:mod:`neuron_morphology.transforms.streamline`
==============================================

.. py:module:: neuron_morphology.transforms.streamline


Module Contents
---------------


Functions
~~~~~~~~~

.. autoapisummary::

   neuron_morphology.transforms.streamline.solve_laplace_2d
   neuron_morphology.transforms.streamline.compute_gradient
   neuron_morphology.transforms.streamline.generate_laplace_field


.. function:: solve_laplace_2d(V: fem.FunctionSpace, domain, bcs: List[fem.bcs.DirichletBCMetaClass])

   Solves the laplace equation with boundary conditions bcs on V


   :Parameters:

       **V: Fenics FunctionSpace object created from a mesh**
           ..

       **bcs: List of Fenics DirichletBC Boundary Conditions**
           ..














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.. function:: compute_gradient(uh, W, bcs=[])


.. function:: generate_laplace_field(top_line: List[Tuple], bottom_line: List[Tuple], mesh_res: float = 20, top_value: float = 1.0, bottom_value: float = 0.0, eps_bounds: float = 1e-08)

   Solve Laplace equation inside a polygon bounded
   by two lines (top_line and bottom_line) and the artificial
   straight side lines connecting the ends of the two lines.
   Apply Dirichlet BC on top_line and bottom_line and
   zero Neuman BC on the side lines.

   Demo of fenics: https://github.com/hplgit/fenics-tutorial/
                   blob/master/pub/python/vol1/ft01_poisson.py

   If top_value and bottom_value defaults are used, value_field
   will be the normalized distance to the top_line

   :Parameters:

       **top_line: line that will have top_value boundary condition**
           ..

       **bottom_line: line that will have bottom_value boundary condition**
           ..

       **mesh_res: resolution of the mesh**
           ..

       **top_value: value for top Dirichlet Boundary**
           ..

       **bottom_value: value for bottom Dirichlet Boundary**
           ..

   :Returns:

       u: returns value at input point e.g. 0.5 = u((0.5, 0.5))
           ..

       grad_u: returns gradient at input point e.g. [0, 1] = u((0.5, 0.5))
           ..

       mesh_coords: coordinates of each vertex in the mesh
           ..

       mesh_values: values at each vertex in the mesh
           ..

       gradient_mesh: gradient at each vertex in the mesh
           ..













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