This folder contains code describing tools for handling different coordinate systems.
The current coordinate transformations implemented are:
- Analytically invertible coordinate transformations such as:
- Circular coordinate transformation (CircularToCartesian/CartesianToCircular):
$x(r,\theta) = r \cos(\theta),$ $y(r,\theta) = r \sin(\theta).$
- Czarny coordinate transformation (CzarnyToCartesian/CartesianToCzarny):
$x(r,\theta) = \frac{1}{\epsilon} \left( 1 - \sqrt{1 + \epsilon(\epsilon + 2 r \cos(\theta)} \right),$ -
$y(r,\theta) = \frac{e\xi r \sin(\theta)}{2 -\sqrt{1 + \epsilon(\epsilon + 2 r \cos(\theta)} },$ with$\xi = 1/\sqrt{1 - \epsilon^2 /4}$ and$e$ and$\epsilon$ given as parameters.
- Barycentric coordinate transformation (BarycentricToCartesian):
$(c_1, c_2, c_3) -> (x,y)$
- Circular coordinate transformation (CircularToCartesian/CartesianToCircular):
- Discrete coordinate transformation defined on bsplines (DiscreteToCartesian):
$x(r,\theta) = \sum_k c_{x,k} B_k(r,\theta),$ $y(r,\theta) = \sum_k c_{y,k} B_k(r,\theta).$
- Combined coordinate transformation which combines two of the coordinate transformations above.
The tools are:
- InverseJacobianMatrix : this tool calculates the inverse Jacobian matrix on the specified coordinate system.
- InvJacobianOPoint : this tool calculates the inverse Jacobian matrix at the O-point on the specified coordinate system.
- MetricTensor : this tool calculates the metric tensor associated with a coordinate transformation.
- VectorMapper : this tool helps when converting vectors stored in a
VectorFieldfrom one coordinate system to another. - other static analysis tools found in
mapping_tools.hpp