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.
More...

#include <GProp_PrincipalProps.hxx>

Public Member Functions
	GProp_PrincipalProps ()
	creates an undefined PrincipalProps. More...

Standard_Boolean	HasSymmetryAxis () const
	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. More...

Standard_Boolean	HasSymmetryAxis (const Standard_Real aTol) const
	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)) More...

Standard_Boolean	HasSymmetryPoint () 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. More...

Standard_Boolean	HasSymmetryPoint (const Standard_Real aTol) const
	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)) More...

void	Moments (Standard_Real &Ixx, Standard_Real &Iyy, Standard_Real &Izz) const
	Ixx, Iyy and Izz return the principal moments of inertia <br> in the current system. Notes : More...

const gp_Vec &	FirstAxisOfInertia () const
	returns the first axis of inertia. <br> 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. More...

const gp_Vec &	SecondAxisOfInertia () const
	returns the second axis of inertia. <br> if the system has a point of symmetry or an axis of symmetry the second and the third axis of symmetry are undefined. More...

const gp_Vec &	ThirdAxisOfInertia () const
	returns the third axis of inertia. <br> This and the above functions return the first, second or third eigen vector of the <br> 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: More...

void	RadiusOfGyration (Standard_Real &Rxx, Standard_Real &Ryy, Standard_Real &Rzz) const
	Returns the principal radii of gyration Rxx, Ryy <br> and Rzz are the radii of gyration of the current system about its three principal axes of inertia. Note that: More...

Friends
GProp_PrincipalProps	GProp_GProps::PrincipalProperties () const
	Computes the principal properties of inertia of the current system. <br> 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. More...

Detailed Description

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.

Constructor & Destructor Documentation

GProp_PrincipalProps::GProp_PrincipalProps ( )

creates an undefined PrincipalProps.

Member Function Documentation

const gp_Vec& GProp_PrincipalProps::FirstAxisOfInertia ( ) const

 returns the first axis of inertia. <br>

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_Boolean GProp_PrincipalProps::HasSymmetryAxis ( ) const

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_Boolean GProp_PrincipalProps::HasSymmetryAxis ( const Standard_Real aTol ) const

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))

Standard_Boolean GProp_PrincipalProps::HasSymmetryPoint ( ) 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_Boolean GProp_PrincipalProps::HasSymmetryPoint ( const Standard_Real aTol ) const

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))

void GProp_PrincipalProps::Moments	(	Standard_Real &	Ixx,
		Standard_Real &	Iyy,
		Standard_Real &	Izz
	)		const

 Ixx, Iyy and Izz return the principal moments of inertia <br>

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.

void GProp_PrincipalProps::RadiusOfGyration	(	Standard_Real &	Rxx,
		Standard_Real &	Ryy,
		Standard_Real &	Rzz
	)		const

  Returns the principal radii of gyration  Rxx, Ryy <br>

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.

const gp_Vec& GProp_PrincipalProps::SecondAxisOfInertia ( ) const

 returns the second axis of inertia. <br>

if the system has a point of symmetry or an axis of symmetry the
second and the third axis of symmetry are undefined.

const gp_Vec& GProp_PrincipalProps::ThirdAxisOfInertia ( ) const

  returns the third axis of inertia. <br>
This and the above functions return the first, second or third eigen vector of the <br>

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.

Friends And Related Function Documentation

GProp_PrincipalProps GProp_GProps::PrincipalProperties ( ) const

friend

        Computes the principal properties of inertia of the current system. <br>

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.

The documentation for this class was generated from the following file:

GProp_PrincipalProps.hxx

Public Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation