Open CASCADE Technology
6.9.1

Implements a general mechanism to compute the global properties of 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. More...
#include <GProp_GProps.hxx>
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 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. 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 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. The coefficients of the matrix are the quadratic moments of inertia. More...  
void  StaticMoments (Standard_Real &Ix, Standard_Real &Iy, Standard_Real &Iz) const 
Returns Ix, Iy, Iz, the static moments of inertia of the 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. 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 
Implements a general mechanism to compute the global properties of 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 :
The global properties computed are :
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);
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 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.
void GProp_GProps::Add  (  const GProp_GProps &  Item, 
const Standard_Real  Density = 1.0 

) 
Either.
gp_Pnt GProp_GProps::CentreOfMass  (  )  const 
Returns the center of mass of the current system. If 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. If no density is attached to the components of the current system the returned value corresponds to :
gp_Mat GProp_GProps::MatrixOfInertia  (  )  const 
returns the matrix of inertia. It is a symmetrical matrix. 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. 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 current system; i.e. the moments of inertia about the three axes of the Cartesian coordinate system.

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