# Curve plot along x = 0 comparing p and w
import numpy as np
tol = 0.001 # avoid hitting points outside the domain
y = np.linspace(-1 + tol, 1 - tol, 101)
points = [(0, y_) for y_ in y] # 2D points
w_line = np.array([w(point) for point in points])
p_line = np.array([p(point) for point in points])
#######################################################################
from vtkplotter.dolfin import plot
from vtkplotter import Line, Latex
pde = r'-T \nabla^{2} D=p, ~\Omega=\left\{(x, y) | x^{2}+y^{2} \leq R\right\}'
tex = Latex(pde, pos=(0, 1.1, .1), s=0.2, c='w')
wline = Line(y, w_line * 10, c='white', lw=4)
pline = Line(y, p_line / 4, c='lightgreen', lw=4)
plot(w, wline, tex, at=0, N=2, bg='bb', text='Deflection')
plot(p, pline, at=1, text='Load')
#######################################################################
#import matplotlib.pyplot as plt
#plot(w)
#plt.plot(y, 50*w_line, 'k', linewidth=2) # magnify w
#plt.plot(y, p_line, 'b--', linewidth=2)
#plt.grid(True)
#plt.xlabel('$y$')
#plt.legend(['Deflection ($\\times 50$)', 'Load'], loc='upper left')
"""
2D histogram with hexagonal binning.
"""
print(__doc__)
from vtkplotter import Plotter, histogram2D, Points, Latex
import numpy as np
vp = Plotter(axes=1, verbose=0, bg="w")
vp.xtitle = "x gaussian, s=1.0"
vp.ytitle = "y gaussian, s=1.5"
vp.ztitle = "dN/dx/dy"
N = 20000
x = np.random.randn(N) * 1.0
y = np.random.randn(N) * 1.5
histo = histogram2D(x, y, c="dr", bins=15, fill=False)
pts = Points([x, y, np.zeros(N)], c="black", alpha=0.1)
f = r'f(x, y)=A \exp \left(-\left(\frac{\left(x-x_{o}\right)^{2}}{2 \sigma_{x}^{2}}+\frac{\left(y-y_{o}\right)^{2}}{2 \sigma_{y}^{2}}\right)\right)'
formula = Latex(f, c='k', s=2).rotateZ(90).pos(5, -2, 1)
vp.show(histo, pts, formula, viewup="z")
Z = np.zeros((n + 2, n + 2), [('U', np.double), ('V', np.double)])
U, V = Z['U'], Z['V']
u, v = U[1:-1, 1:-1], V[1:-1, 1:-1]
r = 20
u[...] = 1.0
U[n // 2 - r:n // 2 + r, n // 2 - r:n // 2 + r] = 0.50
V[n // 2 - r:n // 2 + r, n // 2 - r:n // 2 + r] = 0.25
u += 0.05 * np.random.uniform(-1, 1, (n, n))
v += 0.05 * np.random.uniform(-1, 1, (n, n))
sy, sx = V.shape
grd = Grid(sx=sx, sy=sy, resx=sx, resy=sy)
grd.lineWidth(0).wireframe(False).lighting(ambient=0.5)
formula = r'(u,v)=(D_u\cdot\Delta u -u v v+F(1-u), D_v\cdot\Delta v +u v v -(F+k)v)'
ltx = Latex(formula, s=15, pos=(0, -sy / 1.9, 0))
print('Du, Dv, F, k, name =', Du, Dv, F, k, name)
for step in range(Nsteps):
for i in range(25):
Lu = (U[0:-2, 1:-1] + U[1:-1, 0:-2] - 4 * U[1:-1, 1:-1] + U[1:-1, 2:] +
U[2:, 1:-1])
Lv = (V[0:-2, 1:-1] + V[1:-1, 0:-2] - 4 * V[1:-1, 1:-1] + V[1:-1, 2:] +
V[2:, 1:-1])
uvv = u * v * v
u += Du * Lu - uvv + F * (1 - u)
v += Dv * Lv + uvv - (F + k) * v
grd.cellColors(V.ravel(), cmap='ocean_r').mapCellsToPoints()
newpts = grd.points()
newpts[:, 2] = grd.getPointArray('CellScalars') * 25 # assign z
from vtkplotter import Latex, Point, show
# https://matplotlib.org/tutorials/text/mathtext.html
latex1 = r'x= \frac{ - b \pm \sqrt {b^2 - 4ac} }{2a}'
latex2 = r'\mathcal{A}\mathrm{sin}(2 \omega t)'
latex3 = r'I(Y | X)=\sum_{x \in \mathcal{X}, y \in \mathcal{Y}} p(x, y) \log \left(\frac{p(x)}{p(x, y)}\right)'
latex4 = r'\Gamma_{\epsilon}(x)=\left[1-e^{-2 \pi \epsilon}\right]^{1-x} \prod_{n=0}^{\infty} \frac{1-\exp (-2 \pi \epsilon(n+1))}{1-\exp (-2 \pi \epsilon(x+n))}'
latex5 = r'\left( \begin{array}{l}{c t^{\prime}} \\ {x^{\prime}} \\ {y^{\prime}} \\ {z^{\prime}}\end{array}\right)=\left( \begin{array}{cccc}{\gamma} & {-\gamma \beta} & {0} & {0} \\ {-\gamma \beta} & {\gamma} & {0} & {0} \\ {0} & {0} & {1} & {0} \\ {0} & {0} & {0} & {1}\end{array}\right) \left( \begin{array}{l}{c t} \\ {x} \\ {y} \\ {z}\end{array}\right)'
latex6 = r'\mathrm{CO}_{2}+6 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}+6 \mathrm{O}_{2}'
latex7 = r'x \mathrm{(arb. units)}'
l = Latex(latex4,
s=1,
c='white',
bg='',
alpha=0.9,
usetex=False,
fromweb=False)
l.crop(0.3, 0.3) # crop top and bottom 30%
l.pos(2, 0, 0)
p = Point()
box = l.box() # return the bounding box of an actor
show(p, l, box, axes=8)
from vtkplotter import Latex, Cube, Point, show
# https://matplotlib.org/tutorials/text/mathtext.html
latex1 = r'x= \frac{ - b \pm \sqrt {b^2 - 4ac} }{2a}'
latex2 = r'$\mathcal{A}\mathrm{sin}(2 \omega t)$'
latex3 = r'I(Y | X)=\sum_{x \in \mathcal{X}, y \in \mathcal{Y}} p(x, y) \log \left(\frac{p(x)}{p(x, y)}\right)'
latex4 = r'\Gamma_{\epsilon}(x)=\left[1-e^{-2 \pi \epsilon}\right]^{1-x} \prod_{n=0}^{\infty} \frac{1-\exp (-2 \pi \epsilon(n+1))}{1-\exp (-2 \pi \epsilon(x+n))}'
latex5 = r'\left( \begin{array}{l}{c t^{\prime}} \\ {x^{\prime}} \\ {y^{\prime}} \\ {z^{\prime}}\end{array}\right)=\left( \begin{array}{cccc}{\gamma} & {-\gamma \beta} & {0} & {0} \\ {-\gamma \beta} & {\gamma} & {0} & {0} \\ {0} & {0} & {1} & {0} \\ {0} & {0} & {0} & {1}\end{array}\right) \left( \begin{array}{l}{c t} \\ {x} \\ {y} \\ {z}\end{array}\right)'
latex6 = r'\mathrm{CO}_{2}+6 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}+6 \mathrm{O}_{2}'
latex7 = r'x~\mathrm{(arb. units)}'
p = Point()
c = Cube().wire()
l = Latex(latex5, s=1, c='white', bg='', alpha=0.9,
fromweb=False).addPos(4, 0, -1)
show(p, c, l, axes=8)
from vtkplotter import Latex
# https://matplotlib.org/tutorials/text/mathtext.html
latex1 = r'x= \frac{ - b \pm \sqrt {b^2 - 4ac} }{2a}'
latex2 = r'\mathcal{A}\mathrm{sin}(2 \omega t)'
latex3 = r'I(Y | X)=\sum_{x \in \mathcal{X}, y \in \mathcal{Y}} p(x, y) \log \left(\frac{p(x)}{p(x, y)}\right)'
latex4 = r'\Gamma_{\epsilon}(x)=\left[1-e^{-2 \pi \epsilon}\right]^{1-x} \prod_{n=0}^{\infty} \frac{1-\exp (-2 \pi \epsilon(n+1))}{1-\exp (-2 \pi \epsilon(x+n))}'
latex5 = r'\left( \begin{array}{l}{c t^{\prime}} \\ {x^{\prime}} \\ {y^{\prime}} \\ {z^{\prime}}\end{array}\right)=\left( \begin{array}{cccc}{\gamma} & {-\gamma \beta} & {0} & {0} \\ {-\gamma \beta} & {\gamma} & {0} & {0} \\ {0} & {0} & {1} & {0} \\ {0} & {0} & {0} & {1}\end{array}\right) \left( \begin{array}{l}{c t} \\ {x} \\ {y} \\ {z}\end{array}\right)'
latex6 = r'\mathrm{CO}_{2}+6 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}+6 \mathrm{O}_{2}'
latex7 = r'x \mathrm{(arb. units)}'
ltx = Latex(latex4,
s=1,
c='darkblue',
bg='',
alpha=0.9,
usetex=False,
fromweb=False)
ltx.crop(0.3, 0.3) # crop top and bottom 30%
ltx.pos(2, 0, 0)
ltx.show(axes=1)