Mapping example in slam

# Authors:
# Guillaume Auzias <guillaume.auzias@univ-amu.fr>
# Julien Barrès <julien.barres@etu.univ-amu.fr>

# License: BSD (3-clause)
# sphinx_gallery_thumbnail_number = 2

Importation of slam modules

import slam.generate_parametric_surfaces as sps
import numpy as np
import slam.topology as stop
import slam.plot as splt
import slam.mapping as smap
import slam.distortion as sdst
from vispy.scene import Line
from visbrain.objects import VispyObj, SourceObj

Generation of an open mesh

K = [-1, -1]
open_mesh = sps.generate_quadric(K, nstep=[5, 5])
open_mesh_boundary = stop.mesh_boundary(open_mesh)
# Visualization
visb_sc = splt.visbrain_plot(mesh=open_mesh, caption="open mesh")
for bound in open_mesh_boundary:
    points = open_mesh.vertices[bound]
    s_rad = SourceObj("rad", points, color="red", symbol="square", radius_min=10)
    visb_sc.add_to_subplot(s_rad)
    lines = Line(pos=open_mesh.vertices[bound], width=10, color="b")
    # wrap the vispy object using visbrain
    l_obj = VispyObj("line", lines)
    visb_sc.add_to_subplot(l_obj)
visb_sc.preview()

Mapping onto a planar disk

disk_mesh = smap.disk_conformal_mapping(open_mesh)
# Visualization
visb_sc2 = splt.visbrain_plot(mesh=disk_mesh, caption="disk mesh")
for bound in open_mesh_boundary:
    points = disk_mesh.vertices[bound]
    s_rad = SourceObj("rad", points, color="red", symbol="square", radius_min=10)
    visb_sc2.add_to_subplot(s_rad)
    lines = Line(pos=disk_mesh.vertices[bound], width=10, color="b")
    # wrap the vispy object using visbrain
    l_obj = VispyObj("line", lines)
    visb_sc2.add_to_subplot(l_obj)
visb_sc2.preview()

Out:

  Computing Laplacian
    Computing mesh weights of type conformal
    -edge length threshold needed for  0  values =  0.0  %
    -number of Nan in weights:  0  =  0.0  %
    -number of Negative values in weights:  4  =  4.0  %
    -nb Nan in Laplacian :  0
    -nb Inf in Laplacian :  0
Boundary Size: (13,)
Laplacian Size: (22, 22)

Compute distortion measures between original and planar representations

angle_diff = sdst.angle_difference(disk_mesh, open_mesh)
area_diff = sdst.area_difference(disk_mesh, open_mesh)
edge_diff = sdst.edge_length_difference(disk_mesh, open_mesh)
print(np.mean(angle_diff))
print(np.mean(area_diff))
print(np.mean(edge_diff))

Out:

2.5522368382187506e-18
-0.03526596276269568
-0.09295198609266887