Package: gdist
Thetvb-gdistmodule is a Cython interface to a C++ library
(https://code.google.com/archive/p/geodesic/) for computing
geodesic distance which is the length of shortest line between two
vertices on a triangulated mesh in three dimensions, such that the line
lies on the surface.The algorithm is due Mitchell, Mount and Papadimitriou, 1987; the implementation
is due to Danil Kirsanov and the Cython interface to Gaurav Malhotra and
Stuart Knock (TVB Team).Original library (published under MIT license):https://code.google.com/archive/p/geodesic/We added a Python wrapped and made small fixes to the original library, to make
it compatible with Cython.To install this, either runpip installtvb-gdistor download
sources from GitHub and runpython setup.py installin current folder.You can also use pip to directly install from GitHub:pip installgit+https://github.com/the-virtual-brain/tvb-gdist.Basic test could be:python
import gdistPython 3, Cython, and a C++ compiler are required unless the Pypi whl files are
compatible with your system.APIsThe module exposes 2 APIs.gdist.compute_gdist(numpy.ndarray[numpy.float64_t, ndim=2] vertices,
numpy.ndarray[numpy.int32_t, ndim=2] triangles,
numpy.ndarray[numpy.int32_t, ndim=1] source_indices = None,
numpy.ndarray[numpy.int32_t, ndim=1] target_indices = None,
double max_distance = GEODESIC_INF,
bool is_one_indexed = False)This is the wrapper function for computing geodesic distance between a
set of sources and targets on a mesh surface.Args:vertices (numpy.ndarray[numpy.float64_t, ndim=2]): Defines x,y,zcoordinates of the mesh’s vertices.triangles (numpy.ndarray[numpy.float64_t, ndim=2]): Defines faces ofthe mesh as index triplets into vertices.source_indices (numpy.ndarray[numpy.int32_t, ndim=1]): Index of thesource on the mesh.target_indices (numpy.ndarray[numpy.int32_t, ndim=1]): Index of thetargets on the mesh.max_distance (double): Propagation algorithm stops after reaching thecertain distance from the source.is_one_indexed (bool): defines if the index of the triangles data isone-indexed.Returns:numpy.ndarray((len(target_indices), ), dtype=numpy.float64): Specifyingthe shortest distance to the target vertices from the nearest source
vertex on the mesh. If no target_indices are provided, all vertices
of the mesh are considered as targets, however, in this case,
specifying max_distance will limit the targets to those vertices
within max_distance of a source. If no source_indices are provided,
it defaults to 0.NOTE: This is the function to use when specifying localised stimuli and
parameter variations. For efficiently using the whole mesh as sources, such
as is required to represent local connectivity within the cortex, see the
local_gdist_matrix() function.Basic usage then looks like::>>> import numpy
>>> temp = numpy.loadtxt("data/flat_triangular_mesh.txt", skiprows=1)
>>> vertices = temp[0:121].astype(numpy.float64)
>>> triangles = temp[121:321].astype(numpy.int32)
>>> src = numpy.array([1], dtype=numpy.int32)
>>> trg = numpy.array([2], dtype=numpy.int32)
>>> import gdist
>>> gdist.compute_gdist(vertices, triangles, source_indices=src, target_indices=trg)
 array([0.2])gdist.local_gdist_matrix(numpy.ndarray[numpy.float64_t, ndim=2] vertices,
numpy.ndarray[numpy.int32_t, ndim=2] triangles,
double max_distance = GEODESIC_INF,
bool is_one_indexed = False)This is the wrapper function for computing geodesic distance from every
vertex on the surface to all those within a distancemax_distanceof
them.Args:vertices (numpy.ndarray[numpy.float64_t, ndim=2]): Defines x,y,zcoordinates of the mesh’s vertices.triangles (numpy.ndarray[numpy.float64_t, ndim=2]): Defines faces ofthe mesh as index triplets into vertices.max_distance (double): Propagation algorithm stops after reaching thecertain distance from the source.is_one_indexed (bool): defines if the index of the triangles data isone-indexed.Returns:scipy.sparse.csc_matrix((N, N), dtype=numpy.float64): where N
is the number of vertices, specifying the shortest distance from all
vertices to all the vertices within max_distance.Basic usage then looks like::>>> import numpy
>>> temp = numpy.loadtxt("data/flat_triangular_mesh.txt", skiprows=1)
>>> import gdist
>>> vertices = temp[0:121].astype(numpy.float64)
>>> triangles = temp[121:321].astype(numpy.int32)
>>> gdist.local_gdist_matrix(vertices, triangles, max_distance=1.0)
 <121x121 sparse matrix of type '<type 'numpy.float64'>'
     with 6232 stored elements in Compressed Sparse Column format>Runtime and guesstimated memory usage as a function of max_distance for the
reg_13 cortical surface mesh, ie containing 2**13 vertices per hemisphere.
::
[[10, 20, 30, 40,  50,  60,  70,  80,  90, 100], # mm
[19, 28, 49, 81, 125, 181, 248, 331, 422, 522], # s
[ 3, 13, 30, 56,  89, 129, 177, 232, 292, 358]] # MB]where memory is a min-guestimate given by: mem_req = nnz * 8 / 1024 / 1024.distance_matrix_of_selected_points(numpy.ndarray[numpy.float64_t, ndim=2] vertices,
numpy.ndarray[numpy.int32_t, ndim=2] triangles,
numpy.ndarray[numpy.int32_t, ndim=1] points,
double max_distance = GEODESIC_INF,
bool is_one_indexed = False)Function for calculating pairwise geodesic distance for a set of points
within a distancemax_distanceof them.Args:vertices (numpy.ndarray[numpy.float64_t, ndim=2]): Defines x,y,zcoordinates of the mesh’s vertices.triangles (numpy.ndarray[numpy.float64_t, ndim=2]): Defines faces ofthe mesh as index triplets into vertices.points (numpy.ndarray[numpy.int32_t, ndim=1]): Indices of the pointsamong which the pairwise distances are to be calculated.max_distance (double): Propagation algorithm stops after reaching thecertain distance from the source.is_one_indexed (bool): defines if the index of the triangles data isone-indexed.Returns:scipy.sparse.csc_matrix((N, N), dtype=numpy.float64): where Nis the number of vertices, specifying the pairwise distances among
the given points.Basic usage then looks like::>>> import numpy
>>> temp = numpy.loadtxt("data/flat_triangular_mesh.txt", skiprows=1)
>>> vertices = temp[0:121].astype(numpy.float64)
>>> triangles = temp[121:321].astype(numpy.int32)
>>> points = numpy.array([2, 5, 10], dtype=numpy.int32)
>>> import gdist
>>> gdist.distance_matrix_of_selected_points(
        vertices, triangles, points
    )
 <121x121 sparse matrix of type '<class 'numpy.float64'>'
    with 6 stored elements in Compressed Sparse Column format>NotesThe obtained matrix will be almost symmetrical due to floating point
imprecision.In order for the algorithm to work the mesh must not be numbered incorrectly
or disconnected or of somehow degenerate.AcknowledgmentsThis project has received funding from the European Union’s Horizon 2020
Framework Programme for Research and Innovation under the Specific Grant
Agreement No. 826421 - VirtualBrainCloud.