// Created on: 1993-08-02
// Created by: Laurent BOURESCHE
// Copyright (c) 1993-1999 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_Ax3_HeaderFile
#define _gp_Ax3_HeaderFile
#include
#include
#include
#include
#include
class gp_Trsf;
//! Describes a coordinate system in 3D space. Unlike a
//! gp_Ax2 coordinate system, a gp_Ax3 can be
//! right-handed ("direct sense") or left-handed ("indirect sense").
//! A coordinate system is defined by:
//! - its origin (also referred to as its "Location point"), and
//! - three orthogonal unit vectors, termed 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.
//! "Direction" is also the "Z Direction".
//! The "main Direction" is always parallel to the cross
//! product of its "X Direction" and "Y Direction".
//! If the coordinate system is right-handed, it satisfies the equation:
//! "main Direction" = "X Direction" ^ "Y Direction"
//! and if it is left-handed, it satisfies the equation:
//! "main Direction" = -"X Direction" ^ "Y Direction"
//! 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 three axes", or
//! - to define geometric transformations.
//! Note:
//! - We refer to the "X Axis", "Y Axis" and "Z Axis",
//! respectively, as the 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".
//! - gp_Ax2 is used to define a coordinate system that must be always right-handed.
class gp_Ax3
{
public:
DEFINE_STANDARD_ALLOC
//! Creates an object corresponding to the reference
//! coordinate system (OXYZ).
gp_Ax3() : vydir (0., 1., 0.)
// vxdir(1.,0.,0.) use default ctor of gp_Dir, as it creates the same dir(1,0,0)
{}
//! Creates a coordinate system from a right-handed
//! coordinate system.
gp_Ax3 (const gp_Ax2& theA);
//! Creates a right handed axis placement with the
//! "Location" point theP and two directions, theN gives the
//! "Direction" and theVx gives the "XDirection".
//! Raises ConstructionError if theN and theVx are parallel (same or opposite orientation).
gp_Ax3 (const gp_Pnt& theP, const gp_Dir& theN, const gp_Dir& theVx)
: axis (theP, theN),
vydir(theN),
vxdir(theN)
{
vxdir.CrossCross (theVx, theN);
vydir.Cross (vxdir);
}
//! Creates an axis placement with the "Location" point
//! and the normal direction .
Standard_EXPORT gp_Ax3 (const gp_Pnt& theP, const gp_Dir& theV);
//! Reverses the X direction of .
void XReverse() { vxdir.Reverse(); }
//! Reverses the Y direction of .
void YReverse() { vydir.Reverse(); }
//! Reverses the Z direction of .
void ZReverse() { axis.Reverse(); }
//! Assigns the origin and "main Direction" of the axis theA1 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 theA1.
//! - The orientation of this coordinate system
//! (right-handed or left-handed) is not modified.
//! Raises ConstructionError if the "Direction" of and the "XDirection" of
//! are parallel (same or opposite orientation) because it is
//! impossible to calculate the new "XDirection" and the new
//! "YDirection".
void SetAxis (const gp_Ax1& theA1);
//! 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" = theV ^ (previous "X Direction" ^ theV).
//! - The orientation of this coordinate system (left- or right-handed) is not modified.
//! Raises ConstructionError if and the previous "XDirection" are parallel
//! because it is impossible to calculate the new "XDirection"
//! and the new "YDirection".
void SetDirection (const gp_Dir& theV);
//! Changes the "Location" point (origin) of .
void SetLocation (const gp_Pnt& theP) { axis.SetLocation (theP); }
//! Changes the "Xdirection" of . The main direction
//! "Direction" is not modified, the "Ydirection" is modified.
//! If is not normal to the main direction then
//! is computed as follows XDirection = Direction ^ (theVx ^ Direction).
//! Raises ConstructionError if is parallel (same or opposite
//! orientation) to the main direction of
void SetXDirection (const gp_Dir& theVx);
//! Changes the "Ydirection" of . The main direction is not
//! modified but the "Xdirection" is changed.
//! If is not normal to the main direction then "YDirection"
//! is computed as follows
//! YDirection = Direction ^ ( ^ Direction).
//! Raises ConstructionError if is parallel to the main direction of
void SetYDirection (const gp_Dir& theVy);
//! Computes the angular value between the main direction of
//! and the main direction of . Returns the angle
//! between 0 and PI in radians.
Standard_Real Angle (const gp_Ax3& theOther) const { return axis.Angle (theOther.axis); }
//! Returns the main axis of . It is the "Location" point
//! and the main "Direction".
const gp_Ax1& Axis() const { return axis; }
//! Computes a right-handed coordinate system with the
//! same "X Direction" and "Y Direction" as those of this
//! coordinate system, then recomputes the "main Direction".
//! If this coordinate system is right-handed, the result
//! returned is the same coordinate system. If this
//! coordinate system is left-handed, the result is reversed.
gp_Ax2 Ax2() const;
//! Returns the main direction of .
const gp_Dir& Direction() const { return axis.Direction(); }
//! Returns the "Location" point (origin) of .
const gp_Pnt& Location() const { return axis.Location(); }
//! Returns the "XDirection" of .
const gp_Dir& XDirection() const { return vxdir; }
//! Returns the "YDirection" of .
const gp_Dir& YDirection() const { return vydir; }
//! Returns True if the coordinate system is right-handed. i.e.
//! XDirection().Crossed(YDirection()).Dot(Direction()) > 0
Standard_Boolean Direct() const { return (vxdir.Crossed (vydir).Dot (axis.Direction()) > 0.); }
//! Returns True if
//! . the distance between the "Location" point of and
//! is lower or equal to theLinearTolerance and
//! . the distance between the "Location" point of and
//! is lower or equal to theLinearTolerance and
//! . the main direction of and the main direction of
//! are parallel (same or opposite orientation).
Standard_Boolean IsCoplanar (const gp_Ax3& theOther, const Standard_Real theLinearTolerance, const Standard_Real theAngularTolerance) const;
//! Returns True if
//! . the distance between and the "Location" point of theA1
//! is lower of equal to theLinearTolerance and
//! . the distance between theA1 and the "Location" point of
//! is lower or equal to theLinearTolerance and
//! . the main direction of and the direction of theA1 are normal.
Standard_Boolean IsCoplanar (const gp_Ax1& theA1, const Standard_Real theLinearTolerance, const Standard_Real theAngularTolerance) const;
Standard_EXPORT void Mirror (const gp_Pnt& theP);
//! Performs the symmetrical transformation of an axis
//! placement with respect to the point theP which is the
//! center of the symmetry.
//! Warnings :
//! 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 Standard_EXPORT gp_Ax3 Mirrored (const gp_Pnt& theP) const;
Standard_EXPORT void Mirror (const gp_Ax1& theA1);
//! Performs the symmetrical transformation of an axis
//! placement with respect to an axis placement which
//! is the axis of the symmetry.
//! The transformation is performed on the "Location"
//! point, on the "XDirection" and "YDirection".
//! The resulting main "Direction" is the cross product between
//! the "XDirection" and the "YDirection" after transformation.
Standard_NODISCARD Standard_EXPORT gp_Ax3 Mirrored (const gp_Ax1& theA1) const;
Standard_EXPORT void Mirror (const gp_Ax2& theA2);
//! Performs the symmetrical transformation of an axis
//! placement with respect to a plane.
//! The axis placement locates the plane of the symmetry :
//! (Location, XDirection, YDirection).
//! The transformation is performed on the "Location"
//! point, on the "XDirection" and "YDirection".
//! The resulting main "Direction" is the cross product between
//! the "XDirection" and the "YDirection" after transformation.
Standard_NODISCARD Standard_EXPORT gp_Ax3 Mirrored (const gp_Ax2& theA2) const;
void Rotate (const gp_Ax1& theA1, const Standard_Real theAng)
{
axis.Rotate (theA1, theAng);
vxdir.Rotate (theA1, theAng);
vydir.Rotate (theA1, theAng);
}
//! Rotates an axis placement. is the axis of the
//! rotation . theAng is the angular value of the rotation
//! in radians.
Standard_NODISCARD gp_Ax3 Rotated (const gp_Ax1& theA1, const Standard_Real theAng) const
{
gp_Ax3 aTemp = *this;
aTemp.Rotate (theA1, theAng);
return aTemp;
}
void Scale (const gp_Pnt& theP, const Standard_Real theS)
{
axis.Scale (theP, theS);
if (theS < 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 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_Ax3 Scaled (const gp_Pnt& theP, const Standard_Real theS) const
{
gp_Ax3 aTemp = *this;
aTemp.Scale (theP, theS);
return aTemp;
}
void Transform (const gp_Trsf& theT)
{
axis.Transform (theT);
vxdir.Transform (theT);
vydir.Transform (theT);
}
//! Transforms an axis placement with a Trsf.
//! The "Location" point, the "XDirection" and the
//! "YDirection" are transformed with theT. The resulting
//! main "Direction" of is the cross product between
//! the "XDirection" and the "YDirection" after transformation.
Standard_NODISCARD gp_Ax3 Transformed (const gp_Trsf& theT) const
{
gp_Ax3 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
//! . The magnitude of the translation is the vector's magnitude.
Standard_NODISCARD gp_Ax3 Translated (const gp_Vec& theV) const
{
gp_Ax3 aTemp = *this;
aTemp.Translate (theV);
return aTemp;
}
void Translate (const gp_Pnt& theP1, const gp_Pnt& theP2) { Translate (gp_Vec (theP1, theP2)); }
//! Translates an axis placement from the point to the
//! point .
Standard_NODISCARD gp_Ax3 Translated (const gp_Pnt& theP1, const gp_Pnt& theP2) const { return Translated (gp_Vec (theP1, theP2)); }
//! 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 : gp_Ax3
// purpose :
// =======================================================================
inline gp_Ax3::gp_Ax3 (const gp_Ax2& theA)
: axis (theA.Axis()),
vydir (theA.YDirection()),
vxdir (theA.XDirection())
{}
// =======================================================================
// function : Ax2
// purpose :
// =======================================================================
inline gp_Ax2 gp_Ax3::Ax2()const
{
gp_Dir aZz = axis.Direction();
if (!Direct())
{
aZz.Reverse();
}
return gp_Ax2 (axis.Location(), aZz, vxdir);
}
// =======================================================================
// function : SetAxis
// purpose :
// =======================================================================
inline void gp_Ax3::SetAxis (const gp_Ax1& theA1)
{
Standard_Boolean isDirect = Direct();
axis = theA1;
vxdir = axis.Direction().CrossCrossed (vxdir, axis.Direction());
if (isDirect)
{
vydir = axis.Direction().Crossed (vxdir);
}
else
{
vydir = vxdir.Crossed (axis.Direction());
}
}
// =======================================================================
// function : SetDirection
// purpose :
// =======================================================================
inline void gp_Ax3::SetDirection (const gp_Dir& theV)
{
Standard_Boolean isDirect = Direct();
axis.SetDirection (theV);
vxdir = theV.CrossCrossed (vxdir, theV);
if (isDirect)
{
vydir = theV.Crossed (vxdir);
}
else
{
vydir = vxdir.Crossed (theV);
}
}
// =======================================================================
// function : SetXDirection
// purpose :
// =======================================================================
inline void gp_Ax3::SetXDirection (const gp_Dir& theVx)
{
Standard_Boolean isDirect = Direct();
vxdir = axis.Direction().CrossCrossed (theVx, axis.Direction());
if (isDirect)
{
vydir = axis.Direction().Crossed (vxdir);
}
else
{
vydir = vxdir.Crossed (axis.Direction());
}
}
// =======================================================================
// function : SetYDirection
// purpose :
// =======================================================================
inline void gp_Ax3::SetYDirection (const gp_Dir& theVy)
{
Standard_Boolean isDirect = Direct();
vxdir = theVy.Crossed (axis.Direction());
vydir = (axis.Direction()).Crossed (vxdir);
if (!isDirect)
{
vxdir.Reverse();
}
}
// =======================================================================
// function : IsCoplanar
// purpose :
// =======================================================================
inline Standard_Boolean gp_Ax3::IsCoplanar (const gp_Ax3& theOther,
const Standard_Real theLinearTolerance,
const Standard_Real theAngularTolerance)const
{
gp_Vec aVec (axis.Location(), theOther.axis.Location());
Standard_Real aD1 = gp_Vec (axis.Direction()).Dot(aVec);
if (aD1 < 0)
{
aD1 = -aD1;
}
Standard_Real aD2 = gp_Vec (theOther.axis.Direction()).Dot(aVec);
if (aD2 < 0)
{
aD2 = -aD2;
}
return (aD1 <= theLinearTolerance && aD2 <= theLinearTolerance &&
axis.IsParallel (theOther.axis, theAngularTolerance));
}
// =======================================================================
// function : IsCoplanar
// purpose :
// =======================================================================
inline Standard_Boolean gp_Ax3::IsCoplanar (const gp_Ax1& theA1,
const Standard_Real theLinearTolerance,
const Standard_Real theAngularTolerance)const
{
gp_Vec aVec (axis.Location(), theA1.Location());
Standard_Real aD1 = gp_Vec (axis.Direction()).Dot (aVec);
if (aD1 < 0)
{
aD1 = -aD1;
}
Standard_Real aD2 = (gp_Vec (theA1.Direction()).Crossed (aVec)).Magnitude();
if (aD2 < 0)
{
aD2 = -aD2;
}
return (aD1 <= theLinearTolerance && aD2 <= theLinearTolerance &&
axis.IsNormal (theA1, theAngularTolerance));
}
#endif // _gp_Ax3_HeaderFile