SO3TangentVector

The left tangent space of SO(3) in some rotation R can be described by

\[ T_R(SO(3)) = \{ s\cdot R | s = -s^T \} \]

where \(s\) are skew symmetric matrices which means they look like

\[ \left(\begin{matrix} 0 & -c & b \\ c & 0 & -a \\ -b & a & 0 \end{matrix}\right).\]

Hence we describe an element of of the tangent space T_R(SO(3)) by the vector \((a,b,c)^T\) which in fact is an vector3d.

Note that \( \{ R\cdot t | t = -t^T \} \) is another possible representation of the tangent space. It is called right tangent space.

We denote whether an SO3TangentVector v is described w.r.t. the left tangent space or right tangent space by the property v.tangentSpace. Moreover we can change the representation of the tangentSpace by using the methods right(v) and left(v).

Syntax

SO3TV = SO3TangentVector(x,y,z)
SO3TV = SO3TangentVector(v,SO3TangentSpace.rightVector)

Input

Output

Options

See also

vector3d.vector3d SO3VectorField.eval SO3VectorFieldHarmonic.eval SO3Fun.grad SO3FunHarmonic.grad