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 // Created on: 1992-02-17
 // Created by: Jean Claude VAUTHIER
 // Copyright (c) 1992-1999 Matra Datavision
 // Copyright (c) 1999-2014 OPEN CASCADE SAS
 //
 // This file is part of Open CASCADE Technology software library.
 //
 // This library is free software; you can redistribute it and/or modify it under
 // the terms of the GNU Lesser General Public License version 2.1 as published
 // by the Free Software Foundation, with special exception defined in the file
 // OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
 // distribution for complete text of the license and disclaimer of any warranty.
 //
 // Alternatively, this file may be used under the terms of Open CASCADE
 // commercial license or contractual agreement.
 
 #ifndef _GProp_PrincipalProps_HeaderFile
 #define _GProp_PrincipalProps_HeaderFile
 
 #include <Standard.hxx>
 #include <Standard_DefineAlloc.hxx>
 #include <Standard_Handle.hxx>
 
 #include <gp_Vec.hxx>
 #include <gp_Pnt.hxx>
 #include <GProp_GProps.hxx>
 #include <Standard_Boolean.hxx>
 
 //! 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.
 class GProp_PrincipalProps
 {
 public:
   DEFINE_STANDARD_ALLOC
 
   //! creates an undefined PrincipalProps.
   Standard_EXPORT GProp_PrincipalProps();
 
   //! 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
   //! analytical  geometry.
   Standard_EXPORT Standard_Boolean HasSymmetryAxis() const;
 
   //! returns true if the geometric system has an axis of symmetry.
   //! aTol  is  relative  tolerance for  checking  equality  of  moments
   //! If  aTol  ==  0,  relative  tolerance  is  ~  1.e-16  (Epsilon(I))
   Standard_EXPORT Standard_Boolean HasSymmetryAxis(const Standard_Real aTol) const;
 
   //! 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
   //! analytical  geometry.
   Standard_EXPORT Standard_Boolean HasSymmetryPoint() const;
 
   //! returns true if the geometric system has a point of symmetry.
   //! aTol  is  relative  tolerance for  checking  equality  of  moments
   //! If  aTol  ==  0,  relative  tolerance  is  ~  1.e-16  (Epsilon(I))
   Standard_EXPORT Standard_Boolean HasSymmetryPoint(const Standard_Real aTol) const;
 
   //! 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.
   Standard_EXPORT void Moments(Standard_Real& Ixx, Standard_Real& Iyy, Standard_Real& Izz) const;
 
   //! returns the first axis of inertia.
   //!
   //! 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.
   Standard_EXPORT const gp_Vec& FirstAxisOfInertia() const;
 
   //! returns the second axis of inertia.
   //!
   //! if the system has a point of symmetry or an axis of symmetry the
   //! second and the third axis of symmetry are undefined.
   Standard_EXPORT const gp_Vec& SecondAxisOfInertia() const;
 
   //! 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.
   //!
   //! if the system has a point of symmetry or an axis of symmetry the
   //! second and the third axis of symmetry are undefined.
   Standard_EXPORT const gp_Vec& ThirdAxisOfInertia() const;
 
   //! 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.
   Standard_EXPORT void RadiusOfGyration(Standard_Real& Rxx,
                                         Standard_Real& Ryy,
                                         Standard_Real& Rzz) const;
 
   friend
     //! Computes the principal properties of inertia of the current system.
     //! 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 function computes the eigen values and the
     //! eigen vectors of the matrix of inertia of the system.
     //! Results are stored by using a presentation framework
     //! of principal properties of inertia
     //! (GProp_PrincipalProps object) which may be
     //! queried to access the value sought.
     Standard_EXPORT GProp_PrincipalProps
     GProp_GProps::PrincipalProperties() const;
 
 protected:
 private:
   Standard_EXPORT GProp_PrincipalProps(const Standard_Real Ixx,
                                        const Standard_Real Iyy,
                                        const Standard_Real Izz,
                                        const Standard_Real Rxx,
                                        const Standard_Real Ryy,
                                        const Standard_Real Rzz,
                                        const gp_Vec&       Vxx,
                                        const gp_Vec&       Vyy,
                                        const gp_Vec&       Vzz,
                                        const gp_Pnt&       G);
 
   Standard_Real i1;
   Standard_Real i2;
   Standard_Real i3;
   Standard_Real r1;
   Standard_Real r2;
   Standard_Real r3;
   gp_Vec        v1;
   gp_Vec        v2;
   gp_Vec        v3;
   gp_Pnt        g;
 };
 
 #endif // _GProp_PrincipalProps_HeaderFile

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