1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
|
"""Draw a z = BesselJ(x,y) surface with a custom color map
and a custom scalar bar with labels in radians"""
import numpy as np
from scipy import special
from scipy.special import jn_zeros
from vedo import ScalarBar3D, Line, show, settings
from vedo.colors import color_map, build_lut
from vedo.pyplot import plot
Nr = 1
Nθ = 3
settings.default_font = "Theemim"
settings.interpolate_scalars_before_mapping = False
axes_opts = dict(
xtitle="x", ytitle="y", ztitle="|f(x,y)|",
xlabel_rotation=90, ylabel_rotation=90, zlabel_rotation=90,
xtitle_rotation=90, ytitle_rotation=90, zaxis_rotation=45,
ztitle_offset=0.03,
)
def custom_lut_surface(name, vmin=0, vmax=1, N=256):
# Create a custom look-up-table for the surface
table = []
x = np.linspace(vmin, vmax, N)
for i in range(N):
rgb = color_map(i, name, 0, N-1)
table.append([x[i], rgb])
return build_lut(table)
def custom_table_scalarbar(name):
# Create a custom table of colors and labels for the scalarbar
table = []
x = np.linspace(-np.pi,np.pi, 401)
labs = ["-:pi" , "-3:pi/4", "-:pi/2", "-:pi/4", "0",
"+:pi/4", "+:pi/2", "+3:pi/4","+:pi"]
for i in range(401):
rgb = color_map(i, name, 0, 400)
if i%50 == 0:
table.append([x[i], rgb, 1, labs[i//50]])
else:
table.append([x[i], rgb])
return table, build_lut(table)
######################################################################
def f(x, y):
d2 = x**2 + y**2
if d2 > 1:
return np.nan
else:
r = np.sqrt(d2)
θ = np.arctan2(y, x)
kr = jn_zeros(Nθ, 4)[Nr]
return special.jn(Nθ, kr * r) * np.exp(1j * Nθ * θ)
p1 = plot(
lambda x,y: np.abs(f(x,y)),
xlim=[-1, 1], ylim=[-1, 1],
bins=(100, 100),
show_nan=False,
axes=axes_opts,
)
# Unpack the 0-element (the surface of the plot) to customize it
msh = p1[0].lighting('glossy')
pts = msh.points # get the points
zvals = pts[:,2] # get the z values
θvals = [np.angle(f(*p[:2])) for p in pts] # get the phases
lut = custom_lut_surface("hsv", vmin=-np.pi, vmax=np.pi)
msh.cmap(lut, θvals) # apply the color map
table, lut = custom_table_scalarbar("hsv")
line = Line((1,-1), (1,1)) # a dummy line to attach the scalarbar to
line.cmap("hsv", [0, 1])
scbar = ScalarBar3D(
line,
title=f"N_r ={Nr}, N_θ ={Nθ}, phase :theta in radians",
label_rotation=90,
categories=table,
c='black',
)
# convert the scalarbar to a 2D object and place it to the bottom
scbar = scbar.clone2d([-0.6,-0.7], size=0.2, rotation=-90, ontop=True)
# Set a specific camera position and orientation (shift-C to see it)
cam = dict(
position=(3.88583, 0.155949, 3.88584),
focal_point=(0, 0, 0), viewup=(-0.7, 0, 0.7), distance=5.4,
)
show(p1, scbar, __doc__, camera=cam).close()
|
