// 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 #include #include #include #include #include #include #include //! 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 //! analitycal 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 //! analitycal 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