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GProp_PrincipalProps Class Reference

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.

#include <GProp_PrincipalProps.hxx>

Public Member Functions

DEFINE_STANDARD_ALLOC GProp_PrincipalProps ()
 creates an undefined PrincipalProps.

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.

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))

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.

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))

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

const gp_VecFirstAxisOfInertia () 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.

const gp_VecSecondAxisOfInertia () 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.

const gp_VecThirdAxisOfInertia () 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:

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

Friends

GProp_PrincipalProps GProp_GProps::PrincipalProperties () const
 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.


Constructor & Destructor Documentation


Member Function Documentation

  • 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.
  • 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.
  • 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


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