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-- File: PrincipalProps.cdl
-- Created: Mon Feb 17 17:50:44 1992
-- Author: Jean Claude VAUTHIER
---Copyright: Matra Datavision 1992
class PrincipalProps
from GProp
---Purpose:
-- 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.
uses Vec from gp,
Pnt from gp
raises UndefinedAxis from GProp
is
Create returns PrincipalProps;
--- Purpose : creates an undefined PrincipalProps.
HasSymmetryAxis (me) returns Boolean is static;
--- Purpose :
-- 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.
HasSymmetryAxis (me; aTol : Real) returns Boolean is static;
--- Purpose :
-- 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))
HasSymmetryPoint (me) returns Boolean is static;
--- Purpose :
-- 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.
HasSymmetryPoint (me; aTol : Real) returns Boolean is static;
--- Purpose :
-- 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))
Moments (me; Ixx, Iyy, Izz: out Real) is static;
--- Purpose : 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.
FirstAxisOfInertia (me) returns Vec
--- Purpose : returns the first axis of inertia.
raises UndefinedAxis
--- Purpose :
-- 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.
---C++: return const&
is static;
SecondAxisOfInertia (me) returns Vec
--- Purpose : returns the second axis of inertia.
raises UndefinedAxis
--- Purpose :
-- if the system has a point of symmetry or an axis of symmetry the
-- second and the third axis of symmetry are undefined.
---C++: return const&
is static;
ThirdAxisOfInertia (me) returns Vec
--- Purpose : 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.
raises UndefinedAxis
--- Purpose :
-- if the system has a point of symmetry or an axis of symmetry the
-- second and the third axis of symmetry are undefined.
---C++: return const&
is static;
RadiusOfGyration (me; Rxx, Ryy, Rzz : out Real) is static;
--- Purpose : 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.
Create (Ixx, Iyy, Izz, Rxx, Ryy, Rzz : Real; Vxx, Vyy, Vzz : Vec; G : Pnt)
returns PrincipalProps
is private;
fields
i1 : Real;
i2 : Real;
i3 : Real;
r1 : Real;
r2 : Real;
r3 : Real;
v1 : Vec;
v2 : Vec;
v3 : Vec;
g : Pnt;
friends
PrincipalProperties from GProps (me)
end PrincipalProps;
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