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Geometric algebra of the physical 3D-space, by which we mean the Clifford algebara over Euclidean, three-dimensional space. More...
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.
A rotor is an even multivector.
A rotor is an even MultiVector.
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.