RigidTrans3

Defines 3-dimensional rigid transformations class. Rigid transformations are comprised of a rotation followed by a translation of the vector space.

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AUTHORS

CHANGES LOG

GOALS

USAGE

Class Summary

class RigidTrans3

{

public:

	// real definition.
typedef	Vector3::real real;

	// Contructors.
	RigidTrans3() ;
	RigidTrans3(const Matrix3& r, const Vector3& t, int) ;
	RigidTrans3(const Matrix3& r, const Vector3& t) ;
	RigidTrans3(const Rotation3& r, const Vector3& t) ;
	RigidTrans3(const Vector3& r, const Vector3& t) ;
	RigidTrans3(const Vector3& u, const Vector3& v, const Vector3& w);
	RigidTrans3(const Vector3& u ,const Vector3& w ,const Vector3& base , int);
	RigidTrans3(int , const Vector3& u ,const Vector3& w ,const Vector3& base);

	// Inspection and propery methods
const Matrix3&	rotation() const ;
Vector3	rotationAngles() const ;
const Vector3&	translation() const ;

	// Operators.
friend Vector3	operator*(const RigidTrans3& rt, const Vector3& v) ;
friend Vector3&	operator*=(Vector3& v,const RigidTrans3& rt) ;
friend RigidTrans3	operator*(const RigidTrans3& rt1, const RigidTrans3& rt2) ;
friend RigidTrans3	operator!(const RigidTrans3& rt) ;
friend ostream&	operator<<(ostream& s, const RigidTrans3& rt) ;
friend istream&	operator>>(istream& s, RigidTrans3& rt);
void	output(FILE* outputFile) const ;
protected:

}; // RigidTrans3

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AUTHORS

Meir Fuchs (meirfux@math.tau.ac.il).

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CHANGES LOG

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GOALS

The RigidTrans3 class was designed to represent a rigid transformation of 3 dimensional space. A rigid transformation is a rotation and then a translation of vector space. The class is based upon the Matrix3 class and the Vector3 class. Although 3-dimensional rotations can be represented more compactly using 3 rotational angles instead of 9 rotational matrix elements, the latter was chosen for considerations of speed and performance.

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USAGE

RigidTrans3 is comprised of a rotation and a translation. The basic constructor requires a rotation specified by either rotational angles or by a rotational matrix and a translation specified by a vector.

    RigidTrans3 T(Vector3(pi, pi, pi/2),  // rotation 
                  Vector3(0, 0, 1));      // translation

A second method of construction is used in reference of base construction. Given an ordered set of 3 points one can construct an axes-system based on these points. A constructor that recieves 3 points returns the RigidTrans3 that transforms the normal axes to the point-based axes system.

Rigid transformations form a group. We can talk of multiplying or applying one rigid transformation on top of the other and we can talk about the inverse of a rigid transformation. These operators are supplied.

    RigidTrans3 T(Vector3(pi/2, 0, 0), Vector3(1, 0, 0));
    RigidTrans3 S(Vector3(-pi/2, 0, 0), Vector3(-1, 0, 0));
    RigidTrans3 I=T*S  // This gives the identity rigid trans since T=!S
    RigidTrans3 J=!I   // J should equal I (or be very close to it).

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typedef Vector3::real real;

real is defined to be float by default. By changing real in Vector3 to double one may change the whole library to work with double precision.

  typedef Vector3::real real;

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RigidTrans3() ;

Instantiates to a an identity rigid transformation. i.e. no rotation and 0 translation.

  RigidTrans3()
    ;

Function is currently defined inline.

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RigidTrans3(const Matrix3& r, const Vector3& t, int) ;

Instantiate a rigid transformation using a linear transformation as rotation and a vector for translation. The int is a dummy int argument used to set this constructor apart from the identically defined public constructor. Note that the matrix itself is not used but rather its rotational parameters, so if a non-rotational matrix is given, a different, rotational Matrix3 will be used in the RigidTrans3 object. Warning: This function is deprecated

  RigidTrans3(const Matrix3& r, const Vector3& t, int)
    ;

Function is currently defined inline.

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RigidTrans3(const Matrix3& r, const Vector3& t) ;

Instantiate a rigid transformation using a linear transformation as rotation and a vector for translation. This constructor is used to instantiate a RigidTrans3 with a given rotational matrix and translational vector without verifying that the matrix is rotational.

  RigidTrans3(const Matrix3& r, const Vector3& t) ;

Function is currently defined inline.

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RigidTrans3(const Rotation3& r, const Vector3& t) ;

Instanitiates a rigid transformation using a Rotation3 object and a translational vector.

  RigidTrans3(const Rotation3& r, const Vector3& t)
    ;

Function is currently defined inline.

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RigidTrans3(const Vector3& r, const Vector3& t) ;

Instanitiates a rigid transformation using the 3 angles given in the rotational vector and the translational vector. The rotational vector is assumes rotations are in the order: around X (Y,Z plane rotation) - around Y (X,Z plane rotation) - around Z (X,Y plane roation).

  RigidTrans3(const Vector3& r, const Vector3& t)
    ;

Function is currently defined inline.

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RigidTrans3(const Vector3& u, const Vector3& v, const Vector3& w);

Returns the rigid transformations which transforms the natural axes to the axis system created by u,v,w. The x-axis lies on c-u, (where c is the mass center of u,v,w,). The z-axis is perpendicular to the u,v,w plane and the y-axis is perpendicular to both x and z.

  RigidTrans3(const Vector3& u, const Vector3& v, const Vector3& w);

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RigidTrans3(const Vector3& u ,const Vector3& w ,const Vector3& base , int);

Returns the rigid transformations which transforms the natural axes to the axis system created by u,w and base (where 'base' is the axis center). The x-axis lies on u-base , the z-axis is perpendicular to the u-base , w-base plane and the y-axis is perpendicular to both x and z.(i.e the first variable is set by default as the local x-axis) The int is a dummy int argument used to set this constructor apart from the identically defined public constructor.

  RigidTrans3(const Vector3& u ,const Vector3& w  ,const Vector3& base , int);

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RigidTrans3(int , const Vector3& u ,const Vector3& w ,const Vector3& base);

Returns the rigid transformations which transforms the new axis system created by u,w and base (where 'base' is the axis center). (this is just inverse of RigidTrans3(const Vector3&,const Vector3&,const Vector3&, int)) The x-axis lies on u-base , the z-axis is perpendicular to the u-trans , w-trans plane and the y-axis is perpendicular to both x and z (i.e the first variable is set by default as the local x-axis) The int is a dummy int argument used to set this constructor apart from the identically defined public constructors.

  RigidTrans3(int , const Vector3& u ,const Vector3& w  ,const Vector3& base);

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const Matrix3& rotation() const ;

Returns linear transformation representing rotation of rigid tranformation.

  const Matrix3& rotation() const                      
;

Function is currently defined inline.

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Vector3 rotationAngles() const ;

Returns vector with axis rotational angles assuming the order of rotation is x-y-z.

  Vector3 rotationAngles() const                            
;

Function is currently defined inline.

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const Vector3& translation() const ;

Returns translation vector of rigid transformation.

  const Vector3& translation() const                        
;

Function is currently defined inline.

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friend Vector3 operator*(const RigidTrans3& rt, const Vector3& v) ;

Apply the rigid transformation rn ob vector v. Apply a rotation followed by a translation

  friend Vector3 operator*(const RigidTrans3& rt, const Vector3& v)                                          
;

Function is currently defined inline.

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friend Vector3& operator*=(Vector3& v,const RigidTrans3& rt) ;

Apply the rigid transformation rn ob vector v. Apply a rotation followed by a translation

  friend Vector3& operator*=(Vector3& v,const RigidTrans3& rt)                                                   
;

Function is currently defined inline.

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friend RigidTrans3 operator*(const RigidTrans3& rt1, const RigidTrans3& rt2) ;

multiply two rigid transformation such that for any vector v (rt1*rt2)*v = rt1*(rt2*v)

  friend RigidTrans3 operator*(const RigidTrans3& rt1, 
			       const RigidTrans3& rt2)                                                                   
;

Function is currently defined inline.

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friend RigidTrans3 operator!(const RigidTrans3& rt) ;

Gives the inverse of a rigid transformation such that for any vector v (rt*!rt)*v = rt*(!rt*v) = v and rt*!rt = RigidTrans3().

  friend RigidTrans3 operator!(const RigidTrans3& rt)                                                                                                    
;

Function is currently defined inline.

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friend ostream& operator<<(ostream& s, const RigidTrans3& rt) ;

prints 3 rotations in X-Y-Z order (see above) and translation vector.

  friend ostream& operator<<(ostream& s, const RigidTrans3& rt)                                                              
;

Function is currently defined inline.

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friend istream& operator>>(istream& s, RigidTrans3& rt);

reads 3 rotations in X-Y-Z order (see above) and translation vector.

  friend istream& operator>>(istream& s, RigidTrans3& rt);

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void output(FILE* outputFile) const ;

Prints the three rotation angles in X-Y-Z order and the translation vector
Author: Oranit Dror (oranit@tau.ac.il)

  void output(FILE* outputFile) const                                                                                                           
;

Function is currently defined inline.

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All Members

public:

	// real definition.
typedef	Vector3::real real;

	// Inspection and propery methods
const Matrix3&	rotation() const ;
Vector3	rotationAngles() const ;
const Vector3&	translation() const ;

	// Operators.
friend Vector3	operator*(const RigidTrans3& rt, const Vector3& v) ;
friend Vector3&	operator*=(Vector3& v,const RigidTrans3& rt) ;
friend RigidTrans3	operator*(const RigidTrans3& rt1, const RigidTrans3& rt2) ;
friend RigidTrans3	operator!(const RigidTrans3& rt) ;
friend ostream&	operator<<(ostream& s, const RigidTrans3& rt) ;
friend istream&	operator>>(istream& s, RigidTrans3& rt);
void	output(FILE* outputFile) const ;
protected:

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Ancestors

Class does not inherit from any other class.

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Descendants

Class is not inherited by any others.

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