps object which activates it.
uses Vec from gp,
     Pnt from gp
     
 raises UndefinedAxis from GProp
 
 is




  Create   returns PrincipalProps;
        --- Purpose : creates an undefined PrincipalProps.   


  HasSymmetryAxis (me)  returns Boolean is static;
    	--- Purpose :
    	--  returns true if the geometric system has an axis of symmetry.  
	--  For  comparing  moments  relative  tolerance  1.e-10  is  used. 
	--  Usually  it  is  enough  for  objects,  restricted  by  faces  with 
	--  analitycal  geometry.
	
  HasSymmetryAxis (me; aTol :  Real)  returns Boolean is static;
    	--- Purpose :
    	--  returns true if the geometric system has an axis of symmetry. 
	--  aTol  is  relative  tolerance for  cheking  equality  of  moments
	--  If  aTol  ==  0,  relative  tolerance  is  ~  1.e-16  (Epsilon(I))


  HasSymmetryPoint (me)  returns Boolean is static;
    	--- Purpose :
    	--  returns true if the geometric system has a point of symmetry. 
	--  For  comparing  moments  relative  tolerance  1.e-10  is  used. 
	--  Usually  it  is  enough  for  objects,  restricted  by  faces  with 
	--  analitycal  geometry.
	
  HasSymmetryPoint (me; aTol :  Real)  returns Boolean is static;
    	--- Purpose :
    	--  returns true if the geometric system has a point of symmetry.
	--  aTol  is  relative  tolerance for  cheking  equality  of  moments 
	--  If  aTol  ==  0,  relative  tolerance  is  ~  1.e-16  (Epsilon(I))


  Moments (me; Ixx, Iyy, Izz: out Real) is static;
    	--- Purpose : Ixx, Iyy and Izz return the principal moments of inertia
-- in the current system.
-- Notes :
-- - If the current system has an axis of symmetry, two
--   of the three values Ixx, Iyy and Izz are equal. They
--   indicate which eigen vectors define an infinity of
--   axes of principal inertia.
-- - If the current system has a center of symmetry, Ixx,
--   Iyy and Izz are equal.


  FirstAxisOfInertia (me)   returns Vec
    	--- Purpose :  returns the first axis of inertia.
     raises UndefinedAxis
    	--- Purpose :
	--  if the system has a point of symmetry there is an infinity of 
	--  solutions. It is not possible to defines the three axis of 
	--  inertia. 
        ---C++: return const&
     is static;

  SecondAxisOfInertia (me)	returns Vec
    	--- Purpose :  returns the second axis of inertia.
     raises  UndefinedAxis
	--- Purpose :
	--  if the system has a point of symmetry or an axis of symmetry the 
	--  second and the third axis of symmetry are undefined.
        ---C++: return const&
     is static;


  ThirdAxisOfInertia (me)   returns Vec
    --- Purpose :  returns the third axis of inertia.
    --     This and the above functions return the first, second or third eigen vector of the
    -- matrix of inertia of the current system.
    -- The first, second and third principal axis of inertia
    -- pass through the center of mass of the current
    -- system. They are respectively parallel to these three eigen vectors.
    -- Note that:
    -- - If the current system has an axis of symmetry, any
    --   axis is an axis of principal inertia if it passes
    --   through the center of mass of the system, and runs
    --   parallel to a linear combination of the two eigen
    --   vectors of the matrix of inertia, corresponding to the
    --  two eigen values which are equal. If the current
    --  system has a center of symmetry, any axis passing
    --  through the center of mass of the system is an axis
    --  of principal inertia. Use the functions
    --  HasSymmetryAxis and HasSymmetryPoint to
    --  check these particular cases, where the returned
    --  eigen vectors define an infinity of principal axis of inertia.
    -- - The Moments function can be used to know which
    --   of the three eigen vectors corresponds to the two
    --   eigen values which are equal.
     raises  UndefinedAxis
	--- Purpose :
	--  if the system has a point of symmetry or an axis of symmetry the
	--  second and the third axis of symmetry are undefined.
        ---C++: return const&
   is static;


  RadiusOfGyration (me; Rxx, Ryy, Rzz : out Real) is static;
    	--- Purpose :  Returns the principal radii of gyration  Rxx, Ryy
-- and Rzz are the radii of gyration of the current
-- system about its three principal axes of inertia.
-- Note that:
-- - If the current system has an axis of symmetry,
--   two of the three values Rxx, Ryy and Rzz are equal.
-- - If the current system has a center of symmetry,
--   Rxx, Ryy and Rzz are equal.





  Create (Ixx, Iyy, Izz, Rxx, Ryy, Rzz : Real; Vxx, Vyy, Vzz : Vec; G : Pnt)
     returns PrincipalProps
     is private;



fields

   i1 : Real;
   i2 : Real;
   i3 : Real;
   r1 : Real;
   r2 : Real;
   r3 : Real;
   v1 : Vec;
   v2 : Vec;
   v3 : Vec;
   g  : Pnt;
   
friends

  PrincipalProperties from GProps (me)
  
end PrincipalProps;