vtkDbiharPatchFilter can be used for generating quadrilateral meshes for surface patches. Surface patches can be combined to form surface meshes for complex geometric objects.

vtkDbiharPatchFilter is a VTK filter/wrapper for biharmonic equation solver library Dbihar written in Fortran. Dbihar Fortran code was downloaded from Netlib. The Dbihar library solves the biharmonic equations in the parametric space.

The filer is intended to simplify the use of Dbihar library in the in the process of generating quadrilateral meshes.

The usual compilers, including a Fortran compiler, VTK compiled with Python (3) Wrapping, Python's h5py, numpy and matplotlib, what else?

The input to vtkDbiharPatchFilter is a vtkPolyData object which contains a vtkPolyLine over a set of points contained within the vtkPolyData object. In addition to the vtkPolyLine boundary the shape of the output patch also depends on the spatial derivatives associated with the vtkPolyData points.

The output from the vtkDbiharPatchFilter is a set of nodes for a structured grid representing the patch surface. The set of nodes is converted to vtkStructuredGrid for visualisation.

Generate centreline. python3 Generate216Centreline.py

Build the C++ executables for running specific generating the spepicic size/shape meshes. The executables look for the generated centrelines as input to generate quads/SMCs/ECs. DBiharMesher-x86/meshGen216

Create an empty directory "vtk" and run script to generate VTK mesh files which will be later used for ATP map generation and visual verification. python3 Dump216MeshLegacyFormat.py

Run script to generate ATP files from the previously generated vtk files. python3 Generate216ATPMesh.py

Run script to write HDF5 files. python3 Write216ATPMeshHdf5.py

EVERYTHING BELOW THIS POINT IS KINDA IRRELEVANT OR OUTDATED... REMOVE?

The examples below are for a model with 4080 quads.

The centreline for the bifurcation model is created by the Python program 'Generate4080Centreline.py'. It contains the branches lengths, angles and radius as input data and passes them to 'CentrelineGenerator.py'. TODO: difference consistent/decreasing radii (Murray's Law) The output centreline is two dimensional and the radii in every point are set as scalars. The resulting vtkPolyData is then saved in a file.

The mesh generator program 'meshGen4080.cxx' starts by reading in the centreline file ('c4080Centreline.vtk') and setting the number of radial quads. It prepares the data for the filter that actually generates the surface points, the 'dbiharPatchFilter' (vtkCentrelineToDbiharPatch?). The points are then used to form the quads. This pipeline is a series of scripts and its input can be altered to get different sized and shaped bifurcation models.

The solution from the mesh generator can be improved with the optional filter 'vtkDbiharPatchSmooth'. It has been developed after undesired distortions appeared in simulations run on the bifurcation model. Some of the joined quads form sharp angles along the daughter branches towards the centre of the bifurcation and the aim of this filter is to smoothen them. To do so it reads in the vtkPolyData solution (i.e. 'quadMeshFullc4080.vtp'), generates two new daughter branches on the basis of this input, attaches them to the existing parent branch and gives the new model as output. The lines of the mesh are more consitent due to the way the boundaries for each branch is defined before the 'vtkDbiharPatchFilter' is applied. The boundary line itself is defined as a consecutive collection of points from the temporary solution (output of meshGenerator) and surrounds one single branch (see following image "Boundary"). Each point is then equipped with a derivative. The magnitude and direction of these vectors are functions and dependent on the properties of the input model. They affect the propagations of the generated lines as well as the shape of the solution.

TODO: Other Meshes (SMCs, ECs) and (rectangular, brick lay)!?