example of curvature directions in slam

# Authors: Julien Lefevre <julien.lefevre@univ-amu.fr>

# License: MIT
# sphinx_gallery_thumbnail_number = 2

NOTE: there is no visualization tool in slam, but we provide at the

end of this script exemplare code to do the visualization with an external solution

---

# importation of slam modules
import slam.generate_parametric_surfaces as sgps
import slam.curvature as scurv

Create quadric mesh

nstep = 20
equilateral = True

K = [1, 0.5]
quadric_mesh = sgps.generate_quadric(
    K,
    nstep=[int(nstep), int(nstep)],
    equilateral=equilateral,
    ax=1,
    ay=1,
    random_sampling=False,
    ratio=0.2,
    random_distribution_type="gaussian",
)

Compute principal directions of curvature

PrincipalCurvatures, PrincipalDir1, PrincipalDir2 \
    = scurv.curvatures_and_derivatives(quadric_mesh)

Calculating vertex normals .... Please wait
Finished calculating vertex normals
Calculating curvature tensors ... Please wait
Finished Calculating curvature tensors
Calculating Principal Components ... Please wait
Finished Calculating principal components

VISUALIZATION USING EXTERNAL TOOLS

import numpy as np import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D

# Visualization of vector fields with matplotlib def visualize(mesh, vector_field, colors=None, params=None):

“”” Visualize a mesh and a vector field over it :param mesh: a mesh with n points :param vector_field: (n,3) array :param colors: (n,3) array :param params: params[0] is the length of the quivers :return: “”” n = mesh.vertices.shape[0] if colors is None:

colors = np.zeros((n, 3)) colors[:, 0] = 1

if params is None:

params = [] params.append(0.1)

fig = plt.figure() ax = Axes3D(fig) ax.plot_trisurf(

mesh.vertices[:, 0], mesh.vertices[:, 1], mesh.vertices[:, 2], triangles=mesh.faces, shade=True,

) plt.quiver(

mesh.vertices[:, 0], mesh.vertices[:, 1], mesh.vertices[:, 2], vector_field[:, 0], vector_field[:, 1], vector_field[:, 2], length=params[0], colors=colors,

)

return fig

visualize(quadric_mesh, PrincipalDir1) plt.show()