GProp_GProps Class Reference

Implements a general mechanism to compute the global properties of <br>

a "compound geometric system" in 3d space by composition of the
global properties of "elementary geometric entities" such as
(curve, surface, solid, set of points). It is possible to compose
the properties of several "compound geometric systems" too.

To computes the global properties of a compound geometric
system you should :
. declare the GProps using a constructor which initializes the
GProps and defines the location point used to compute the inertia
. compose the global properties of your geometric components with
the properties of your system using the method Add.

To compute the global properties of the geometric components of
the system you should use the services of the following classes :
More...

#include <GProp_GProps.hxx>

Inheritance diagram for GProp_GProps:

Public Member Functions
	GProp_GProps ()
	The origin (0, 0, 0) of the absolute cartesian coordinate system is used to compute the global properties. More...
	GProp_GProps (const gp_Pnt &SystemLocation)
	The point SystemLocation is used to compute the gobal properties <br> of the system. For more accuracy it is better to define this point closed to the location of the system. For example it could be a point around the centre of mass of the system. This point is referred to as the reference point for this framework. For greater accuracy it is better for the reference point to be close to the location of the system. It can, for example, be a point near the center of mass of the system. At initialization, the framework is empty; i.e. it retains no dimensional information such as mass, or inertia. However, it is now able to bring together global properties of various other systems, whose global properties have already been computed using another framework. To do this, use the function Add to define the components of the system. Use it once per component of the system, and then use the interrogation functions available to access the computed values. More...
void	Add (const GProp_GProps &Item, const Standard_Real Density=1.0)
	Either More...
Standard_Real	Mass () const
	Returns the mass of the current system. <br> If no density is attached to the components of the current system the returned value corresponds to : More...
gp_Pnt	CentreOfMass () const
	Returns the center of mass of the current system. If <br> the gravitational field is uniform, it is the center of gravity. The coordinates returned for the center of mass are expressed in the absolute Cartesian coordinate system. More...
gp_Mat	MatrixOfInertia () const
	returns the matrix of inertia. It is a symmetrical matrix. <br> The coefficients of the matrix are the quadratic moments of inertia. | Ixx Ixy Ixz | matrix = | Ixy Iyy Iyz | | Ixz Iyz Izz | The moments of inertia are denoted by Ixx, Iyy, Izz. The products of inertia are denoted by Ixy, Ixz, Iyz. The matrix of inertia is returned in the central coordinate system (G, Gx, Gy, Gz) where G is the centre of mass of the system and Gx, Gy, Gz the directions parallel to the X(1,0,0) Y(0,1,0) Z(0,0,1) directions of the absolute cartesian coordinate system. It is possible to compute the matrix of inertia at another location point using the Huyghens theorem (you can use the method of package GProp : HOperator). More...
void	StaticMoments (Standard_Real &Ix, Standard_Real &Iy, Standard_Real &Iz) const
	Returns Ix, Iy, Iz, the static moments of inertia of the <br> current system; i.e. the moments of inertia about the three axes of the Cartesian coordinate system. More...
Standard_Real	MomentOfInertia (const gp_Ax1 &A) const
	computes the moment of inertia of the material system about the axis A. More...
GProp_PrincipalProps	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...
Standard_Real	RadiusOfGyration (const gp_Ax1 &A) const
	Returns the radius of gyration of the current system about the axis A. More...

Protected Attributes
gp_Pnt	g
gp_Pnt	loc
Standard_Real	dim
gp_Mat	inertia

Detailed Description

Implements a general mechanism to compute the global properties of <br>

a "compound geometric system" in 3d space by composition of the
global properties of "elementary geometric entities" such as
(curve, surface, solid, set of points). It is possible to compose
the properties of several "compound geometric systems" too.

To computes the global properties of a compound geometric
system you should :
. declare the GProps using a constructor which initializes the
GProps and defines the location point used to compute the inertia
. compose the global properties of your geometric components with
the properties of your system using the method Add.

To compute the global properties of the geometric components of
the system you should use the services of the following classes :

• class PGProps for a set of points,
  
• class CGProps for a curve,
  
• class SGProps for a surface,
  
• class VGProps for a "solid".
  The classes CGProps, SGProps, VGProps are generic classes and
  must be instantiated for your application.
  
  
  The global properties computed are :
  

the dimension (length, area or volume)

• the mass,
  
• the centre of mass,
  
• the moments of inertia (static moments and quadratic moments),
  
• the moment about an axis,
  
• the radius of gyration about an axis,
  
• the principal properties of inertia :
  (sea also class PrincipalProps)
  . the principal moments,
  . the principal axis of inertia,
  . the principal radius of gyration,
  
  
  
  Example of utilisation in a simplified C++ implementation :
  
  //declares the GProps, the point (0.0, 0.0, 0.0) of the
  //absolute cartesian coordinate system is used as
  //default reference point to compute the centre of mass
  GProp_GProps System ();
  
  //computes the inertia of a 3d curve
  Your_CGProps Component1 (curve, ....);
  
  //computes the inertia of surfaces
  Your_SGprops Component2 (surface1, ....);
  Your_SGprops Component3 (surface2,....);
  
  //composes the global properties of components 1, 2, 3
  //a density can be associated with the components, the
  //density can be defaulted to 1.
  Real Density1 = 2.0;
  Real Density2 = 3.0;
  System.Add (Component1, Density1);
  System.Add (Component2, Density2);
  System.Add (Component3);
  
  //returns the centre of mass of the system in the
  //absolute cartesian coordinate system
  gp_Pnt G = System.CentreOfMass ();
  
  //computes the principales inertia of the system
  GProp_PrincipalProps Pp = System.PrincipalProperties();
  
  //returns the principal moments and radius of gyration
  Real Ixx, Iyy, Izz, Rxx, Ryy, Rzz;
  Pp.Moments (Ixx, Iyy, Izz);
  Pp.RadiusOfGyration (Ixx, Iyy, Izz);
  
  
  

Constructor & Destructor Documentation

GProp_GProps::GProp_GProps

(

)

The origin (0, 0, 0) of the absolute cartesian coordinate system
is used to compute the global properties.

GProp_GProps::GProp_GProps

(

const gp_Pnt &

SystemLocation

)

The point SystemLocation is used to compute the gobal properties <br>

of the system. For more accuracy it is better to define this
point closed to the location of the system. For example it could
be a point around the centre of mass of the system.
This point is referred to as the reference point for
this framework. For greater accuracy it is better for
the reference point to be close to the location of the
system. It can, for example, be a point near the
center of mass of the system.
At initialization, the framework is empty; i.e. it
retains no dimensional information such as mass, or
inertia. However, it is now able to bring together
global properties of various other systems, whose
global properties have already been computed
using another framework. To do this, use the
function Add to define the components of the
system. Use it once per component of the system,
and then use the interrogation functions available to
access the computed values.

Member Function Documentation

void GProp_GProps::Add	(	const GProp_GProps &	Item,
		const Standard_Real	Density = 1.0
	)

Either

• initializes the global properties retained by this
  framework from those retained by the framework Item, or
  
• brings together the global properties still retained by
  this framework with those retained by the framework Item.
  The value Density, which is 1.0 by default, is used as
  the density of the system analysed by Item.
  Sometimes the density will have already been given at
  the time of construction of the framework Item. This
  may be the case for example, if Item is a
  GProp_PGProps framework built to compute the
  global properties of a set of points ; or another
  GProp_GProps object which already retains
  composite global properties. In these cases the real
  density was perhaps already taken into account at the
  time of construction of Item. Note that this is not
  checked: if the density of parts of the system is taken
  into account two or more times, results of the
  computation will be false.
  Notes :
  
• The point relative to which the inertia of Item is
  computed (i.e. the reference point of Item) may be
  different from the reference point in this
  framework. Huygens' theorem is applied
  automatically to transfer inertia values to the
  reference point in this framework.
  
• The function Add is used once per component of
  the system. After that, you use the interrogation
  functions available to access values computed for the system.
  
• The system whose global properties are already
  brought together by this framework is referred to
  as the current system. However, the current system
  is not retained by this framework, which maintains
  only its global properties.
  Exceptions
  Standard_DomainError if Density is less than or
  equal to gp::Resolution().
  

gp_Pnt GProp_GProps::CentreOfMass

(

)

const

Returns the center of mass of the current system. If <br>

the gravitational field is uniform, it is the center of gravity.
The coordinates returned for the center of mass are
expressed in the absolute Cartesian coordinate system.

Standard_Real GProp_GProps::Mass

(

)

const

 Returns the mass of the current system. <br>

If no density is attached to the components of the
current system the returned value corresponds to :

• the total length of the edges of the current
  system if this framework retains only linear
  properties, as is the case for example, when
  using only the LinearProperties function to
  combine properties of lines from shapes, or
  
• the total area of the faces of the current system if
  this framework retains only surface properties,
  as is the case for example, when using only the
  SurfaceProperties function to combine
  properties of surfaces from shapes, or
  
• the total volume of the solids of the current
  system if this framework retains only volume
  properties, as is the case for example, when
  using only the VolumeProperties function to
  combine properties of volumes from solids.
  Warning
  A length, an area, or a volume is computed in the
  current data unit system. The mass of a single
  object is obtained by multiplying its length, its area
  or its volume by the given density. You must be
  consistent with respect to the units used.
  

gp_Mat GProp_GProps::MatrixOfInertia

(

)

const

returns the matrix of inertia. It is a symmetrical matrix. <br>

The coefficients of the matrix are the quadratic moments of
inertia.

| Ixx Ixy Ixz |
matrix = | Ixy Iyy Iyz |
| Ixz Iyz Izz |

The moments of inertia are denoted by Ixx, Iyy, Izz.
The products of inertia are denoted by Ixy, Ixz, Iyz.
The matrix of inertia is returned in the central coordinate
system (G, Gx, Gy, Gz) where G is the centre of mass of the
system and Gx, Gy, Gz the directions parallel to the X(1,0,0)
Y(0,1,0) Z(0,0,1) directions of the absolute cartesian
coordinate system. It is possible to compute the matrix of
inertia at another location point using the Huyghens theorem
(you can use the method of package GProp : HOperator).

Standard_Real GProp_GProps::MomentOfInertia

(

const gp_Ax1 &

A

)

const

computes the moment of inertia of the material system about the
axis A.

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.

Standard_Real GProp_GProps::RadiusOfGyration

(

const gp_Ax1 &

A

)

const

Returns the radius of gyration of the current system about the axis A.

void GProp_GProps::StaticMoments	(	Standard_Real &	Ix,
		Standard_Real &	Iy,
		Standard_Real &	Iz
	)		const

 Returns Ix, Iy, Iz, the static moments of inertia of the <br>

current system; i.e. the moments of inertia about the
three axes of the Cartesian coordinate system.

Field Documentation

Standard_Real GProp_GProps::dim

protected

gp_Pnt GProp_GProps::g

protected

gp_Mat GProp_GProps::inertia

protected

gp_Pnt GProp_GProps::loc

protected

---

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

• GProp_GProps.hxx