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Eagle::PhysicalSpace Namespace Reference

Geometric algebra of the physical 3D-space, by which we mean the Clifford algebara over Euclidean, three-dimensional space. More...

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Typedefs

Functions


Detailed Description

Geometric algebra of the physical 3D-space, by which we mean the Clifford algebara over Euclidean, three-dimensional space.

It can reflect the properties of a flat, 3-dimensional manifold or the tangential space of a curved, 3-dimensional manifold.

Note:
The classes in PhysicalSpace are currently implemented to operate on the double type. It were easy to change this to a generic template instead, in case the need arises. For now, this appears to be an overhead to always write <> in an instance, even though a typedef could fix that easily as well. If there is a real need to instantiate geometric algebra over other types than doubles, we can do it then.

Typedef Documentation

A rotor is an even multivector.

A rotor is an even MultiVector.


Function Documentation

double Eagle::PhysicalSpace::dot ( const vector &  a,
const vector &  b 
) [inline]

Euclidan Inner (dot) product of two vectors.

Compute the Euclidean dot product (inner product) of two vectors.

vector Eagle::PhysicalSpace::dot ( const bivector &  a,
const vector &  b 
) [inline]

Inner (dot) product of a bivector and a vector.

(A xy + B yz + C zx)|(ax+ by+ cz) = ( -Aa y + Ca z + Ab x - Bb z + Bc y - Cc x) = (Ab-Cc) x + (Bc - Aa) y + ( Ca - Bb) z

vector Eagle::PhysicalSpace::dot ( const trivector &  a,
const bivector &  b 
) [inline]

xyz ( xy + yz + zx ) = xyz xy + xyz yz + xyz zx =

-xzy xy - xyz zy - yxz zx = zxy xy = -zyx xy - xyz zy - yxz zx z x y

OddMultiVector Eagle::PhysicalSpace::operator* ( const bivector &  a,
const vector &  b 
) [inline]

Geometric product of bivector and vector yields an odd multivector, the sum of a vector and trivector.

An odd multivector is dual to a rotor, an even multivector.

point Eagle::PhysicalSpace::operator- ( const point &  P,
const vector &  v 
) [inline]
Todo:
Use computational constructor for '-'