Geom::Ax2 Class Reference

#include <Ax2.h>

Public Member Functions
	Ax2 ()=default
	Creates an indefinite coordinate system. More...
	Ax2 (const Geom::Pnt &P, const Geom::Dir &N, const Geom::Dir &Vx)
	Ax2 (const Geom::Pnt &P, const Geom::Dir &V)
	Ax2 (const Geom::Pnt &aP, const Geom::Dir &aZDir, const Geom::Dir &aYDir, const Geom::Dir &aXDir)
void	setAxis (const Geom::Ax1 &A1)
void	setDirection (const Geom::Dir &V)
void	setLocation (const Geom::Pnt &P)
	Changes the "Location" point (origin) of <me>. More...
void	setXDirection (const Geom::Dir &Vx)
void	setYDirection (const Geom::Dir &Vy)
double	angle (const Ax2 &Other) const
const Geom::Ax1 &	axis () const
const Geom::Dir &	direction () const
	Returns the main direction of <me>. More...
const Geom::Pnt &	location () const
	Returns the "Location" point (origin) of <me>. More...
const Geom::Dir &	xDirection () const
	Returns the "XDirection" of <me>. More...
const Geom::Dir &	yDirection () const
	Returns the "YDirection" of <me>. More...
bool	isCoplanar (const Ax2 &Other, const double LinearTolerance, const double AngularTolerance) const
bool	isCoplanar (const Geom::Ax1 &A1, const double LinearTolerance, const double AngularTolerance) const
void	mirror (const Geom::Pnt &P)
Ax2	mirrored (const Geom::Pnt &P) const
void	mirror (const Geom::Ax1 &A1)
Ax2	mirrored (const Geom::Ax1 &A1) const
void	mirror (const Ax2 &A2)
Ax2	mirrored (const Ax2 &A2) const
void	rotate (const Geom::Ax1 &A1, const double Ang)
Ax2	rotated (const Geom::Ax1 &A1, const double Ang) const
void	scale (const Geom::Pnt &P, const double S)
Ax2	scaled (const Geom::Pnt &P, const double S) const
void	transform (const Geom::Trsf &T)
Ax2	transformed (const Geom::Trsf &T) const
void	translate (const Geom::Vec &V)
Ax2	translated (const Geom::Vec &V) const
void	translate (const Geom::Pnt &P1, const Geom::Pnt &P2)
Ax2	translated (const Geom::Pnt &P1, const Geom::Pnt &P2) const
bool	isEqual (const Ax2 &Other, const double tolerance) const

Detailed Description

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 <br> 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 Geom::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 <br> Direction", respectively, as their unit vectors.
  The "Z Axis" is also the "main Axis".
  

Constructor & Destructor Documentation

Ax2() [1/4]

Geom::Ax2::Ax2 ( )

default

Creates an indefinite coordinate system.

Ax2() [2/4]

Geom::Ax2::Ax2	(	const Geom::Pnt &	P,
		const Geom::Dir &	N,
		const Geom::Dir &	Vx
	)

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 <br> Direction" = (N ^ Vx) ^ N,
  Exception: raises ConstructionError if N and Vx are parallel (same or opposite orientation).
  

Ax2() [3/4]

Geom::Ax2::Ax2	(	const Geom::Pnt &	P,
		const Geom::Dir &	V
	)

Creates - a coordinate system with an origin P, where V
gives the "main Direction" (here, "X Direction" and "Y <br> Direction" are defined automatically).

Ax2() [4/4]

Geom::Ax2::Ax2	(	const Geom::Pnt &	aP,
		const Geom::Dir &	aZDir,
		const Geom::Dir &	aYDir,
		const Geom::Dir &	aXDir
	)

Member Function Documentation

angle()

double Geom::Ax2::angle

(

const Ax2 &

Other

)

const

Computes the angular value, in radians, between the main direction of
<me> and the main direction of <Other>. Returns the angle
between 0 and PI in radians.

axis()

const Geom::Ax1& Geom::Ax2::axis

(

)

const

Returns the main axis of <me>. It is the "Location" point
and the main "Direction".

direction()

const Geom::Dir& Geom::Ax2::direction

(

)

const

Returns the main direction of <me>.

isCoplanar() [1/2]

bool Geom::Ax2::isCoplanar	(	const Ax2 &	Other,
		const double	LinearTolerance,
		const double	AngularTolerance
	)		const

isCoplanar() [2/2]

bool Geom::Ax2::isCoplanar	(	const Geom::Ax1 &	A1,
		const double	LinearTolerance,
		const double	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.

isEqual()

bool Geom::Ax2::isEqual	(	const Ax2 &	Other,
		const double	tolerance
	)		const

location()

const Geom::Pnt& Geom::Ax2::location

(

)

const

Returns the "Location" point (origin) of <me>.

mirror() [1/3]

void Geom::Ax2::mirror

(

const Geom::Pnt &

P

)

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.
    

mirror() [2/3]

void Geom::Ax2::mirror

(

const Geom::Ax1 &

A1

)

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.
    

mirror() [3/3]

void Geom::Ax2::mirror

(

const Ax2 &

A2

)

Performs a symmetrical transformation of this coordinate
system with respect to:

• the plane defined by the origin, "X Direction" and "Y <br> 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.
    

mirrored() [1/3]

Ax2 Geom::Ax2::mirrored

(

const Geom::Pnt &

P

)

const

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.
    

mirrored() [2/3]

Ax2 Geom::Ax2::mirrored

(

const Geom::Ax1 &

A1

)

const

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.
    

mirrored() [3/3]

Ax2 Geom::Ax2::mirrored

(

const Ax2 &

A2

)

const

Performs a symmetrical transformation of this coordinate
system with respect to:

• the plane defined by the origin, "X Direction" and "Y <br> 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.
    

rotate()

void Geom::Ax2::rotate	(	const Geom::Ax1 &	A1,
		const double	Ang
	)

rotated()

Ax2 Geom::Ax2::rotated	(	const Geom::Ax1 &	A1,
		const double	Ang
	)		const

Rotates an axis placement. <A1> is the axis of the
rotation . Ang is the angular value of the rotation
in radians.

scale()

void Geom::Ax2::scale	(	const Geom::Pnt &	P,
		const double	S
	)

scaled()

Ax2 Geom::Ax2::scaled	(	const Geom::Pnt &	P,
		const double	S
	)		const

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.

setAxis()

void Geom::Ax2::setAxis

(

const Geom::Ax1 &

A1

)

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 <br> Direction" of this coordinate system.

setDirection()

void Geom::Ax2::setDirection

(

const Geom::Dir &

V

)

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 <br> Direction" of this coordinate system.

setLocation()

void Geom::Ax2::setLocation

(

const Geom::Pnt &

P

)

Changes the "Location" point (origin) of <me>.

setXDirection()

void Geom::Ax2::setXDirection

(

const Geom::Dir &

Vx

)

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.

setYDirection()

void Geom::Ax2::setYDirection

(

const Geom::Dir &

Vy

)

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.

transform()

void Geom::Ax2::transform

(

const Geom::Trsf &

T

)

transformed()

Ax2 Geom::Ax2::transformed

(

const Geom::Trsf &

T

)

const

Transforms an axis placement with a Trsf.
The "Location" point, the "XDirection" and the
"YDirection" are transformed with T. The resulting
main "Direction" of <me> is the cross product between
the "XDirection" and the "YDirection" after transformation.

translate() [1/2]

void Geom::Ax2::translate

(

const Geom::Vec &

V

)

translate() [2/2]

void Geom::Ax2::translate	(	const Geom::Pnt &	P1,
		const Geom::Pnt &	P2
	)

translated() [1/2]

Ax2 Geom::Ax2::translated

(

const Geom::Vec &

V

)

const

Translates an axis plaxement in the direction of the vector
<V>. The magnitude of the translation is the vector's magnitude.

translated() [2/2]

Ax2 Geom::Ax2::translated	(	const Geom::Pnt &	P1,
		const Geom::Pnt &	P2
	)		const

Translates an axis placement from the point <P1> to the
point <P2>.

xDirection()

const Geom::Dir& Geom::Ax2::xDirection

(

)

const

Returns the "XDirection" of <me>.

yDirection()

const Geom::Dir& Geom::Ax2::yDirection

(

)

const

Returns the "YDirection" of <me>.

---

The documentation for this class was generated from the following file:

• D:/CadworkJobs/Softwareprojekte/Lexocad/V28.0/lexocad/Geom/include/Geom/Ax2.h