Eagle::PhysicalSpace::bivector Class Reference

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

#include <elementary/eagle/PhysicalSpace.hpp>

Inheritance diagram for Eagle::PhysicalSpace::bivector:

Public Member Functions
	bivector ()
	Default constructor, sets all elements to zero.
template<OperatorID_t CompType>
	bivector (const bivector &l, const bivector &r, const Operator< CompType > &C)
	Generic Computational Constructor for operations on two bi-vectors.
template<OperatorID_t CompType>
	bivector (const bivector &l, const double &scalar, const Operator< CompType > &C)
	Generic Computational Constructor for operations on bi-vector and scalar.
template<OperatorID_t 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 (numerically equivalent to the cross product)
	bivector (double x, double y, double z)
	Component-wise construction of a bivector.
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.
vector	operator* () const
	Star operator, yields the vector that is dual to this bi-vector.
bivector	operator+ (const bivector &r) const
	Addition operator.
bivector	operator- () const
	Unary minus.
bivector	operator- (const bivector &r) const
	Subtraction operator.
bivector	unit () const
	Yield a bivector of unit area.

Friends
double	dot (const bivector &a, const bivector &b)
	Inner product of two bivectors (note: this actually involves an implicit metric!)
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.

Detailed Description

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

It is represented by three numbers, like a vector, but has different algebraic properties.

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;

Member Function Documentation

operator()()

vector Eagle::PhysicalSpace::bivector::operator() ( const vector &  v ) const

inline

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);

References dot.