Generating parametric surfaces 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 sgps
import slam.plot as splt
import numpy as np

Generating a quadrix surface

K = [1, 1]
quadric = sgps.generate_quadric(
    K,
    nstep=[20, 20],
    ax=3,
    ay=1,
    random_sampling=True,
    ratio=0.3,
    random_distribution_type="gamma",
)
quadric_mean_curv = sgps.quadric_curv_mean(K)(
    np.array(quadric.vertices[:, 0]), np.array(quadric.vertices[:, 1])
)

visb_sc = splt.visbrain_plot(
    mesh=quadric, tex=quadric_mean_curv, caption="quadric", cblabel="mean curvature"
)

visb_sc.preview()

Generating an ellipsiods

nstep = 50
randomSampling = True
a = 2
b = 1
ellips = sgps.generate_ellipsiod(a, b, nstep, randomSampling)

visb_sc = splt.visbrain_plot(mesh=ellips, caption="ellipsoid")

visb_sc.preview()

Generating a sphere

sphere_regular = sgps.generate_sphere_icosahedron(subdivisions=3, radius=4)


visb_sc = splt.visbrain_plot(mesh=sphere_regular, caption="sphere_regular")

visb_sc.preview()

Generating a more randomized sphere (random sampling with the same number of vertices)

sphere_random = sgps.generate_sphere_random_sampling(
    vertex_number=sphere_regular.vertices.shape[0], radius=4
)

visb_sc = splt.visbrain_plot(
    mesh=sphere_random, caption="sphere_random", visb_sc=visb_sc
)

visb_sc.preview()

Computation of the volume and volume error of the spheres

analytical_vol = (4 / 3) * np.pi * np.power(4, 3)
print(
    "volume error for regular sampling: {:.3f}".format(
        sphere_regular.volume - analytical_vol
    )
)
print(
    "volume error for random sampling: {:.3f}".format(
        sphere_random.volume - analytical_vol
    )
)

Out:

volume error for regular sampling: -2.307
volume error for random sampling: -5.000