Helper Module for Deep Learning.

Module that provides spherical sampling & associated utilities.

pynet.models.spherical.sampling.downsample(vertices, target_vertices)[source]¶

Downsample by finding nearest neighbors.

Parameters

vertices: array (n_samples, n_dim)

points of data set.

target_vertices: array (n_query, n_dim)

points to find nearest neighbors for.

Returns

nearest_idx: array (n_query, )

index of nearest neighbor in target_vertices for every point in vertices.

pynet.models.spherical.sampling.get_angle_with_xaxis(center, normal, point)[source]¶

Project a point to the sphere tangent plane and compute the angle with the x-axis.

Parameters

center: array (3, )

a point in the plane.

normal: array (3, )

the normal to the plane.

points: array (3, )

the points to be projected.

pynet.models.spherical.sampling.get_rectangular_projection(node, size=5, zoom=5)[source]¶

Project rectangular grid in 2D sapce into 3D spherical space.

Parameters

node: array (3, )

a point in the sphere.

size: int, default 5

the rectangular grid size.

zoom: int, default 5

scale factor applied on the unit sphere to control the neighborhood density.

Returns

grid_in_sphere: array (size**2, 3)

zoomed rectangular grid on the sphere.

grid_in_tplane: array (size**2, 3)

zoomed rectangular grid in the tangent space.

pynet.models.spherical.sampling.icosahedron(order=3)[source]¶

Define an icosahedron mesh of any order.

Parameters

order: int, default 3

the icosahedron order.

Returns

vertices: array (N, 3)

the icosahedron vertices.

triangles: array (N, 3)

the icosahedron triangles.

pynet.models.spherical.sampling.interpolate(vertices, target_vertices, target_triangles)[source]¶

Interpolate missing data.

Parameters

vertices: array (n_samples, n_dim)

points of data set.

target_vertices: array (n_query, n_dim)

points to find interpolated texture for.

target_triangles: array (n_query, 3)

the mesh geometry definition.

Returns

interp_textures: array (n_query, n_feats)

the interplatedd textures.

pynet.models.spherical.sampling.middle_point(point_1, point_2, vertices, middle_point_cache)[source]¶

Find a middle point and project to the unit sphere.

pynet.models.spherical.sampling.neighbors(vertices, triangles, depth=1, direct_neighbor=False)[source]¶

Build mesh vertices neighbors.

Parameters

vertices: array (N, 3)

the icosahedron vertices.

triangles: array (N, 3)

the icosahedron triangles.

depth: int, default 1

depth to stop the neighbors search, only paths of length <= depth are returned.

direct_neighbor: bool, default False

each spherical surface is composed of two types of vertices: 1) 12 vertices with each having only 5 direct neighbors; and 2) the remaining vertices with each having 6 direct neighbors. For those vertices with 6 neighbors, DiNe assigns the index 1 to the center vertex and the indices 2–7 to its neighbors sequentially according to the angle between the vector of center vertex to neighboring vertex and the x-axis in the tangent plane. For the 12 vertices with only 5 neighbors, DiNe assigns the indices both 1 and 2 to the center vertex, and indices 3–7 to the neighbors in the same way as those vertices with 6 neighbors.

Returns

neighs: dict

a dictionary with vertices row index as keys and a dictionary of neighbors vertices row indexes organized by rungs as values.

pynet.models.spherical.sampling.neighbors_rec(vertices, triangles, size=5, zoom=5)[source]¶

Build rectangular grid neighbors and weights.

Parameters

vertices: array (N, 3)

the icosahedron vertices.

triangles: array (N, 3)

the icosahedron triangles.

size: int, default 5

the rectangular grid size.

zoom: int, default 5

scale factor applied on the unit sphere to control the neighborhood density.

Returns

neighs: array (N, size**2, 3)

grid samples neighbors for each vertex.

weights: array (N, size**2, 3)

grid samples weights with neighbors for each vertex.

grid_in_sphere: array (N, size**2, 3)

zoomed rectangular grid on the sphere vertices.

pynet.models.spherical.sampling.normalize(vertex)[source]¶

Return vertex coordinates fixed to the unit sphere.

pynet.models.spherical.sampling.number_of_ico_vertices(order=3)[source]¶

Get the number of vertices of an icosahedron of specific order.

Parameters

order: int, default 3

the icosahedron order.

Returns

vertices: array (N, 3)

the icosahedron vertices.

triangles: array (N, 3)

the icosahedron triangles.

pynet.models.spherical.sampling.triangles_to_edges(triangles, return_index=False)[source]¶

Given a list of triangles, return a list of edges.

Parameters

triangles: array int (N, 3)

Vertex indices representing triangles.

Returns

edges: array int (N * 3, 2)

Vertex indices representing edges.

triangles_index: array (N * 3, )

Triangle indexes.

pynet.models.spherical.sampling.vertex_adjacency_graph(vertices, triangles)[source]¶

Build a networkx graph representation of the vertices and their connections in the mesh.

Parameters

vertices: array (N, 3)

the icosahedron vertices.

triangles: array (N, 3)

the icosahedron triangles.

Returns

graph: networkx.Graph

Graph representing vertices and edges between them where vertices are nodes and edges are edges

Examples

This is useful for getting nearby vertices for a given vertex, potentially for some simple smoothing techniques. >>> graph = mesh.vertex_adjacency_graph >>> graph.neighbors(0) > [1, 3, 4]