mirror of
https://git.dev.opencascade.org/repos/occt.git
synced 2025-04-10 18:51:21 +03:00
474 lines
18 KiB
C++
474 lines
18 KiB
C++
// Copyright (c) 1991-1999 Matra Datavision
|
|
// Copyright (c) 1999-2014 OPEN CASCADE SAS
|
|
//
|
|
// This file is part of Open CASCADE Technology software library.
|
|
//
|
|
// This library is free software; you can redistribute it and/or modify it under
|
|
// the terms of the GNU Lesser General Public License version 2.1 as published
|
|
// by the Free Software Foundation, with special exception defined in the file
|
|
// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
|
|
// distribution for complete text of the license and disclaimer of any warranty.
|
|
//
|
|
// Alternatively, this file may be used under the terms of Open CASCADE
|
|
// commercial license or contractual agreement.
|
|
|
|
#ifndef _gp_Ax2_HeaderFile
|
|
#define _gp_Ax2_HeaderFile
|
|
|
|
#include <gp_Ax1.hxx>
|
|
#include <gp_Dir.hxx>
|
|
#include <Precision.hxx>
|
|
|
|
class Standard_ConstructionError;
|
|
class gp_Pnt;
|
|
class gp_Trsf;
|
|
class gp_Vec;
|
|
|
|
//! Describes a right-handed coordinate system in 3D space.
|
|
//! A coordinate system is defined by:
|
|
//! - its origin (also referred to as its "Location point"), and
|
|
//! - three orthogonal unit vectors, termed respectively the
|
|
//! "X Direction", the "Y Direction" and the "Direction" (also
|
|
//! referred to as the "main Direction").
|
|
//! The "Direction" of the coordinate system is called its
|
|
//! "main Direction" because whenever this unit vector is
|
|
//! modified, the "X Direction" and the "Y Direction" are
|
|
//! recomputed. However, when we modify either the "X
|
|
//! Direction" or the "Y Direction", "Direction" is not modified.
|
|
//! The "main Direction" is also the "Z Direction".
|
|
//! Since an Ax2 coordinate system is right-handed, its
|
|
//! "main Direction" is always equal to the cross product of
|
|
//! its "X Direction" and "Y Direction". (To define a
|
|
//! left-handed coordinate system, use gp_Ax3.)
|
|
//! A coordinate system is used:
|
|
//! - to describe geometric entities, in particular to position
|
|
//! them. The local coordinate system of a geometric
|
|
//! entity serves the same purpose as the STEP function
|
|
//! "axis placement two axes", or
|
|
//! - to define geometric transformations.
|
|
//! Note: we refer to the "X Axis", "Y Axis" and "Z Axis",
|
|
//! respectively, as to axes having:
|
|
//! - the origin of the coordinate system as their origin, and
|
|
//! - the unit vectors "X Direction", "Y Direction" and "main
|
|
//! Direction", respectively, as their unit vectors.
|
|
//! The "Z Axis" is also the "main Axis".
|
|
class gp_Ax2
|
|
{
|
|
public:
|
|
|
|
DEFINE_STANDARD_ALLOC
|
|
|
|
//! Creates an object corresponding to the reference
|
|
//! coordinate system (OXYZ).
|
|
gp_Ax2() : vydir(0.,1.,0.)
|
|
// vxdir(1.,0.,0.) use default ctor of gp_Dir, as it creates the same dir(1,0,0)
|
|
{}
|
|
|
|
//! Creates an axis placement with an origin P such that:
|
|
//! - N is the Direction, and
|
|
//! - the "X Direction" is normal to N, in the plane
|
|
//! defined by the vectors (N, Vx): "X
|
|
//! Direction" = (N ^ Vx) ^ N,
|
|
//! Exception: raises ConstructionError if N and Vx are parallel (same or opposite orientation).
|
|
gp_Ax2 (const gp_Pnt& P, const gp_Dir& N, const gp_Dir& Vx)
|
|
: axis (P, N),
|
|
vydir (N),
|
|
vxdir (N)
|
|
{
|
|
vxdir.CrossCross(Vx, N);
|
|
vydir.Cross(vxdir);
|
|
}
|
|
|
|
//! Creates - a coordinate system with an origin P, where V
|
|
//! gives the "main Direction" (here, "X Direction" and "Y
|
|
//! Direction" are defined automatically).
|
|
Standard_EXPORT gp_Ax2(const gp_Pnt& P, const gp_Dir& V);
|
|
|
|
//! Assigns the origin and "main Direction" of the axis A1 to
|
|
//! this coordinate system, then recomputes its "X Direction" and "Y Direction".
|
|
//! Note: The new "X Direction" is computed as follows:
|
|
//! new "X Direction" = V1 ^(previous "X Direction" ^ V)
|
|
//! where V is the "Direction" of A1.
|
|
//! Exceptions
|
|
//! Standard_ConstructionError if A1 is parallel to the "X
|
|
//! Direction" of this coordinate system.
|
|
void SetAxis (const gp_Ax1& A1);
|
|
|
|
//! Changes the "main Direction" of this coordinate system,
|
|
//! then recomputes its "X Direction" and "Y Direction".
|
|
//! Note: the new "X Direction" is computed as follows:
|
|
//! new "X Direction" = V ^ (previous "X Direction" ^ V)
|
|
//! Exceptions
|
|
//! Standard_ConstructionError if V is parallel to the "X
|
|
//! Direction" of this coordinate system.
|
|
void SetDirection (const gp_Dir& V);
|
|
|
|
//! Changes the "Location" point (origin) of <me>.
|
|
void SetLocation (const gp_Pnt& theP) { axis.SetLocation (theP); }
|
|
|
|
//! Changes the "Xdirection" of <me>. The main direction
|
|
//! "Direction" is not modified, the "Ydirection" is modified.
|
|
//! If <Vx> is not normal to the main direction then <XDirection>
|
|
//! is computed as follows XDirection = Direction ^ (Vx ^ Direction).
|
|
//! Exceptions
|
|
//! Standard_ConstructionError if Vx or Vy is parallel to
|
|
//! the "main Direction" of this coordinate system.
|
|
void SetXDirection (const gp_Dir& theVx)
|
|
{
|
|
vxdir = axis.Direction().CrossCrossed (theVx, axis.Direction());
|
|
vydir = axis.Direction().Crossed (vxdir);
|
|
}
|
|
|
|
//! Changes the "Ydirection" of <me>. The main direction is not
|
|
//! modified but the "Xdirection" is changed.
|
|
//! If <Vy> is not normal to the main direction then "YDirection"
|
|
//! is computed as follows
|
|
//! YDirection = Direction ^ (<Vy> ^ Direction).
|
|
//! Exceptions
|
|
//! Standard_ConstructionError if Vx or Vy is parallel to
|
|
//! the "main Direction" of this coordinate system.
|
|
void SetYDirection (const gp_Dir& theVy)
|
|
{
|
|
vxdir = theVy.Crossed (axis.Direction());
|
|
vydir = (axis.Direction()).Crossed (vxdir);
|
|
}
|
|
|
|
//! Computes the angular value, in radians, between the main direction of
|
|
//! <me> and the main direction of <theOther>. Returns the angle
|
|
//! between 0 and PI in radians.
|
|
Standard_Real Angle (const gp_Ax2& theOther) const { return axis.Angle (theOther.axis); }
|
|
|
|
//! Returns the main axis of <me>. It is the "Location" point
|
|
//! and the main "Direction".
|
|
const gp_Ax1& Axis() const { return axis; }
|
|
|
|
//! Returns the main direction of <me>.
|
|
const gp_Dir& Direction() const { return axis.Direction(); }
|
|
|
|
//! Returns the "Location" point (origin) of <me>.
|
|
const gp_Pnt& Location() const { return axis.Location(); }
|
|
|
|
//! Returns the "XDirection" of <me>.
|
|
const gp_Dir& XDirection() const { return vxdir; }
|
|
|
|
//! Returns the "YDirection" of <me>.
|
|
const gp_Dir& YDirection() const { return vydir; }
|
|
|
|
Standard_Boolean IsCoplanar (const gp_Ax2& Other, const Standard_Real LinearTolerance, const Standard_Real AngularTolerance) const;
|
|
|
|
//! Returns True if
|
|
//! . the distance between <me> and the "Location" point of A1
|
|
//! is lower of equal to LinearTolerance and
|
|
//! . the main direction of <me> and the direction of A1 are normal.
|
|
//! Note: the tolerance criterion for angular equality is given by AngularTolerance.
|
|
Standard_Boolean IsCoplanar (const gp_Ax1& A1, const Standard_Real LinearTolerance, const Standard_Real AngularTolerance) const;
|
|
|
|
//! Performs a symmetrical transformation of this coordinate
|
|
//! system with respect to:
|
|
//! - the point P, and assigns the result to this coordinate system.
|
|
//! Warning
|
|
//! This transformation is always performed on the origin.
|
|
//! In case of a reflection with respect to a point:
|
|
//! - the main direction of the coordinate system is not changed, and
|
|
//! - the "X Direction" and the "Y Direction" are simply reversed
|
|
//! In case of a reflection with respect to an axis or a plane:
|
|
//! - the transformation is applied to the "X Direction"
|
|
//! and the "Y Direction", then
|
|
//! - the "main Direction" is recomputed as the cross
|
|
//! product "X Direction" ^ "Y Direction".
|
|
//! This maintains the right-handed property of the
|
|
//! coordinate system.
|
|
Standard_EXPORT void Mirror (const gp_Pnt& P);
|
|
|
|
//! Performs a symmetrical transformation of this coordinate
|
|
//! system with respect to:
|
|
//! - the point P, and creates a new one.
|
|
//! Warning
|
|
//! This transformation is always performed on the origin.
|
|
//! In case of a reflection with respect to a point:
|
|
//! - the main direction of the coordinate system is not changed, and
|
|
//! - the "X Direction" and the "Y Direction" are simply reversed
|
|
//! In case of a reflection with respect to an axis or a plane:
|
|
//! - the transformation is applied to the "X Direction"
|
|
//! and the "Y Direction", then
|
|
//! - the "main Direction" is recomputed as the cross
|
|
//! product "X Direction" ^ "Y Direction".
|
|
//! This maintains the right-handed property of the
|
|
//! coordinate system.
|
|
Standard_NODISCARD Standard_EXPORT gp_Ax2 Mirrored (const gp_Pnt& P) const;
|
|
|
|
//! Performs a symmetrical transformation of this coordinate
|
|
//! system with respect to:
|
|
//! - the axis A1, and assigns the result to this coordinate systeme.
|
|
//! Warning
|
|
//! This transformation is always performed on the origin.
|
|
//! In case of a reflection with respect to a point:
|
|
//! - the main direction of the coordinate system is not changed, and
|
|
//! - the "X Direction" and the "Y Direction" are simply reversed
|
|
//! In case of a reflection with respect to an axis or a plane:
|
|
//! - the transformation is applied to the "X Direction"
|
|
//! and the "Y Direction", then
|
|
//! - the "main Direction" is recomputed as the cross
|
|
//! product "X Direction" ^ "Y Direction".
|
|
//! This maintains the right-handed property of the
|
|
//! coordinate system.
|
|
Standard_EXPORT void Mirror (const gp_Ax1& A1);
|
|
|
|
//! Performs a symmetrical transformation of this coordinate
|
|
//! system with respect to:
|
|
//! - the axis A1, and creates a new one.
|
|
//! Warning
|
|
//! This transformation is always performed on the origin.
|
|
//! In case of a reflection with respect to a point:
|
|
//! - the main direction of the coordinate system is not changed, and
|
|
//! - the "X Direction" and the "Y Direction" are simply reversed
|
|
//! In case of a reflection with respect to an axis or a plane:
|
|
//! - the transformation is applied to the "X Direction"
|
|
//! and the "Y Direction", then
|
|
//! - the "main Direction" is recomputed as the cross
|
|
//! product "X Direction" ^ "Y Direction".
|
|
//! This maintains the right-handed property of the
|
|
//! coordinate system.
|
|
Standard_NODISCARD Standard_EXPORT gp_Ax2 Mirrored (const gp_Ax1& A1) const;
|
|
|
|
//! Performs a symmetrical transformation of this coordinate
|
|
//! system with respect to:
|
|
//! - the plane defined by the origin, "X Direction" and "Y
|
|
//! Direction" of coordinate system A2 and assigns the result to this coordinate systeme.
|
|
//! Warning
|
|
//! This transformation is always performed on the origin.
|
|
//! In case of a reflection with respect to a point:
|
|
//! - the main direction of the coordinate system is not changed, and
|
|
//! - the "X Direction" and the "Y Direction" are simply reversed
|
|
//! In case of a reflection with respect to an axis or a plane:
|
|
//! - the transformation is applied to the "X Direction"
|
|
//! and the "Y Direction", then
|
|
//! - the "main Direction" is recomputed as the cross
|
|
//! product "X Direction" ^ "Y Direction".
|
|
//! This maintains the right-handed property of the
|
|
//! coordinate system.
|
|
Standard_EXPORT void Mirror (const gp_Ax2& A2);
|
|
|
|
//! Performs a symmetrical transformation of this coordinate
|
|
//! system with respect to:
|
|
//! - the plane defined by the origin, "X Direction" and "Y
|
|
//! Direction" of coordinate system A2 and creates a new one.
|
|
//! Warning
|
|
//! This transformation is always performed on the origin.
|
|
//! In case of a reflection with respect to a point:
|
|
//! - the main direction of the coordinate system is not changed, and
|
|
//! - the "X Direction" and the "Y Direction" are simply reversed
|
|
//! In case of a reflection with respect to an axis or a plane:
|
|
//! - the transformation is applied to the "X Direction"
|
|
//! and the "Y Direction", then
|
|
//! - the "main Direction" is recomputed as the cross
|
|
//! product "X Direction" ^ "Y Direction".
|
|
//! This maintains the right-handed property of the
|
|
//! coordinate system.
|
|
Standard_NODISCARD Standard_EXPORT gp_Ax2 Mirrored (const gp_Ax2& A2) const;
|
|
|
|
void Rotate (const gp_Ax1& theA1, const Standard_Real theAng)
|
|
{
|
|
gp_Pnt aTemp = axis.Location();
|
|
aTemp.Rotate (theA1, theAng);
|
|
axis.SetLocation (aTemp);
|
|
vxdir.Rotate (theA1, theAng);
|
|
vydir.Rotate (theA1, theAng);
|
|
axis.SetDirection (vxdir.Crossed (vydir));
|
|
}
|
|
|
|
//! Rotates an axis placement. <theA1> is the axis of the rotation.
|
|
//! theAng is the angular value of the rotation in radians.
|
|
Standard_NODISCARD gp_Ax2 Rotated (const gp_Ax1& theA1, const Standard_Real theAng) const
|
|
{
|
|
gp_Ax2 aTemp = *this;
|
|
aTemp.Rotate (theA1, theAng);
|
|
return aTemp;
|
|
}
|
|
|
|
void Scale (const gp_Pnt& theP, const Standard_Real theS)
|
|
{
|
|
gp_Pnt aTemp = axis.Location();
|
|
aTemp.Scale (theP, theS);
|
|
axis.SetLocation (aTemp);
|
|
if (theS < 0.0)
|
|
{
|
|
vxdir.Reverse();
|
|
vydir.Reverse();
|
|
}
|
|
}
|
|
|
|
//! Applies a scaling transformation on the axis placement.
|
|
//! The "Location" point of the axisplacement is modified.
|
|
//! Warnings :
|
|
//! If the scale <S> is negative :
|
|
//! . the main direction of the axis placement is not changed.
|
|
//! . The "XDirection" and the "YDirection" are reversed.
|
|
//! So the axis placement stay right handed.
|
|
Standard_NODISCARD gp_Ax2 Scaled (const gp_Pnt& theP, const Standard_Real theS) const
|
|
{
|
|
gp_Ax2 aTemp = *this;
|
|
aTemp.Scale (theP, theS);
|
|
return aTemp;
|
|
}
|
|
|
|
void Transform (const gp_Trsf& theT)
|
|
{
|
|
gp_Pnt aTemp = axis.Location();
|
|
aTemp.Transform (theT);
|
|
axis.SetLocation (aTemp);
|
|
vxdir.Transform (theT);
|
|
vydir.Transform (theT);
|
|
axis.SetDirection (vxdir.Crossed (vydir));
|
|
}
|
|
|
|
//! Transforms an axis placement with a Trsf.
|
|
//! The "Location" point, the "XDirection" and the "YDirection" are transformed with theT.
|
|
//! The resulting main "Direction" of <me> is the cross product between
|
|
//! the "XDirection" and the "YDirection" after transformation.
|
|
Standard_NODISCARD gp_Ax2 Transformed (const gp_Trsf& theT) const
|
|
{
|
|
gp_Ax2 aTemp = *this;
|
|
aTemp.Transform (theT);
|
|
return aTemp;
|
|
}
|
|
|
|
void Translate (const gp_Vec& theV) { axis.Translate (theV); }
|
|
|
|
//! Translates an axis plaxement in the direction of the vector <theV>.
|
|
//! The magnitude of the translation is the vector's magnitude.
|
|
Standard_NODISCARD gp_Ax2 Translated (const gp_Vec& theV) const
|
|
{
|
|
gp_Ax2 aTemp = *this;
|
|
aTemp.Translate (theV);
|
|
return aTemp;
|
|
}
|
|
|
|
void Translate (const gp_Pnt& theP1, const gp_Pnt& theP2) { axis.Translate (theP1, theP2); }
|
|
|
|
//! Translates an axis placement from the point <theP1> to the point <theP2>.
|
|
Standard_NODISCARD gp_Ax2 Translated (const gp_Pnt& theP1, const gp_Pnt& theP2) const
|
|
{
|
|
gp_Ax2 aTemp = *this;
|
|
aTemp.Translate (theP1, theP2);
|
|
return aTemp;
|
|
}
|
|
|
|
//! Dumps the content of me into the stream
|
|
Standard_EXPORT void DumpJson (Standard_OStream& theOStream, Standard_Integer theDepth = -1) const;
|
|
|
|
//! Inits the content of me from the stream
|
|
Standard_EXPORT Standard_Boolean InitFromJson (const Standard_SStream& theSStream, Standard_Integer& theStreamPos);
|
|
|
|
private:
|
|
|
|
gp_Ax1 axis;
|
|
gp_Dir vydir;
|
|
gp_Dir vxdir;
|
|
|
|
};
|
|
|
|
// =======================================================================
|
|
// function : SetAxis
|
|
// purpose :
|
|
// =======================================================================
|
|
inline void gp_Ax2::SetAxis (const gp_Ax1& theA1)
|
|
{
|
|
Standard_Real a = theA1.Direction() * vxdir;
|
|
if (Abs(Abs(a) - 1.) <= Precision::Angular())
|
|
{
|
|
if (a > 0.)
|
|
{
|
|
vxdir = vydir;
|
|
vydir = axis.Direction();
|
|
axis = theA1;
|
|
}
|
|
else
|
|
{
|
|
vxdir = axis.Direction();
|
|
axis = theA1;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
axis = theA1;
|
|
vxdir = axis.Direction().CrossCrossed (vxdir, axis.Direction());
|
|
vydir = axis.Direction().Crossed (vxdir);
|
|
}
|
|
}
|
|
|
|
// =======================================================================
|
|
// function : SetDirection
|
|
// purpose :
|
|
// =======================================================================
|
|
inline void gp_Ax2::SetDirection (const gp_Dir& theV)
|
|
{
|
|
Standard_Real a = theV * vxdir;
|
|
if (Abs(Abs(a) - 1.) <= Precision::Angular())
|
|
{
|
|
if(a > 0.)
|
|
{
|
|
vxdir = vydir;
|
|
vydir = axis.Direction();
|
|
axis.SetDirection (theV);
|
|
}
|
|
else
|
|
{
|
|
vxdir = axis.Direction();
|
|
axis.SetDirection (theV);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
axis.SetDirection (theV);
|
|
vxdir = theV.CrossCrossed (vxdir, theV);
|
|
vydir = theV.Crossed (vxdir);
|
|
}
|
|
}
|
|
|
|
// =======================================================================
|
|
// function : IsCoplanar
|
|
// purpose :
|
|
// =======================================================================
|
|
inline Standard_Boolean gp_Ax2::IsCoplanar (const gp_Ax2& theOther,
|
|
const Standard_Real theLinearTolerance,
|
|
const Standard_Real theAngularTolerance) const
|
|
{
|
|
const gp_Dir& DD = axis.Direction();
|
|
const gp_Pnt& PP = axis.Location();
|
|
const gp_Pnt& OP = theOther.axis.Location();
|
|
Standard_Real D1 = (DD.X() * (OP.X() - PP.X())
|
|
+ DD.Y() * (OP.Y() - PP.Y())
|
|
+ DD.Z() * (OP.Z() - PP.Z()));
|
|
if (D1 < 0)
|
|
{
|
|
D1 = -D1;
|
|
}
|
|
return D1 <= theLinearTolerance
|
|
&& axis.IsParallel (theOther.axis, theAngularTolerance);
|
|
}
|
|
|
|
// =======================================================================
|
|
// function : IsCoplanar
|
|
// purpose :
|
|
// =======================================================================
|
|
inline Standard_Boolean gp_Ax2::IsCoplanar (const gp_Ax1& theA,
|
|
const Standard_Real theLinearTolerance,
|
|
const Standard_Real theAngularTolerance) const
|
|
{
|
|
const gp_Dir& DD = axis.Direction();
|
|
const gp_Pnt& PP = axis.Location();
|
|
const gp_Pnt& AP = theA.Location();
|
|
Standard_Real D1 = (DD.X() * (AP.X() - PP.X()) +
|
|
DD.Y() * (AP.Y() - PP.Y()) +
|
|
DD.Z() * (AP.Z() - PP.Z()));
|
|
if (D1 < 0)
|
|
{
|
|
D1 = -D1;
|
|
}
|
|
return D1 <= theLinearTolerance
|
|
&& axis.IsNormal (theA, theAngularTolerance);
|
|
}
|
|
|
|
#endif // _gp_Ax2_HeaderFile
|