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droplet.py
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droplet.py
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# scikit-image is used for image processing:
from skimage import data, io
import skimage.feature
import skimage.viewer
import skimage
# NOTE: CP is an API for the NIST database used for the water Equation of State:
from CoolProp.CoolProp import PropsSI
# Imports and physical parameters
import copy
import sys
import numpy as np
import scipy
#from matplotlib import pyplot as plt
import matplotlib.image as mpimg
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.patches import FancyArrowPatch
from mpl_toolkits.mplot3d import proj3d
#%matplotlib notebook
# Local library
from ddgclib import *
from ddgclib._complex import *
from ddgclib._sphere import *
from ddgclib._curvatures import * #plot_surface#, curvature
from ddgclib._sessile import *
from ddgclib._capillary_rise_flow import * #plot_surface#, curvature
from ddgclib._eos import *
from ddgclib._plotting import *
#from ddgclib.curvatures import plot_surface, curvature
# Equation of state for water droplet:
def eos(P=101.325, T=298.15):
# P in kPa T in K
return PropsSI('D','T|liquid',298.15,'P',101.325,'Water') # density kg /m3
# Surface tension of water gamma(T):
def IAPWS(T=298.15):
T_C = 647.096 # K, critical temperature
return 235.8e-3 * (1 -(T/T_C))**1.256 * (1 - 0.625*(1 - (T/T_C))) # N/m
# Local compression (approx. Hooke's law)
def local_compressive_forces(v, r):
# Compute the distance of vertex from great sphere centre:
gsc = -R * np.sin(theta_p) # great sphere centre
gsc = -R * np.sin(theta_p) # great sphere centre
# gsc = +2.3830646612262073e-05 -R * np.sin(theta_p) # great sphere centre
# gsc = +3e-05 -R * np.sin(theta_p) # great sphere centre
# gsc = +3.5e-05 -R * np.sin(theta_p) # great sphere centre
# gsc = +4.5e-05 -R * np.sin(theta_p) # great sphere centre
if 0:
N_f0 = np.array(
#[0.0, 0.0, R * np.sin(theta_p)]) - v.x_a # First approximation
[0.0, 0.0, gsc]) - v.x_a # First approximation
if 1:
N_f0 = v.x_a - np.array([0.0, 0.0, gsc])
#N_f0 = v.x_a - np.array([0.0, 0.0, -(R-R * np.sin(theta_p))])
print(f' N_f0 = {N_f0}')
print(f' np.linalg.norm(N_f0) = {np.linalg.norm(N_f0)}')
# Compute the norm:
d = np.linalg.norm(N_f0)
print(f' d = {d}')
print(f' R = {R}')
#@print(f' r = {r}')
if d < R:
N_f0 = normalized(N_f0)[0]
#return N_f0 * (r - d)
#return N_f0 * (R - d)
return N_f0 * (R - d)
else:
return np.array([0.0, 0.0, 0.0])
def mean_flow(HC, bV, params, tau, print_out=False):
(gamma, rho, g, r, theta_p, K_f, h) = params
print('.')
# Compute interior curvatures
#(HNda_v_cache, K_H_cache, C_ijk_v_cache, HN_i, HNdA_ij_dot_hnda_i,
# K_H_2, HNdA_i_Cij) = int_curvatures(HC, bV, r, theta_p, printout=False)
(HN_i, C_ij, K_H_i, HNdA_i_Cij, Theta_i,
HNdA_i_cache, HN_i_cache, C_ij_cache, K_H_i_cache, HNdA_i_Cij_cache,
Theta_i_cache) = HC_curvatures_sessile(HC, bV, r, theta_p, printout=0)
# if bV is None:
#bV = HC.boundary() #TODO: Check it again it is not working properly
# Move boundary vertices:
bV_new = set()
for v in HC.V:
print(f'.')
print(f'v.x = {v.x}')
if v.x[0] == 0.0 and v.x[1] == 0.0:
print(f'='*10)
# Compute boundary movements
# Note: boundaries is fixed for now, this is legacy:
if v in bV:
rati = (np.pi - np.array(Theta_i) / 2 * np.pi)
#TODO: THis is not the actual sector ration (wrong angle)
# rati = np.array(Theta_i) / (2 * np.pi)
# print(f' rati = 2 * np.pi /np.array(Theta_i)= { rati}')
if 0:
#TODO: len(bV) is sector fraction
H_K = HNda_v_cache[v.x] * np.array([0, 0, -1]) * len(bV)
print(f'K_H in bV = {H_K }')
K_H = ((np.sum(H_K) / 2.0) / C_ijk_v_cache[v.x] ) ** 2
K_H = ((np.sum(H_K) / 2.0) ) ** 2
print(f'K_H in bV = {K_H}')
print(f'K_H - K_f in bV = {K_H - K_f}')
K_H_dA = K_H_i_cache[v.x] * np.sum(C_ij_cache[v.x])
#TODO: Adjust for other geometric approximations:
l_a = 2 * np.pi * r / len(bV) # arc length
Xi = 1
# Gauss-Bonnet: int_M K dA + int_dM kg ds = 2 pi Xi
# NOTE: Area should be height of spherical cap
# h = R - r * 4np.tan(theta_p)
# Approximate radius of the great shpere K = (1/R)**2:
#R_approx = 1 / np.sqrt(K_f)
R_approx = 1 / np.sqrt(K_H_i_cache[v.x])
theta_p_approx = np.arccos(np.min([r / R_approx, 1]))
h = R_approx - r * np.tan(theta_p_approx)
A_approx = 2 * np.pi * R_approx * h # Area of spherical cap
#print(f'A_approx = {A_approx}')
# A_approx # Approximate area of the spherical cap
#kg_ds = 2 * np.pi * Xi - K_f * (A_approx)
#kg_ds = 2 * np.pi * Xi - K_H_dA * (A_approx)
kg_ds = 2 * np.pi * Xi - K_H_i_cache[v.x] * (A_approx)
# TODO: This is NOT the correct arc length (wrong angle)
ds = 2 * np.pi * r # Arc length of whole spherical cap
#print(f'ds = {ds}')
k_g = kg_ds / ds # / 2.0
#print(f'k_g = {k_g}')
print(f' R_approx * k_g = {R_approx * k_g}')
phi_est = np.arctan(R_approx * k_g)
# Compute boundary forces
# N m-1
print(f' phi_est = { phi_est}')
print(f' theta_p = {theta_p}')
gamma_bt = gamma * (np.cos(phi_est)
- np.cos(theta_p)) * np.array([0, 0, 1.0])
print(f' phi_est = {phi_est * 180/np.pi}')
F_bt = gamma_bt * l_a # N
print(f' F_bt = {F_bt}')
F_bt = np.zeros_like(F_bt) # Fix boundaries for now
print(f' F_bt = {F_bt}')
#new_vx = v.x + tau * F_bt
# new_vx = v.x + 1e-1 * F_bt
# New: 2021.09.29
if 1:
dc = local_compressive_forces(v, r)
# Weak compressibility and gravity for solver stability
if 1:
#dc = 1e-1 * dc #
dc = dc #
#dg = 1e-3 * dg #
print(f' dc = {dc}')
new_vx = v.x + F_bt + dc
new_vx = tuple(new_vx)
if print_out:
print('.')
print(f'K_H_i_cache[v.x = {v.x}] = {K_H_i_cache[v.x]}')
print(f'HNdA_i_cache[v.x = {v.x}] = {HNdA_i_cache[v.x]}')
print(f' rati = {rati}')
# rati = (2 * np.pi - np.array(Theta_i))/np.pi
# print(f' rati = (2 * np.pi - Theta_i)/np.pi = { rati}')
print(
f'HNdA_i_cache[1] * rati[1] = {HNdA_i_cache[v.x] * rati[1]}')
print(f'K_H_i = {K_H_i}')
print(f'K_f = {K_f}')
print(f'K_H_i_cache[v.x] = {K_H_i_cache[v.x]}')
# TEST; UNDO:
if 0:
HC.V.move(v, new_vx)
bV_new.add(HC.V[new_vx])
if print_out:
print(f'K_H_dA= {K_H_dA}')
print(f'l_a= {l_a}')
print(f'R_approx = {R_approx}')
print(f'theta_p_approx = {theta_p_approx * 180 / np.pi}')
print(f'Theta_i = {Theta_i}')
print(f'phi_est = {phi_est * 180 / np.pi}')
#print(f'dK[i] = {dK[i]}')
# Current main code:
else:
#H = np.dot(HNdA_i_cache[v.x], np.array([0, 0, 1]))
H = HN_i_cache[v.x] #TODO: Why is this sometimes negative? Should never be
#H = np.abs(H)
print(f' H = {H}')
#print(f' np.dot(HN_i_cache[v.x], np.array([0, 0, 1])) = {np.dot(HN_i_cache[v.x], np.array([0, 0, 1]))}')
#print(f' HN_i_cache[v.x] = {HN_i_cache[v.x]}')
#print(f' H = {H}')
#
height = np.max([v.x_a[2], 0.0])
if 0:
df = gamma * H # Hydrostatic pressure
print(f' HNdA_i_cache[v.x] = {HNdA_i_cache[v.x]}')
#print(f'HNdA_i_Cij_cache[v.x] = {HNdA_i_Cij_cache[v.x]}')
df = gamma * H # Hydrostatic pressure
print(f' gamma * H = { gamma * H}')
print(f' HNdA_i_cache[v.x] = {HNdA_i_cache[v.x]}')
print(f' HN_i = {HNdA_i_cache[v.x]}')
print(f' rho * g * height = {rho * g * height}')
print(f' height = {height}')
H = HNdA_i_cache[v.x]
dg = np.array([0, 0, -rho * g * height])
df = gamma * H #- (rho * g * height)
#df = 2* gamma * H - 1e-3*(rho * g * height)
#f_k = f + tau * df
print(f' df = {df}')
#print(f' gamma = {gamma}')
# Add compressive forces:
dc = local_compressive_forces(v, r)
# Weak compressibility and gravity for solver stability
if 1:
#dc = 1e-1 * dc #
dc = dc #
dg = 1e-3 * dg #
print(f' dc = {dc}')
print(f' dg = {dg}')
#print(f;)
#f_k = v.x_a + np.array([0, 0, tau * df]).
#f_k = v.x_a + df + dc + dg
f_k = v.x_a + df + dc + dg
#f_k = v.x_a + df #+ dc
f_k[2] = np.max([f_k[2], 0.0])
new_vx = tuple(f_k)
#VA.append(v.x_a)
# Move interior complex
if print_out:
print('.')
print(f'HNdA_i_cache[{v.x}] = {HNdA_i_cache[v.x]}')
print(f'HN_i_cache[{v.x}] = {HN_i_cache[v.x]}')
print(f'H = {H}')
print(f'v.x_a = {v.x_a}')
print(f'df = {df}')
print(f'height = {height}')
print(f'np.max([f_k[2], 0.0]) = {np.max([f_k[2], 0.0])}')
print(f'f_k = {f_k}')
HC.V.move(v, new_vx)
if print_out:
print(f'bV_new = {bV_new}')
return HC, bV_new
def incr(HC, bV, params, tau=1e-5, plot=False, verbosity=1):
HC.dim = 3 # Rest in case visualization has changed
if verbosity == 2:
print_out = True
else:
print_out = False
# Update the progress
HC, bV = mean_flow(HC, bV, params, tau=tau, print_out=print_out)
# Compute progress of Capillary rise:
if verbosity == 1:
print('.')
#current_Jurin_err(HC)
# Plot in Polyscope:
if plot:
pass
#ps_inc(surface, HC)
#HC.plot_complex()
#plt.close
return HC, bV
def ps_inc(surface, HC):
#F, nn, HC, bV, K_f, H_f = cap_rise_init_N(r, theta_p, gamma, N=N,
# refinement=refinement,
# equilibrium=True
# )
HC.dim = 2 # The dimension has changed to 2 (boundary surface)
HC.vertex_face_mesh()
points = np.array(HC.vertices_fm)
triangles = np.array(HC.simplices_fm_i)
### Register a point cloud
# `my_points` is a Nx3 numpy array
my_points = points
ps_cloud = ps.register_point_cloud("my points", my_points)
# ps_cloud.set_color((0.0, 0.0, 0.0))
verts = my_points
newPositions = verts
surface.update_vertex_positions(newPositions)
try:
with timeout(0.1, exception=RuntimeError):
# perform a potentially very slow operation
ps.show()
except RuntimeError:
pass
# Parameters
if 1:
refinement = 0
T_0 = 273.15 + 25 # K, initial tmeperature
P_0 = 101.325 # kPa, Ambient pressure
gamma = IAPWS(T_0) # N/m, surface tension of water at 20 deg C
#rho_0 = eos(P=P_0, T=T_0) # kg/m3, density
rho_0 = 998.2071 # kg/m3, density, STP
g = 9.81 # m/s2
theta_p = (63 / 75) * 20 + 30
#theta_p = 0.0
theta_p = theta_p * np.pi / 180.0
r = ((44 / 58) * 0.25 + 1.0) * 1e-3 # height mm --> m # Radius
h = ((3 / 58) * 0.25 + 0.5) * 1e-3 # height mm --> m
v = np.pi * (
3 * r ** 2 * h + h ** 3) / 6.0 # Volume in m3 (Segment of a sphere, see note above)
Volume, V = v, v
#TEMP:
# r, h, v, V, Volume = r*1e3, h*1e3, v*1e3, V*1e3, Volume*1e3
m_0 = rho_0 * Volume # kg, initial mass (kg/m3 * m3)
print(f'theta_p = {theta_p * 180.0 / np.pi}')
print(f'm_0 = {m_0}')
print(f'r = {r * 1e3} mm')
print(f'h = {h * 1e3} mm')
print(f'v = {v * 1e9} mm^3')
print(f'V = {V * 1e9} mm^3')
print(f'Volume = {Volume * 1e9} mm^3')
# define params tuple used in solver:
rho = rho_0
R = r / np.cos(theta_p) # = R at theta = 0
# Exact values:
K_f = (1 / R) ** 2
params = (gamma, rho, g, r, theta_p, K_f, h)
#from ddgclib.curvatures import plot_surface, curvature
# Colour scheme for surfaces
db = np.array([129, 160, 189]) / 255 # Dark blue
lb = np.array([176, 206, 234]) / 255 # Light blue
# droplet data:
if 1:
# Find the Abscissa using scale interpolations
voxels = 126 # Voxels between 100 and 200 in 4.c
voxels_m = 126 * (33/100.0)
# Fig. 5 is the droplet at 133 s, we read off the contact angle, radius and heigh from Fig. 4.c
# The ratios below are the voxel fractions of where we read off the scales:
# process cropped image
img_str = '../data/hydrophillic_cropped_murray.png'
I_png = plt.imread(img_str)
def rgb2gray(rgb):
return np.dot(rgb[..., :3], [0.2989, 0.5870, 0.1140])
gray = rgb2gray(I_png)
if 0:
plt.imshow(gray, cmap=plt.get_cmap('gray'), vmin=0, vmax=1)
scale = 189 # voxels / 0.5 mm (from the bar given in the paper)
scale = 189 / 0.5 # voxels / mm
np.max(gray), np.min(gray)
# Edgte detection
if 1:
# read command-line arguments
# filename = sys.argv[1]
filename = img_str
# sigma = 0.2
# low_threshold = float(sys.argv[3])
# high_threshold = float(sys.argv[4])
sigma = 5.0 # 2.0
sigma = 10.0 # 2.0
low_threshold = 0.1
high_threshold = 0.3
image = skimage.io.imread(fname=filename, as_gray=True)
# viewer = skimage.viewer(image=image)
viewer = skimage.viewer.ImageViewer(image=image)
if 0:
viewer.show()
image_cropped = image # [210:400,180:440]
sigma = 2.0
# sigma = 5.0
# sigma = 5.5
# low_threshold = 0.2#0.66#0.05
low_threshold = 0.001 # 0.05
# low_threshold = 0.2#0.05
high_threshold = 0.50
# max, min pair was = (0.4862258831709623, 0.0)
edges = skimage.feature.canny(
image=image_cropped,
sigma=sigma,
low_threshold=low_threshold,
high_threshold=high_threshold,
)
viewer = skimage.viewer.ImageViewer(edges)
# Show skimage plots
if 0:
viewer.show()
plt.show()
# Convert coordinates from edge data:
ypos, xpos = np.argwhere(edges)[:, 0], np.argwhere(edges)[:, 1]
xpos, ypos
#np.savetxt('./data/output_murray.txt', np.argwhere(edges),
# delimiter=';')
x0 = 2 + int(
919 / 2.0) # TODO: Detect maximum of edge contour to find symmetry automatically
y0 = 2 + image_cropped.shape[0]
x = (xpos - x0) / scale # voxels --> mm
y = (-ypos + y0) / scale # voxels --> mm
data_xyz = np.zeros([len(x), 3])
for ind, (x_i, y_i) in enumerate(zip(x, y)):
data_xyz[ind, 0] = x_i
data_xyz[ind, 2] = y_i
#data_xyz
#data_xyz[]
#print(f'data_xyz = {data_xyz}')
# Matplotlib scatter plot:
if 1:
plt.figure()
plt.scatter(x, y)
plt.ylim((0, 1))
plt.xlabel('mm')
plt.ylabel('mm')
#plt.show()
# Mean flow simulation
h_cylinder = V / ( np.pi * r**2 ) # V = np.pi * r**2 * h
h_cylinder, h, r
print(f'h_cylinder = {h_cylinder}')
# Cube test
if 0:
HC = Complex(3, domain=[(0, 1), ] * 3)
#HC = Complex(3, domain=[(-1, 1), ] * 3)
HC.triangulate()
for i in range(1):
HC.refine_all()
#v = HC.V[(0.0, 0.0, 0.0)]
#HC.V.remove(v)
#bV = HC.boundary()
bV = HC.boundary()
trimlist = []
for v in HC.V:
if v not in bV:
trimlist.append(v)
for v in trimlist:
HC.V.remove(v)
if 1:
HC.dim = 3
HC.vertex_face_mesh()
HC.simplices_fm
fig, axes, fig_s, axes_s = HC.plot_complex(point_color=db,
line_color=db,
complex_color_f=lb,
complex_color_e=db
)
#plot.show()
bV = set()
(HN_i, C_ij, K_H_i, HNdA_i_Cij, Theta_i,
HNdA_i_cache, HN_i_cache, C_ij_cache, K_H_i_cache, HNdA_i_Cij_cache,
Theta_i_cache) = HC_curvatures(HC, bV, r, theta_p, printout=0)
int_C = 0
for cij in C_ij_cache:
# print(f'cij = {cij}')
# print(f'C_ij_cache[cij] = {C_ij_cache[cij] }')
int_C += np.sum(C_ij_cache[cij])
pass
# int_C = np.sum(HN_i)
print(f'int_C = {int_C}')
print(f'int_C/6.0 = {int_C / 6.0}')
print(f'int_C/6.0 = {int_C / 6.0}')
print(f'V = {1} m^3')
fig, axes, fig_s, axes_s = HC.plot_complex(point_color=db,
line_color=db,
complex_color_f=lb,
complex_color_e=db
)
# Compute simplices:
HC.dim = 2
HC.vertex_face_mesh()
HC.simplices_fm
# Sphere test
if 0:
R = 1
N = 50
Theta = np.linspace(0.0, np.pi, N) # range of theta
Phi = np.linspace(0.0, 2 * np.pi, N) # range of phi
#Phi = np.linspace(0.0, 0.5*np.pi, N) # range of phi
HC, bV = sphere_N(R, Phi, Theta, N=N,
refinement=1, cdist=1e-10
, equilibrium=True
)
HC.plot_complex()
plot.show()
# Old sphere
if 0:
pass
def sphere(R, theta, phi):
return R * np.cos(theta) * np.sin(phi), R * np.sin(theta) * np.sin(phi), R * np.cos(phi)
x, y, z = sphere(R, theta, phi)
if 0:
# Theta = [0.0, 0.0, (1/2.0)*np.pi, np.pi, 1.5*np.pi, 2.0*np.pi]
Theta = [0.0, 0.0, (1.0 / 3.0) * 2 * np.pi, (2.0 / 3.0) * 2 * np.pi,
2 * np.pi]
Thata = np.linspace(0, 2 * np.pi, 10)
# Phi = [0.0, np.pi, (1/2.0)*np.pi, (1/2.0)*np.pi, (1/2.0)*np.pi, (1/2.0)*np.pi]
# Phi = [0.0, np.pi, (1 / 2.0) * np.pi, (1 / 2.0) * np.pi, (1 / 2.0) * np.pi]
Phi = np.linspace(0, 2 * np.pi, 10)
F = []
for theta, phi in zip(Theta, Phi):
x, y, z = sphere(R, theta, phi)
F.append(np.array([x, y, z]))
#F = np.array(F)
# Spherical cap test
if 0:
# Parameters for a water droplet in air at standard laboratory conditions
gamma = 0.0728 # N/m, surface tension of water at 20 deg C
rho = 1000 # kg/m3, density
g = 9.81 # m/s2
N = 7
refinement = 0#1
#theta_p = 45 * np.pi / 180.0 # Three phase contact angle
theta_p = 0.0 * np.pi / 180.0 # Three phase contact angle
r = 1e-3 # Radius of the tube (1 mm)
#NOTE: MERGING DOES NOT WORK CORRECTLY WITH 1e-3, FIX FOR MICRODROPLETS
#r = 1 # Radius of the tube (1 mm)
r = np.array(r, dtype=np.longdouble)
R = r / np.cos(theta_p)
equilibrium = 1 #
cdist = 1e-8
theta_p = np.array(theta_p, dtype=np.longdouble)
H_f, K_f, dA, k_g_f, dC = analytical_cap(r, theta_p)
print(f'H_f, K_f, dA, k_g_f, dC = {H_f, K_f, dA, k_g_f, dC}')
k_K = k_g_f / K_f #TODO: We no longer need this?
h_jurin = 2 * gamma * np.cos(theta_p) / (rho * g * r)
# Prepare film and move it to 0.0
F, nn, HC, bV, K_f, H_f = cap_rise_init_N(r, theta_p, gamma, N=N,
refinement=refinement,
equilibrium=equilibrium
)
#h = 0.0
params = (gamma, rho, g, r, theta_p, K_f, h)
# HC.V.print_out()
HC.V.merge_all(cdist=cdist)
# Add boundary centroid:
if 0:
int_x, int_y, int_z = 0.0, 0.0, 0.0
for v in bV:
int_x += v.x_a[0]
int_y += v.x_a[1]
int_z += v.x_a[2]
int_x = int_x/len(bV)
int_y = int_y/len(bV)
int_z = int_z/len(bV)
vc = HC.V[(int_x, int_y, int_z)]
#print(f'bV = {bV}')
for v in bV:
#print(f'v.x = {v.x}')
v.connect(vc)
for v in HC.V:
#print(f'v.nn = {v.nn}')
#print(f'v.x = {v.x}')
#print(f'len(v.nn) = {len(v.nn)}')
pass
HC.V.merge_all(cdist=cdist)
bV = set([]) # We closed the boundary
#print(f'bV = {bV}')
if 0:
HC.plot_complex()
plot.show()
(HN_i, C_ij, K_H_i, HNdA_i_Cij, Theta_i,
HNdA_i_cache, HN_i_cache, C_ij_cache, K_H_i_cache, HNdA_i_Cij_cache,
Theta_i_cache) = HC_curvatures(HC, bV, r, theta_p, printout=0)
int_C = 0
for cij in C_ij_cache:
# print(f'cij = {cij}')
# print(f'C_ij_cache[cij] = {C_ij_cache[cij] }')
int_C += np.sum(C_ij_cache[cij])
pass
# int_C = np.sum(HN_i)
print(f'len(bV) = {len(bV)}')
print(f'int_C = {int_C}')
print(f'int_C/6.0 = {int_C / 6.0}')
print(f'int_C/6.0 = {int_C / 6.0}')
theta = np.arcsin(r/R) # sin (theta) = a /R
print(f'theta = {theta * 180 /np.pi}')
V = (np.pi/3.0) * R**3 * (2 + np.cos(theta)
* (1 - np.cos(theta))**2)
A = 2* np.pi * R**2 * (1 - np.cos(theta))
print(f'V = {V} m^3')
V_sphere = (4/3.0) * np.pi * R**3
A_sphere = 4 * np.pi * R**2
print(f'V (half sphere) = {V_sphere/ 2.0} m^3')
#print(f'V (half sphere)/int_C = {(V_sphere/ 2.0)/int_C} m^3')
print(f'A = {A} m^2')
print(f'A_sphere (half sphere) = {A_sphere/2.0} m^2')
print(f'intC - circ = {int_C - np.pi * R**2} m^2')
#
print('=====================')
print('Mean normal approach:')
print('=====================')
print(f'HN_i = {HN_i}')
print(f'HNdA_i_cache = {HNdA_i_cache}')
print(f'K_H_i = {K_H_i}')
print(f'C_ij = {C_ij}')
#
print('=====================')
print('Sphere radius:')
print('=====================')
print(f'R = {R}')
print(f'verex radia from centre of sphere:')
for v in HC.V:
print(f'v.x = {v.x}')
N_f0 = np.array(
[0.0, 0.0, R * np.sin(theta_p)]) - v.x_a # First approximation
print(f'N_f0 = {N_f0}')
print(f'np.linalg.norm(N_f0) = {np.linalg.norm(N_f0)}')
N_f0 = normalized(N_f0)[0]
if 0:
ps = pplot_surface(HC)
# View the point cloud and mesh we just registered in the 3D UI
ps.show()
HC.plot_complex()
plot.show()
# Cylinder init attempt:
if 0:
# Initiate a cubical complex
HC = Complex(3, domain=[(-r, r), ] * 3)
HC.triangulate()
refinement = 1
for i in range(refinement):
HC.refine_all()
# for v in HC2V:
# HC.refine_star(v)
del_list = []
for v in HC.V:
if np.any(v.x_a == -r) or np.any(v.x_a == r):
if np.any(v.x_a[2] == -r):
if np.any(v.x_a[0:2] == -r) or np.any(v.x_a[0:2] == r):
continue
else:
del_list.append(v)
else:
continue
else:
del_list.append(v)
for v in del_list:
HC.V.remove(v)
# Shrink to circle and move to zero
for v in HC.V:
x = v.x_a[0]
y = v.x_a[1]
f_k = [x * np.sqrt(r ** 2 - y ** 2 / 2.0) / r,
y * np.sqrt(r ** 2 - x ** 2 / 2.0) / r, v.x_a[2]]
HC.V.move(v, tuple(f_k))
# Move up to zero (NOTE: DO NOT DO THIS IN THE CIRCLE LOOP
# BECUASE SAME VERTEX INDEX BREAKS CONNECTIONS IN LOOP DURING MOVE:
# TODO: FIX THIS IN THE hyperct LIBRARY CODE)
for v in HC.V:
if (v.x_a[2] == -r) or (v.x_a[2] == 0.0):
continue
f_k = [v.x_a[0], v.x_a[1], v.x_a[2] + r]
HC.V.move(v, tuple(f_k))
for v in HC.V:
if (v.x_a[2] == 2 * r) or (v.x_a[2] == -r):
continue
f_k = [v.x_a[0], v.x_a[1], v.x_a[2] + r]
HC.V.move(v, tuple(f_k))
for v in HC.V:
if (v.x_a[2] == 2 * r) or (v.x_a[2] == r):
continue
f_k = [v.x_a[0], v.x_a[1], v.x_a[2] + r]
HC.V.move(v, tuple(f_k))
## Move to h
for v in HC.V:
if (v.x_a[2] == 0.0) or (v.x_a[2] == r):
continue
f_k = [v.x_a[0], v.x_a[1], v.x_a[2] + h_cylinder - 2 * r]
HC.V.move(v, tuple(f_k))
for v in HC.V:
if (v.x_a[2] == r):
f_k = [v.x_a[0], v.x_a[1], v.x_a[2] + 0.5 * h_cylinder - r]
HC.V.move(v, tuple(f_k))
# Find set of boundary vertices
bV = set()
for v in HC.V:
# print('-')
# print(f'v.x_a = {v.x_a}')
# print(f'v.x_a[2] == 0.0 = {v.x_a[2] == 0.0}')
if v.x_a[2] == 0.0:
bV.add(v)
# print(f'bV = {bV}')
else:
continue
# Remove extra vertices
# NEW 2021.10.07
if 0:
del_list2 = []
for v in HC.V:
if v.x_a[2] > h_cylinder:
del_list2.append(v)
for v in del_list2:
HC.V.remove(v)
# Test plot
if 0:
HC.dim = 3 # In case this changed for polyscope surface
fig, axes, fig_s, axes_s = HC.plot_complex(point_color=db,
line_color=db,
complex_color_f=lb,
complex_color_e=db
)
cdist=1e-5
HC.V.merge_all(cdist=cdist)
# Experimental refinement:
if 0:
for i in range(1):
HC_V = copy.copy(HC.V)
for v in HC_V:
if v.x_a[2] == h_cylinder:
HC.refine_star(v)
elif 0:
#exclude_set =
#refine_all_star(self, exclude=set())
HC.dim = 2
exclude_set = set()
for v in HC.V:
if v.x_a[2] < h_cylinder:
exclude_set.add(v)
for i in range(1):
HC.refine_all_star(exclude=exclude_set)
#HC.dim = 3
if 0:
fig, axes, fig_s, axes_s = HC.plot_complex(point_color=db,
line_color=db,
complex_color_f=lb,
complex_color_e=db
)
# Below can be used to confirm above bV
if 0:
for bv in bV:
print(f'bv = {bv}')
HC.dim = 2
bV2 = HC.boundary()
print('bV2')
for bv in bV2:
print(f'bv = {bv}')
# axes.set_xlim3d(-(0.1*r + r) , 0.1*r + r)
# axes.set_ylim3d(-(0.1*r + r) , 0.1*r + r)
# axes.set_zlim3d(-(0.1*r + r) , 0.1*r + 2*r)
# Test volumes:
if 0:
(HN_i, C_ij, K_H_i, HNdA_i_Cij, Theta_i,
HNdA_i_cache, HN_i_cache, C_ij_cache, K_H_i_cache, HNdA_i_Cij_cache,
Theta_i_cache) = HC_curvatures(HC, bV, r, theta_p, printout=0)
int_C = 0
for cij in C_ij_cache:
#print(f'cij = {cij}')
#print(f'C_ij_cache[cij] = {C_ij_cache[cij] }')
int_C += np.sum(C_ij_cache[cij])
pass
#int_C = np.sum(HN_i)
print(f'int_C = {int_C}')
print(f'int_C/6.0 = {int_C/6.0}')
print(f'V = {V * 1e9} mm^3')
print(f'int_C= {int_C * 1e9} mm^3')
print(f'int_C/6.0 = {int_C/6.0 * 1e9} mm^3')
print(f'int_C = {int_C * 1e6} mm^2')
A_cylinder = 2 * np.pi * r * h_cylinder
A_cylinder = A_cylinder + (np.pi * r**2) # not including bottom face
print(f'A_cylinder = {A_cylinder * 1e6} mm^2')
# Cylinder init 2 attempt:
if 1:
theta_p_test = 0
N = 7
cdist = 1e-7
refinement = 0
F, nn, HC, bV, K_f, H_f = cap_rise_init_N(r, theta_p, gamma, N=N,
refinement=refinement,
cdist=cdist,
equilibrium=0
)
# Lowers
if 1:
v_list = []
nn_list = []
nn_ind = 0
HC.dim = 2
yl_b = HC.boundary(HC.V)
HC.dim = 3
#print(f'yl_b = {yl_b}')
for v in yl_b:
#print(f' v in boundary = {v.x_a}')
v_list.append(v.x_a)
nn_list.append([])
for v2 in v.nn:
if v2 in yl_b:
nn_list[nn_ind].append(v2.x_a)
nn_ind += 1
#v_array = np.array(v_list)
#print(f'v_list = {v_list}')
#print(f'nn_list = {nn_list}')
# Move to h_cylinder
for v in HC.V:
f_k = [v.x_a[0], v.x_a[1], v.x_a[2] + h_cylinder]
HC.V.move(v, tuple(f_k))
# Create new ground layer
nn_ind = 0
for va in v_list:
va_n = va #- np.array([0, 0, h_cylinder])
v = HC.V[tuple(va_n)]
for va2 in nn_list[nn_ind]:
va2_n = va2 #- np.array([0, 0, h_cylinder])
v2 = HC.V[tuple(va2_n)]
v.connect(v2)
nn_ind += 1
# Add half way layer (in future can add more)
if 1:
nn_ind = 0
for va in v_list:
va_n = va + 0.5* np.array([0, 0, h_cylinder])
v = HC.V[tuple(va_n)]
# Connect lower
v_l = HC.V[tuple(va)]
v.connect(v_l)
# Connect upper
va_u = va + np.array([0, 0, h_cylinder])
v_u = HC.V[tuple(va_u)]
v.connect(v_u)
for va2 in nn_list[nn_ind]:
va2_n = va2 + 0.5* np.array([0, 0, h_cylinder])
v2 = HC.V[tuple(va2_n)]
v.connect(v2)
# Connect lower
v_l = HC.V[tuple(va2_n- 0.5* np.array([0, 0, h_cylinder]))]
v.connect(v_l)
# Connect upper
va_u = va2 + np.array([0, 0, h_cylinder])
v_u = HC.V[tuple(va_u)]
v.connect(v_u)
nn_ind += 1
# Remove extra vertices
# NEW 2021.10.07
if 0:
del_list2 = []
for v in HC.V:
if v.x_a[2] > h_cylinder:
del_list2.append(v)
for v in del_list2:
HC.V.remove(v)
# Test plot
if 0:
HC.dim = 3 # In case this changed for polyscope surface
fig, axes, fig_s, axes_s = HC.plot_complex(point_color=db,
line_color=db,
complex_color_f=lb,
complex_color_e=db
)
# cdist = 1e-5
# HC.V.merge_all(cdist=cdist)
# Sanity checks for cylinder and volume, connect all to COM
if 0:
## Compute volume
# Compute COM
f = []
for v in HC.V:
f.append(v.x_a)
f = np.array(f)
# COM = numpy.average(nonZeroMasses[:,:3], axis=0, weights=nonZeroMasses[:,3])
com = np.average(f, axis=0)
com
bf = []
for v in bV:
bf.append(v.x_a)
bf = np.array(bf)
# COM = numpy.average(nonZeroMasses[:,:3], axis=0, weights=nonZeroMasses[:,3])
bcom = np.average(bf, axis=0)
bcom
HC2 = copy.copy(HC)
for v in HC2.V:
v.connect(HC2.V[tuple(com)])
for v in bV:
v.connect(HC2.V[tuple(bcom)])