Order scattered points to create a spline/line

[eivindtn]

Hi again @marcomusy, As in #349, we talked about ordering points in the "right" order, so it's possible to create lines/splines and increase the resolution of points from the intersection curve between two meshes. And you have added the function mesh.join(reset= True) which are great, and working with the intersectwith() . However, is it possible to use this function for scattered points along a line? Like for the smoothed points (pts) from the example examples/advanced/moving_least_squares1D

I have tried to create a mesh from the pts, but havent suceed into order the points, so I can increase the resolution by creating a spline. I think the issue is that I haven't figured how to create the mesh.lines() boundaries. Im not sure, but it is right that mesh.lines() need to be defined in order to order points with the function mesh.join(reset= True)?

I have tried to reconstruct one of my issue with the moving least square example:

from vedo import *
import numpy as np

N = 4  # nr. of iterations

# build some initial cloud of noisy points along a line
pts = [ (sin(6*x), cos(2*x)*x, cos(9*x)) for x in np.arange(0,2, .001)]
# pts = [ (0, sin(x), cos(x)) for x in arange(0,6, .002) ]
# pts = [(sqrt(x), sin(x), x/5) for x in arange(0, 16, 0.01)]

pts += np.random.randn(len(pts), 3) /20  # add noise
np.random.shuffle(pts)  # make sure points are not ordered

pts = Points(pts, r=5)

for i in range(1, N):
    pts = pts.clone().smoothMLS1D(f=0.4).color(i)

    if i == N-1:
        # at the last iteration make sure points
        # are separated by tol (in % of bbox)
        pts.clean(tol=0.02)

msh  = Mesh(pts).triangulate()
print(msh.lines()) # empty array
msh2 = msh.clone().join(reset=True)
msh2.points() # only one point           I think I do something strange here
# trying to create a spline from the pts
sph = Spline(pts)
show(pts, sph, N=2).close() 

[marcomusy]

This situation is very different from the one discussed in the other issue where te intersection implicitly defines the order of the points. In this case, which is way more general, there is no way a priori to identify the connectivity of the points. You may think of trying to order them by x,y, or z but that's obviously not enough:

from vedo import *
import numpy as np

N = 3  # nr. of iterations

# build some initial cloud of noisy points along a line
pts = [ (sin(6*x), cos(2*x)*x, cos(9*x)) for x in np.arange(0,2, .001)]

pts += np.random.randn(len(pts), 3) /30  # add noise
np.random.shuffle(pts)  # make sure points are not ordered

# try to sort them along y..
pts = utils.sortByColumn(pts, 1)

pts = Points(pts, r=9).c('r')

for i in range(1, N):
    pts = pts.clone().smoothMLS1D(f=0.4)
    if i == N-1:
        pts.clean(tol=0.02)

# trying to create a spline from the pts
sph = Line(pts)
show(pts, sph, axes=1)

I guess You need to "navigate" iteratively along closest point from a seed and fixing a threshold (?).
Maybe there's some more clever algorithm to achieve the same , but I can't think of any.

[eivindtn]

You're right! I see now that this is a very general case compared to the other issue. And selecting this example wasn't the best choice, regarding comparing it to my issue. I will look into it, and come back to you later!
Anyway, thank you!

[eivindtn]

I will close this issue for now since I haven't find a clever solution for the problem above. And I also see that it isn't so related to my wanted approach. Thanks!