Geom::Ax3 Class Reference

#include <Ax3.h>

Public Member Functions
	Ax3 ()
	Creates an indefinite coordinate system. More...
	Ax3 (const Geom::Ax2 &A)
	Ax3 (const Geom::Pnt &P, const Geom::Dir &N, const Geom::Dir &Vx)
	Ax3 (const Geom::Pnt &P, const Geom::Dir &V)
void	xReverse ()
	Reverses the X direction of <me>. More...
void	yReverse ()
	Reverses the Y direction of <me>. More...
void	zReverse ()
	Reverses the Z direction of <me>. More...
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 Ax3 &Other) const
const Geom::Ax1 &	axis () const
Geom::Ax2	axis2 () 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	direct () const
bool	isCoplanar (const Ax3 &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)
Ax3	mirrored (const Geom::Pnt &P) const
void	mirror (const Geom::Ax1 &A1)
Ax3	mirrored (const Geom::Ax1 &A1) const
void	mirror (const Geom::Ax2 &A2)
Ax3	mirrored (const Geom::Ax2 &A2) const
void	rotate (const Geom::Ax1 &A1, const double Ang)
Ax3	rotated (const Geom::Ax1 &A1, const double Ang) const
void	scale (const Geom::Pnt &P, const double S)
Ax3	scaled (const Geom::Pnt &P, const double S) const
void	transform (const Geom::Trsf &T)
Ax3	transformed (const Geom::Trsf &T) const
void	translate (const Geom::Vec &V)
Ax3	translated (const Geom::Vec &V) const
void	translate (const Geom::Pnt &P1, const Geom::Pnt &P2)
Ax3	translated (const Geom::Pnt &P1, const Geom::Pnt &P2) const

Detailed Description

Describes a coordinate system in 3D space. Unlike a
Geom::Ax2 coordinate system, a 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 <br> 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.
  "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".
  
• Geom::Ax2 is used to define a coordinate system that must be always right-handed.
  

Constructor & Destructor Documentation

Ax3() [1/4]

Geom::Ax3::Ax3

(

)

Creates an indefinite coordinate system.

Ax3() [2/4]

Geom::Ax3::Ax3

(

const Geom::Ax2 &

A

)

Creates a coordinate system from a right-handed
coordinate system.

Ax3() [3/4]

Geom::Ax3::Ax3	(	const Geom::Pnt &	P,
		const Geom::Dir &	N,
		const Geom::Dir &	Vx
	)

Creates a right handed axis placement with the
"Location" point P and two directions, N gives the
"Direction" and Vx gives the "XDirection".
Raises ConstructionError if N and Vx are parallel (same or opposite orientation).

Ax3() [4/4]

Geom::Ax3::Ax3	(	const Geom::Pnt &	P,
		const Geom::Dir &	V
	)

Creates an axis placement with the "Location" point

and the normal direction <V>.

Member Function Documentation

angle()

double Geom::Ax3::angle

(

const Ax3 &

Other

)

const

Computes the angular value 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::Ax3::axis

(

)

const

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

axis2()

Geom::Ax2 Geom::Ax3::axis2

(

)

const

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.

direct()

bool Geom::Ax3::direct

(

)

const

Returns True if the coordinate system is right-handed. i.e.
XDirection().Crossed(YDirection()).Dot(Direction()) > 0

direction()

const Geom::Dir& Geom::Ax3::direction

(

)

const

Returns the main direction of <me>.

isCoplanar() [1/2]

bool Geom::Ax3::isCoplanar	(	const Ax3 &	Other,
		const double	LinearTolerance,
		const double	AngularTolerance
	)		const

Returns True if
. the distance between the "Location" point of <me> and
<Other> is lower or equal to LinearTolerance and
. the distance between the "Location" point of <Other> and
<me> is lower or equal to LinearTolerance and
. the main direction of <me> and the main direction of
<Other> are parallel (same or opposite orientation).

isCoplanar() [2/2]

bool Geom::Ax3::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 distance between A1 and the "Location" point of <me>
is lower or equal to LinearTolerance and
. the main direction of <me> and the direction of A1 are normal.

location()

const Geom::Pnt& Geom::Ax3::location

(

)

const

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

mirror() [1/3]

void Geom::Ax3::mirror

(

const Geom::Ax1 &

A1

)

mirror() [2/3]

void Geom::Ax3::mirror

(

const Geom::Ax2 &

A2

)

mirror() [3/3]

void Geom::Ax3::mirror

(

const Geom::Pnt &

P

)

mirrored() [1/3]

Ax3 Geom::Ax3::mirrored

(

const Geom::Ax1 &

A1

)

const

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.

mirrored() [2/3]

Ax3 Geom::Ax3::mirrored

(

const Geom::Ax2 &

A2

)

const

Performs the symmetrical transformation of an axis
placement with respect to a plane.
The axis placement <A2> 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.

mirrored() [3/3]

Ax3 Geom::Ax3::mirrored

(

const Geom::Pnt &

P

)

const

Performs the symmetrical transformation of an axis
placement with respect to the point P 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.

rotate()

void Geom::Ax3::rotate	(	const Geom::Ax1 &	A1,
		const double	Ang
	)

rotated()

Ax3 Geom::Ax3::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::Ax3::scale	(	const Geom::Pnt &	P,
		const double	S
	)

scaled()

Ax3 Geom::Ax3::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 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::Ax3::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.
  
• The orientation of this coordinate system
  (right-handed or left-handed) is not modified.
  Raises ConstructionError if the "Direction" of <A1> and the "XDirection" of <me>
  are parallel (same or opposite orientation) because it is
  impossible to calculate the new "XDirection" and the new
  "YDirection".
  

setDirection()

void Geom::Ax3::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).
  
• The orientation of this coordinate system (left- or right-handed) is not modified.
  Raises ConstructionError if <V< and the previous "XDirection" are parallel
  because it is impossible to calculate the new "XDirection"
  and the new "YDirection".
  

setLocation()

void Geom::Ax3::setLocation

(

const Geom::Pnt &

P

)

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

setXDirection()

void Geom::Ax3::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).
Raises ConstructionError if <Vx> is parallel (same or opposite
orientation) to the main direction of <me>

setYDirection()

void Geom::Ax3::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).
Raises ConstructionError if <Vy> is parallel to the main direction of <me>

transform()

void Geom::Ax3::transform

(

const Geom::Trsf &

T

)

transformed()

Ax3 Geom::Ax3::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::Ax3::translate	(	const Geom::Pnt &	P1,
		const Geom::Pnt &	P2
	)

translate() [2/2]

void Geom::Ax3::translate

(

const Geom::Vec &

V

)

translated() [1/2]

Ax3 Geom::Ax3::translated	(	const Geom::Pnt &	P1,
		const Geom::Pnt &	P2
	)		const

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

translated() [2/2]

Ax3 Geom::Ax3::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.

xDirection()

const Geom::Dir& Geom::Ax3::xDirection

(

)

const

Returns the "XDirection" of <me>.

xReverse()

void Geom::Ax3::xReverse

(

)

Reverses the X direction of <me>.

yDirection()

const Geom::Dir& Geom::Ax3::yDirection

(

)

const

Returns the "YDirection" of <me>.

yReverse()

void Geom::Ax3::yReverse

(

)

Reverses the Y direction of <me>.

zReverse()

void Geom::Ax3::zReverse

(

)

Reverses the Z direction of <me>.

---

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

• D:/CadworkJobs/SoftwareProjekte/Lexocad/LexoGit/Lexocad/lexocad/Geom/include/Geom/Ax3.h