def fitSphere(coords, c='r', alpha=1, wire=1, legend=None):
'''
Fits a sphere to a set of points.
Extra info is stored in actor.radius, actor.center, actor.residue
[**Example1**](https://github.com/marcomusy/vtkplotter/blob/master/examples/advanced/fitspheres1.py)
[**Example2**](https://github.com/marcomusy/vtkplotter/blob/master/examples/advanced/fitspheres2.py)
'''
coords = np.array(coords)
n = len(coords)
A = np.zeros((n, 4))
A[:, :-1] = coords*2
A[:, 3] = 1
f = np.zeros((n, 1))
x = coords[:, 0]
y = coords[:, 1]
z = coords[:, 2]
f[:, 0] = x*x + y*y + z*z
C, residue, rank, sv = np.linalg.lstsq(A, f) # solve AC=f
if rank < 4:
return None
t = (C[0]*C[0]) + (C[1]*C[1]) + (C[2]*C[2]) + C[3]
radius = np.sqrt(t)[0]
center = np.array([C[0][0], C[1][0], C[2][0]])
if len(residue):
residue = np.sqrt(residue[0])/n
else:
residue = 0
s = vs.sphere(center, radius, c, alpha, wire=wire, legend=legend)
s.info['radius'] = radius
s.info['center'] = center
s.info['residue'] = residue
return s
def fitSphere(coords, c='r', alpha=1, wire=1, legend=None):
'''
Fits a sphere to a set of points.
Extra info is stored in actor.radius, actor.center, actor.residue
'''
coords = np.array(coords)
n = len(coords)
A = np.zeros((n, 4))
A[:, :-1] = coords * 2
A[:, 3] = 1
f = np.zeros((n, 1))
x = coords[:, 0]
y = coords[:, 1]
z = coords[:, 2]
f[:, 0] = x * x + y * y + z * z
C, residue, rank, sv = np.linalg.lstsq(A, f, rcond=None) # solve AC=f
if rank < 4: return None
t = (C[0] * C[0]) + (C[1] * C[1]) + (C[2] * C[2]) + C[3]
radius = np.sqrt(t)[0]
center = np.array([C[0][0], C[1][0], C[2][0]])
if len(residue): residue = np.sqrt(residue[0]) / n
else: residue = 0
s = vs.sphere(center, radius, c, alpha, wire=wire, legend=legend)
setattr(s, 'radius', radius)
setattr(s, 'center', center)
setattr(s, 'residue', residue)
return s
def myloop(*event):
global counts # this is needed because counts is being modified:
counts += 0.1
# reference 'actor' is not modified so doesnt need to be global
# (internal properties of the object are, but python doesn't know..)
actor.pos([0, counts / 20, 0]).color(counts) # move cube and change color
rp = [u(-1, 1), u(0, 1), u(-1, 1)] # a random position
s = sphere(rp, r=0.05, c='blue 0.2')
vp.render(s, resetcam=True) # show() would cause exiting the loop
# waste cpu time to slow down program
for i in range(100000):
sin(i)
printc('#', end='')
# Generate a time sequence of 3D shapes (from a sphere to a tetrahedron)
# as noisy cloud points, and smooth it with Moving Least Squares (smoothMLS3D).
# This make a simultaneus fit in 4D (space+time).
# smoothMLS3D method returns a vtkActor where points are color coded
# in bins of fitted time.
# Data itself can suggest a meaningful time separation based on the spatial
# distribution of points.
# The nr neighbours in the local 4D fitting must be specified.
#
import numpy as np
from vtkplotter import Plotter
from vtkplotter.shapes import sphere
from vtkplotter.analysis import smoothMLS3D
vp = Plotter(N=2, axes=0)
# generate uniform points on sphere (tol separates points by 2% of actor size)
cc = sphere(res=200).clean(tol=0.02).coordinates()
a, b, noise = .2, .4, .1 # some random warping paramenters, and noise factor
for i in range(5): # generate a time sequence of 5 shapes
cs = cc + a * i * cc**2 + b * i * cc**3 # warp sphere in weird ways
# set absolute time of points actor, and add 1% noise on positions
vp.points(cs, c=i, alpha=0.5).gaussNoise(1.0).time(0.2 * i)
vp.show(at=0, zoom=1.4) # show input clouds as func(time)
asse = smoothMLS3D(vp.actors, neighbours=50)
vp.addScalarBar3D(asse, at=1, pos=(-2, 0, -1)) # color indicates fitted time
vp.show(asse, at=1, zoom=1.4, axes=4, interactive=1)