Mapping example in slam

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

# License: MIT
# 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.mapping as smap
import slam.distortion as sdst

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)

Mapping onto a planar disk

disk_mesh = smap.disk_conformal_mapping(open_mesh)

  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:  12  =  11.538461538461538  %
    -nb Nan in Laplacian :  0
    -nb Inf in Laplacian :  0
Boundary Size: (14,)
Laplacian Size: (23, 23)

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))

1.4802973661668754e-17
-0.017776906751143608
-0.05311587143257269

VISUALIZATION USING EXTERNAL TOOLS

# Visualization with visbrain import slam.plot as splt from vispy.scene import Line from visbrain.objects import VispyObj, SourceObj # Visualization of the open mesh 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()

# Visualization of the same mesh mapped onto a disk 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()