Curvature Calculation

We present the following methods. In the first method a CGAL surface mesh is required. This method fits a polynomial to the surface

start = time.time()
k_max_monge, k_min_monge = pma.algorithms.curvature_fitting.monge_surface_mesh_fitting(
   cgal_mesh, d_fitting=3, d_monge=3, knn=300, internal=True
)
end = time.time()

print("time taken:", end-start)

If only points are available the following method applies normal section fitting

# if the data is a set of points, we can apply the normal section fitting method
points = surface_mesh.points()

start = time.time()
# assumes the points are in the form dims * points
point_surface = pma.arrays.Pointsurface(points.T)
# the following is the is ordered max, min and ordered principal directions
k_max_min, d_max_min = point_surface.compute_principle_curvatures(
   neighbours=300, external=False
)
end = time.time()

print(end-start)

we can plot the results of the first and second methods

plotter_1 = pv.BackgroundPlotter()
mesh_1 = pv.PolyData(points)
mesh_1.point_arrays['max_curvature'] = k_max_monge
plotter_1.add_mesh(mesh_1)
plotter_1.show()

plotter_2 = pv.BackgroundPlotter()
mesh_2 = pv.PolyData(points)
mesh_2.point_arrays['max_curvature'] = k_max_min[0]
plotter_2.add_mesh(mesh_2)
plotter_2.show()