Eagle::STA::CartesianChart4D::bivector Class Reference

A four-dimensional Bi-Vector which is span by two vectors to define a plane. More...

#include </home/werner/origo/vish/ocean/eagle/STA.hpp>

List of all members.

Public Types

• typedef Coordinates
  < CartesianChart4D >::bivector Base_t

Public Member Functions

• template<char CompType> bivector (const bivector &l, const bivector &r, const Operator< CompType > &C)

  Generic Computational Constructor for operations on two bi-vectors.
  

• template<char CompType> bivector (const bivector &l, const double &scalar, const Operator< CompType > &C)

  Generic Computational Constructor for operations on bi-vector and scalar.
  

• template<char CompType> bivector (const double &scalar, const bivector &l, const Operator< CompType > &C)

  Generic Computational Constructor for operations on scalar and bi-vector.
  

• bivector (const vector &a, const vector &b)

  Construct bivector from two vectors.
  

• bivector inv () const

  Compute the inverse bivector.
  

• vector operator() (const vector &v) const

  Compute UvU, which is a 90 degree rotation of the vector v along the plane U.
  

• bivector operator* () const

  Star operator, yields the bivector that is dual to this bi-vector.
  

• bivector operator+ (const bivector &r) const

  Addition operator.
  

• bivector operator- (const bivector &r) const

  Subtraction operator.
  

• bivector operator- () const

  Unary minus.
  

• const double & tx () const
• double & tx ()
• const double & ty () const
• double & ty ()
• const double & tz () const
• double & tz ()
• bivector unit () const

  Yield a bivector of unit area.
  

• double xt () const
• const double & xy () const
• double & xy ()
• double xz () const
• double yt () const
• double yx () const
• const double & yz () const
• double & yz ()
• double zt () const
• const double & zx () const
• double & zx ()
• double zy () const

Friends

• double dot (const bivector &a, const bivector &b)

  Inner product of two bivectors (note: this actually involves an implicit metric!)
  

• double norm (const bivector &v)

  The norm of a bivector.
  

• double norm2 (const bivector &v)

  Compute the squared norm of a bivector, which is the area span by the plane.
  

• bivector operator* (const bivector &v, double r)

  Scale bivector.
  

• bivector operator* (double r, const bivector &b)

  Scale bivector.
  

• bivector operator/ (const bivector &b, double r)

  Divide bivector by scalar.
  

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Detailed Description

A four-dimensional Bi-Vector which is span by two vectors to define a plane.

It is represented by six numbers in the STA.

Bi-vectors are useful specify rotations. The sum of a bivector and a scalar yields a rotor, which can be applied to any object such as a vector (sweeping a direction) or another bivector (sweeping a plane).

A bi-vector is constructed from two vectors:

   vector A, B;
   bivector AB = bivector(A,B);

The wedge operator of two vectors also yields a bi-vector and is the same operation:

   vector A, B;
   bivector& AB = A^B;

Alternatively the bivector can be setup by explicit specification of its component, which corresponds to a normal vector. Given a bivector, the associated normal vector can be retrieved using the star operator:

   bivector A;
   vector normalA = *A;

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Member Function Documentation

vector Eagle::STA::CartesianChart4D::bivector::operator()

(

const vector &

v

)

const

Compute UvU, which is a 90 degree rotation of the vector v along the plane U.

Parameters:

this	The bivector U. vector v; bivector U; vector v_rotated = U(v);

bivector Eagle::STA::CartesianChart4D::bivector::operator*

(

)

const [inline]

Star operator, yields the bivector that is dual to this bi-vector.

CHECK SIGNS and http://mathworld.wolfram.com/DualBivector.html

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

• ocean/eagle/STA.hpp