Rotation3

Defines a rotation of 3-dimensional space.

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AUTHORS
CHANGES LOG
GOALS
USAGE

Class Summary

class Rotation3
{
public:
// define real type
typedef Vector3::real real;
// Constructors
Rotation3();
Rotation3(const real a, const real b, const real c, const real d);
explicit Rotation3(const Matrix3& m);
Rotation3(const real& xr, const real& yr, const real& zr);
explicit Rotation3(const real m[3][3]);
explicit Rotation3(const double m[3][3]);
Rotation3(const Vector3& v1, const Vector3& v2, const Vector3& v3);
// Inspection methods and properties.
const real operator[](const unsigned short index) const;
Vector3 row(const unsigned short r) const;
Vector3 column(const unsigned short col) const;
real element(const unsigned short r, const unsigned short col) const;
real rotX() const;
real rotY() const;
real rotZ() const;
Vector3 rotationAngles() const;
real trace() const;
real dist2(const Rotation3& r) const;
real dist(const Rotation3& r) const;
// Operators
operator Matrix3() const;
Rotation3& operator*=(const Rotation3 &);
friend Rotation3 operator*(const Rotation3&, const Rotation3&);
friend Rotation3 operator!(const Rotation3&);
friend Vector3 operator*(const Rotation3&, const Vector3&);
friend ostream& operator<<(ostream& s, const Rotation3& t);
protected:
Rotation3(const real a, const real b, const real c, const real d, int);
}; // Rotation3

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AUTHORS

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

Copyright: SAMBA group, Tel-Aviv Univ. Israel, 1997.

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CHANGES LOG

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GOALS

Rotation3 hold a 3-dimensional rotation compactly. Using quaternions a rotation may be held compactly without sacrificing much on the performance side. Rotation3 should support most of the methods implemented in Matrix3.

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USAGE

Rotation3 hosts a set of constructors, operators and inspection methods. Below are just several examples of how one may use the class. 

    Rotation3 ra(1.0, 1.1, -1.3);  // rotation angles.
    Rotation3 rb(0.9, -2.3, 0.1);  // rotation angles.

    Matrix3 a= ra;
    Matrix3 b= rb;

    Rotation3 rab = ra*rb;
    Matrix3 ab = a*b;  // rab should be = to ab;

    Vector3 v(1.0, 2.0, 3.0);
    cout !rab*v;

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typedef Vector3::real real;

real is defined using the real defined in Vector3 class. By default this is of type float. For example , changing Vector3::real's defintion to double will turn the gamb library's vector operations to double precision. 

  typedef Vector3::real real;

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Rotation3();

Default constructor: 0 matrix. 

  Rotation3();

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Rotation3(const real a, const real b, const real c, const real d);

Instantiate a rotation using 4 quaternion parameters. 

  Rotation3(const real a, const real b, const real c, const real d);

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explicit Rotation3(const Matrix3& m);

Instantiate a Rotation3 using a rotation matrix. If the matrix is not a rotation matrix the parameters will be normalized. 

  explicit Rotation3(const Matrix3& m);

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Rotation3(const real& xr, const real& yr, const real& zr);

Creates a Rotation3 object. given rotational angles around the x axis (xr), around the y axis (yr) and around the z axis (zr) a linear transformation that rotates space in the order x-y-z is created. Rotation in this order is the default representation for the gamb++ library rotational transformations. 

  Rotation3(const real& xr, const real& yr, const real& zr);

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explicit Rotation3(const real m[3][3]);

Use a 3x3 real 2D array matrix to initialize a Rotation3. If matrix is not a rotation it is "normalized". 

  explicit Rotation3(const real m[3][3]);

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explicit Rotation3(const double m[3][3]);

Use a 3x3 double prec. 2D array matrix to initialize a Rotation3. If matrix is not a rotation it is "normalized". 

  explicit Rotation3(const double m[3][3]);

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Rotation3(const Vector3& v1, const Vector3& v2, const Vector3& v3);

Constructs a Rotation3 using the 3 given matrix row vectors. If matrix is not a rotation it is "normalized". 

  Rotation3(const Vector3& v1, const Vector3& v2, const Vector3& v3);

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const real operator[](const unsigned short index) const;

Returns the ith element of quaternion representing the rotation. index may take values from 0 to 3. Otherwise results are undefined. 

  const real operator[](const unsigned short index) const;

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Vector3 row(const unsigned short r) const;

Returns a vector matching the r'th row of the rotation matrix representing the rotation object . r must be in the range 1..3 or run time errors may occur. 

  Vector3 row(const unsigned short r) const;

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Vector3 column(const unsigned short col) const;

Returns a vector matching the col'th column of the rotation matrix representing the rotation object . r must be in the range 1..3 or run time errors may occur. 

  Vector3 column(const unsigned short col) const;

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real element(const unsigned short r, const unsigned short col) const;

Returns the numerical value at position row, col in the 3X3 matrix representing the rotation. row, col should be within the range of 1..3 or run time errors may occur. / Use the matrix(ij) familiy of methods for faster access. 

  real element(const unsigned short r, const unsigned short col) const;

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real rotX() const;

Returns the rotation around the x-axis for a rotational matrix assuming rotations are performed in the order of x-y-z. 

  real rotX() const;

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real rotY() const;

Returns the rotation around the y-axis for a rotational matrix assuming rotations are performed in the order of x-y-z. 

  real rotY() const;

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real rotZ() const;

Returns the rotation around the z-axis for a rotational matrix assuming rotations are performed in the order of x-y-z. 

  real rotZ() const;

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Vector3 rotationAngles() const;

Returns 3 rotation angles assuming rotations are performed in the order of x-y-z. 

  Vector3 rotationAngles() const;

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real trace() const;

Returns the trace of the rotation matrix representing the rotation. 

  real trace() const;

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real dist2(const Rotation3& r) const;

Returns squared distance between 2 rotations. Currently this is implemented by taking the euclidean distance between the 4 parameters of the quternion. 

  real dist2(const Rotation3& r) const;

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real dist(const Rotation3& r) const;

Returns distance between 2 rotations. Currently this is implemented by taking the euclidean distance between the 4 parameters of the quternion. 

  real dist(const Rotation3& r) const;

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operator Matrix3() const;

Convert a Rotation3 object to Matrix3 type. 

  operator Matrix3() const;

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Rotation3& operator*=(const Rotation3 &);

In place multiplication with a given rotation object. 

  Rotation3& operator*=(const Rotation3 &);

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friend Rotation3 operator*(const Rotation3&, const Rotation3&);

Multiplication of two rotations. 

  friend Rotation3 operator*(const Rotation3&, const Rotation3&);

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friend Rotation3 operator!(const Rotation3&);

Inverse rotation. 

  friend Rotation3 operator!(const Rotation3&);

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friend Vector3 operator*(const Rotation3&, const Vector3&);

Rotation by vector multiplication. 

  friend Vector3 operator*(const Rotation3&, const Vector3&);

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friend ostream& operator<<(ostream& s, const Rotation3& t);

Output rotation in quaternion format. 

  friend ostream& operator<<(ostream& s, const Rotation3& t);

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Rotation3(const real a, const real b, const real c, const real d, int);

Instantiate a rotation using 4 quaternion parameters. This version differs from the public version. It dows not normalize the quaternion and does not make sure the 4 parameters actually represent a rotation. 

  Rotation3(const real a, const real b, const real c, const real d, int);

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All Members

public:
// define real type
typedef Vector3::real real;
// Constructors
explicit Rotation3(const Matrix3& m);
explicit Rotation3(const real m[3][3]);
explicit Rotation3(const double m[3][3]);
// Inspection methods and properties.
const real operator[](const unsigned short index) const;
Vector3 row(const unsigned short r) const;
Vector3 column(const unsigned short col) const;
real element(const unsigned short r, const unsigned short col) const;
real rotX() const;
real rotY() const;
real rotZ() const;
Vector3 rotationAngles() const;
real trace() const;
real dist2(const Rotation3& r) const;
real dist(const Rotation3& r) const;
// Operators
operator Matrix3() const;
Rotation3& operator*=(const Rotation3 &);
friend Rotation3 operator*(const Rotation3&, const Rotation3&);
friend Rotation3 operator!(const Rotation3&);
friend Vector3 operator*(const Rotation3&, const Vector3&);
friend ostream& operator<<(ostream& s, const Rotation3& t);
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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