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353 lines
13 KiB
C++
353 lines
13 KiB
C++
// Copyright (c) 1991-1999 Matra Datavision
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// Copyright (c) 1999-2014 OPEN CASCADE SAS
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//
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// This file is part of Open CASCADE Technology software library.
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//
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// This library is free software; you can redistribute it and/or modify it under
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// the terms of the GNU Lesser General Public License version 2.1 as published
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// by the Free Software Foundation, with special exception defined in the file
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// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
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// distribution for complete text of the license and disclaimer of any warranty.
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//
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// Alternatively, this file may be used under the terms of Open CASCADE
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// commercial license or contractual agreement.
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#ifndef _gp_Ax2_HeaderFile
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#define _gp_Ax2_HeaderFile
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#include <Standard.hxx>
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#include <Standard_DefineAlloc.hxx>
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#include <Standard_Handle.hxx>
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#include <gp_Ax1.hxx>
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#include <gp_Dir.hxx>
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#include <Standard_Real.hxx>
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#include <Standard_Boolean.hxx>
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class Standard_ConstructionError;
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class gp_Pnt;
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class gp_Dir;
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class gp_Ax1;
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class gp_Trsf;
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class gp_Vec;
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//! Describes a right-handed coordinate system in 3D space.
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//! A coordinate system is defined by:
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//! - its origin (also referred to as its "Location point"), and
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//! - three orthogonal unit vectors, termed respectively the
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//! "X Direction", the "Y Direction" and the "Direction" (also
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//! referred to as the "main Direction").
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//! The "Direction" of the coordinate system is called its
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//! "main Direction" because whenever this unit vector is
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//! modified, the "X Direction" and the "Y Direction" are
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//! recomputed. However, when we modify either the "X
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//! Direction" or the "Y Direction", "Direction" is not modified.
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//! The "main Direction" is also the "Z Direction".
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//! Since an Ax2 coordinate system is right-handed, its
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//! "main Direction" is always equal to the cross product of
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//! its "X Direction" and "Y Direction". (To define a
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//! left-handed coordinate system, use gp_Ax3.)
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//! A coordinate system is used:
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//! - to describe geometric entities, in particular to position
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//! them. The local coordinate system of a geometric
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//! entity serves the same purpose as the STEP function
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//! "axis placement two axes", or
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//! - to define geometric transformations.
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//! Note: we refer to the "X Axis", "Y Axis" and "Z Axis",
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//! respectively, as to axes having:
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//! - the origin of the coordinate system as their origin, and
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//! - the unit vectors "X Direction", "Y Direction" and "main
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//! Direction", respectively, as their unit vectors.
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//! The "Z Axis" is also the "main Axis".
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class gp_Ax2
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{
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public:
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DEFINE_STANDARD_ALLOC
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//! Creates an object corresponding to the reference
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//! coordinate system (OXYZ).
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gp_Ax2();
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//! Creates an axis placement with an origin P such that:
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//! - N is the Direction, and
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//! - the "X Direction" is normal to N, in the plane
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//! defined by the vectors (N, Vx): "X
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//! Direction" = (N ^ Vx) ^ N,
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//! Exception: raises ConstructionError if N and Vx are parallel (same or opposite orientation).
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gp_Ax2(const gp_Pnt& P, const gp_Dir& N, const gp_Dir& Vx);
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//! Creates - a coordinate system with an origin P, where V
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//! gives the "main Direction" (here, "X Direction" and "Y
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//! Direction" are defined automatically).
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Standard_EXPORT gp_Ax2(const gp_Pnt& P, const gp_Dir& V);
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//! Assigns the origin and "main Direction" of the axis A1 to
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//! this coordinate system, then recomputes its "X Direction" and "Y Direction".
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//! Note: The new "X Direction" is computed as follows:
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//! new "X Direction" = V1 ^(previous "X Direction" ^ V)
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//! where V is the "Direction" of A1.
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//! Exceptions
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//! Standard_ConstructionError if A1 is parallel to the "X
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//! Direction" of this coordinate system.
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void SetAxis (const gp_Ax1& A1);
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//! Changes the "main Direction" of this coordinate system,
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//! then recomputes its "X Direction" and "Y Direction".
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//! Note: the new "X Direction" is computed as follows:
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//! new "X Direction" = V ^ (previous "X Direction" ^ V)
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//! Exceptions
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//! Standard_ConstructionError if V is parallel to the "X
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//! Direction" of this coordinate system.
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void SetDirection (const gp_Dir& V);
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//! Changes the "Location" point (origin) of <me>.
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void SetLocation (const gp_Pnt& P);
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//! Changes the "Xdirection" of <me>. The main direction
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//! "Direction" is not modified, the "Ydirection" is modified.
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//! If <Vx> is not normal to the main direction then <XDirection>
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//! is computed as follows XDirection = Direction ^ (Vx ^ Direction).
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//! Exceptions
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//! Standard_ConstructionError if Vx or Vy is parallel to
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//! the "main Direction" of this coordinate system.
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void SetXDirection (const gp_Dir& Vx);
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//! Changes the "Ydirection" of <me>. The main direction is not
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//! modified but the "Xdirection" is changed.
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//! If <Vy> is not normal to the main direction then "YDirection"
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//! is computed as follows
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//! YDirection = Direction ^ (<Vy> ^ Direction).
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//! Exceptions
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//! Standard_ConstructionError if Vx or Vy is parallel to
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//! the "main Direction" of this coordinate system.
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void SetYDirection (const gp_Dir& Vy);
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//! Computes the angular value, in radians, between the main direction of
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//! <me> and the main direction of <Other>. Returns the angle
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//! between 0 and PI in radians.
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Standard_Real Angle (const gp_Ax2& Other) const;
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//! Returns the main axis of <me>. It is the "Location" point
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//! and the main "Direction".
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const gp_Ax1& Axis() const;
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//! Returns the main direction of <me>.
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const gp_Dir& Direction() const;
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//! Returns the "Location" point (origin) of <me>.
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const gp_Pnt& Location() const;
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//! Returns the "XDirection" of <me>.
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const gp_Dir& XDirection() const;
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//! Returns the "YDirection" of <me>.
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const gp_Dir& YDirection() const;
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Standard_Boolean IsCoplanar (const gp_Ax2& Other, const Standard_Real LinearTolerance, const Standard_Real AngularTolerance) const;
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//! Returns True if
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//! . the distance between <me> and the "Location" point of A1
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//! is lower of equal to LinearTolerance and
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//! . the main direction of <me> and the direction of A1 are normal.
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//! Note: the tolerance criterion for angular equality is given by AngularTolerance.
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Standard_Boolean IsCoplanar (const gp_Ax1& A1, const Standard_Real LinearTolerance, const Standard_Real AngularTolerance) const;
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//! Performs a symmetrical transformation of this coordinate
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//! system with respect to:
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//! - the point P, and assigns the result to this coordinate system.
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//! Warning
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//! This transformation is always performed on the origin.
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//! In case of a reflection with respect to a point:
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//! - the main direction of the coordinate system is not changed, and
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//! - the "X Direction" and the "Y Direction" are simply reversed
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//! In case of a reflection with respect to an axis or a plane:
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//! - the transformation is applied to the "X Direction"
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//! and the "Y Direction", then
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//! - the "main Direction" is recomputed as the cross
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//! product "X Direction" ^ "Y Direction".
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//! This maintains the right-handed property of the
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//! coordinate system.
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Standard_EXPORT void Mirror (const gp_Pnt& P);
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//! Performs a symmetrical transformation of this coordinate
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//! system with respect to:
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//! - the point P, and creates a new one.
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//! Warning
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//! This transformation is always performed on the origin.
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//! In case of a reflection with respect to a point:
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//! - the main direction of the coordinate system is not changed, and
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//! - the "X Direction" and the "Y Direction" are simply reversed
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//! In case of a reflection with respect to an axis or a plane:
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//! - the transformation is applied to the "X Direction"
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//! and the "Y Direction", then
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//! - the "main Direction" is recomputed as the cross
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//! product "X Direction" ^ "Y Direction".
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//! This maintains the right-handed property of the
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//! coordinate system.
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Standard_EXPORT gp_Ax2 Mirrored (const gp_Pnt& P) const;
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//! Performs a symmetrical transformation of this coordinate
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//! system with respect to:
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//! - the axis A1, and assigns the result to this coordinate systeme.
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//! Warning
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//! This transformation is always performed on the origin.
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//! In case of a reflection with respect to a point:
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//! - the main direction of the coordinate system is not changed, and
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//! - the "X Direction" and the "Y Direction" are simply reversed
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//! In case of a reflection with respect to an axis or a plane:
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//! - the transformation is applied to the "X Direction"
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//! and the "Y Direction", then
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//! - the "main Direction" is recomputed as the cross
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//! product "X Direction" ^ "Y Direction".
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//! This maintains the right-handed property of the
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//! coordinate system.
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Standard_EXPORT void Mirror (const gp_Ax1& A1);
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//! Performs a symmetrical transformation of this coordinate
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//! system with respect to:
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//! - the axis A1, and creates a new one.
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//! Warning
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//! This transformation is always performed on the origin.
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//! In case of a reflection with respect to a point:
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//! - the main direction of the coordinate system is not changed, and
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//! - the "X Direction" and the "Y Direction" are simply reversed
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//! In case of a reflection with respect to an axis or a plane:
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//! - the transformation is applied to the "X Direction"
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//! and the "Y Direction", then
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//! - the "main Direction" is recomputed as the cross
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//! product "X Direction" ^ "Y Direction".
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//! This maintains the right-handed property of the
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//! coordinate system.
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Standard_EXPORT gp_Ax2 Mirrored (const gp_Ax1& A1) const;
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//! Performs a symmetrical transformation of this coordinate
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//! system with respect to:
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//! - the plane defined by the origin, "X Direction" and "Y
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//! Direction" of coordinate system A2 and assigns the result to this coordinate systeme.
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//! Warning
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//! This transformation is always performed on the origin.
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//! In case of a reflection with respect to a point:
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//! - the main direction of the coordinate system is not changed, and
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//! - the "X Direction" and the "Y Direction" are simply reversed
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//! In case of a reflection with respect to an axis or a plane:
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//! - the transformation is applied to the "X Direction"
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//! and the "Y Direction", then
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//! - the "main Direction" is recomputed as the cross
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//! product "X Direction" ^ "Y Direction".
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//! This maintains the right-handed property of the
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//! coordinate system.
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Standard_EXPORT void Mirror (const gp_Ax2& A2);
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//! Performs a symmetrical transformation of this coordinate
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//! system with respect to:
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//! - the plane defined by the origin, "X Direction" and "Y
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//! Direction" of coordinate system A2 and creates a new one.
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//! Warning
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//! This transformation is always performed on the origin.
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//! In case of a reflection with respect to a point:
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//! - the main direction of the coordinate system is not changed, and
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//! - the "X Direction" and the "Y Direction" are simply reversed
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//! In case of a reflection with respect to an axis or a plane:
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//! - the transformation is applied to the "X Direction"
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//! and the "Y Direction", then
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//! - the "main Direction" is recomputed as the cross
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//! product "X Direction" ^ "Y Direction".
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//! This maintains the right-handed property of the
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//! coordinate system.
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Standard_EXPORT gp_Ax2 Mirrored (const gp_Ax2& A2) const;
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void Rotate (const gp_Ax1& A1, const Standard_Real Ang);
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//! Rotates an axis placement. <A1> is the axis of the
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//! rotation . Ang is the angular value of the rotation
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//! in radians.
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gp_Ax2 Rotated (const gp_Ax1& A1, const Standard_Real Ang) const;
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void Scale (const gp_Pnt& P, const Standard_Real S);
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//! Applies a scaling transformation on the axis placement.
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//! The "Location" point of the axisplacement is modified.
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//! Warnings :
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//! If the scale <S> is negative :
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//! . the main direction of the axis placement is not changed.
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//! . The "XDirection" and the "YDirection" are reversed.
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//! So the axis placement stay right handed.
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gp_Ax2 Scaled (const gp_Pnt& P, const Standard_Real S) const;
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void Transform (const gp_Trsf& T);
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//! Transforms an axis placement with a Trsf.
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//! The "Location" point, the "XDirection" and the
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//! "YDirection" are transformed with T. The resulting
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//! main "Direction" of <me> is the cross product between
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//! the "XDirection" and the "YDirection" after transformation.
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gp_Ax2 Transformed (const gp_Trsf& T) const;
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void Translate (const gp_Vec& V);
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//! Translates an axis plaxement in the direction of the vector
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//! <V>. The magnitude of the translation is the vector's magnitude.
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gp_Ax2 Translated (const gp_Vec& V) const;
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void Translate (const gp_Pnt& P1, const gp_Pnt& P2);
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//! Translates an axis placement from the point <P1> to the
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//! point <P2>.
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gp_Ax2 Translated (const gp_Pnt& P1, const gp_Pnt& P2) const;
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protected:
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private:
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gp_Ax1 axis;
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gp_Dir vydir;
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gp_Dir vxdir;
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};
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#include <gp_Ax2.lxx>
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#endif // _gp_Ax2_HeaderFile
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