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):
  - \((c_1, c_2, c_3) -> (x,y)\)
Discrete coordinate transformation defined on B-splines (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 VectorField from one coordinate system to another.
other static analysis tools found in mapping_tools.hpp