def test_split_rect_1():
# two functions from https://stackoverflow.com/a/9997374
def ccw(A,B,C):
return (C[1]-A[1]) * (B[0]-A[0]) > (B[1]-A[1]) * (C[0]-A[0])
# Return true if line segments AB and CD intersect
def intersect(A,B,C,D):
return ccw(A,C,D) != ccw(B,C,D) and ccw(A,B,C) != ccw(A,B,D)
mesh = om.read_trimesh('../data/rect.obj')
mesh_pts = mesh.points()
mesh_edges = mesh.ev_indices()
x = np.linspace(-1, 1, 101)
y = T.basis(5)(x)
# export Chebyshev polynomial
pts = np.zeros((x.size, 3))
pts[:, 0] = x
pts[:, 1] = y
mu.write_obj_lines('../data/curve_Chebyshev.obj', pts, [np.arange(pts.shape[0])])
edges = [np.array([0,0], 'i')]
ratios = [0.0]
for i in range(1, x.size-2):
A = np.array([x[i], y[i]])
B = np.array([x[i+1], y[i+1]])
temp_x = []
temp_e = []
temp_u = []
for e in mesh_edges:
C = mesh_pts[e[0], :2]
D = mesh_pts[e[1], :2]
if intersect(A, B, C, D):
# A = (x1, y1), B = (x2, y2)
# C = (x3, y3), D = (x4, y4)
u = ((A[0]-C[0])*(A[1]-B[1])-(A[1]-C[1])*(A[0]-B[0]))/((A[0]-B[0])*(C[1]-D[1])-(A[1]-B[1])*(C[0]-D[0]))
temp_e.append(e)
temp_u.append(u)
temp_x.append(C[0]*(1-u)+D[0]*u)
order = np.argsort(np.array(temp_x))
edges.extend([temp_e[i] for i in order])
ratios.extend([temp_u[i] for i in order])
edges.append(np.array([2,2], 'i'))
ratios.append(0.0)
edges = np.array(edges, 'i')
#print(ratios)
ratios = np.array(ratios, 'd')
pts0 = mesh_pts[edges[:, 0], :]
pts1 = mesh_pts[edges[:, 1], :]
pts = np.multiply(pts0, 1.-ratios[:, np.newaxis]) + \
np.multiply(pts1, ratios[:, np.newaxis])
mu.write_obj_lines('../data/curve.obj', pts, [np.arange(pts.shape[0])])
# print(on_edges, ratios)
mesh, curve_idx = mu.split_mesh_complete(mesh.points(),
mesh.face_vertex_indices(),
edges, ratios)
# print(curve_idx)
om.write_mesh('../data/mesh_split.obj', mesh)
def _create_Tderiv(self, k, n):
r"""Create the n'th derivative of the k'th Chebyshev polynomial."""
if not self._use_mp:
return ChebyshevT.basis(k).deriv(n)
else:
if n == 0:
return lambda x: mp.chebyt(k, x)
# Since the Chebyshev derivatives attain high values near the
# borders +-1 and usually are subtracted to obtain small values,
# minimizing their relative error (i.e. fixing the number of
# correct decimal places (dps)) is not enough to get precise
# results. Hence, the below `moredps` variable is set to higher
# values close to the border.
extradps = 5
pos = mp.fprod(
[mp.mpf(k**2 - p**2) / (2 * p + 1) for p in range(n)])
neg = (-1)**(k + n) * pos
if n == 1:
def dTk(x):
with mp.extradps(extradps):
x = clip(x, -1.0, 1.0)
if mp.almosteq(x, mp.one): return pos
if mp.almosteq(x, -mp.one): return neg
moredps = max(
0,
int(-math.log10(
min(abs(x - mp.one), abs(x + mp.one))) / 2))
moredps = min(moredps, 100)
with mp.extradps(moredps):
t = mp.acos(x)
return k * mp.sin(k * t) / mp.sin(t)
return dTk
if n == 2:
def ddTk(x):
with mp.extradps(extradps):
x = clip(x, -1.0, 1.0)
if mp.almosteq(x, mp.one): return pos
if mp.almosteq(x, -mp.one): return neg
moredps = max(
0,
int(-math.log10(
min(abs(x - mp.one), abs(x + mp.one))) * 1.5) +
2)
moredps = min(moredps, 100)
with mp.extradps(moredps):
t = mp.acos(x)
s = mp.sin(t)
return -k**2 * mp.cos(k * t) / s**2 + k * mp.cos(
t) * mp.sin(k * t) / s**3
return ddTk
raise NotImplementedError(
'Derivatives of order > 2 not implemented.')
import matplotlib.pyplot as plt
from numpy.polynomial import Chebyshev as T
x = np.linspace(-2, 2, 100)
for i in range(6):
ax = plt.plot(x, T.basis(i)(x), lw=2, label="T_%d" % i)
# ...
plt.legend(loc="lower right")
# <matplotlib.legend.Legend object at 0x3b3ee10>
plt.show()
#figure_width = 0.35*text_width
#figure_height = 0.75*figure_width #(figure_width / golden_ratio) #figure_width
figure_width = 0.75*text_width
figure_height = (figure_width / golden_ratio) #figure_width
figure_size = [figure_width, figure_height]
config.load_config_medium()
#fig = plt.figure(figsize=figure_size, dpi=100)
fig, axes = plt.subplots(nrows=1, ncols=1, sharex=True, sharey=True, squeeze=False, figsize=figure_size, dpi=100)
ax = axes[0][0]
x = np.linspace(-1, 1, 100)
for i in range(6):
ax.plot(x, T.basis(i)(x), lw=1.0, color=colors[i], label="$t_%d(x)$"%i)
#ax.plot(x, pow(x, i), lw=1.0, color=colors[i], label="$x^%d$"%i)
ax.set_xlabel(r"$x$")
ax.set_ylabel(r"$t_n(x)$", rotation=90)
ax.set_xlim(-1.1, 1.1)
ax.set_ylim(-1.1, 1.1)
ax.xaxis.labelpad = 5
ax.yaxis.labelpad = 2
# Shrink current axis's height by 10% on the bottom
#box = ax.get_position()
#ax.set_position([box.x0, box.y0 - 0.1*box.height, box.width, 0.9*box.height]) #left, bottom, width, height
plt.subplots_adjust(top=0.85, left=0.12, bottom=0.12, right=0.98) # Legend on top
import matplotlib.pyplot as plt from numpy.polynomial import Chebyshev as T x = np.linspace(-1, 1, 100) for i in range(6): ax = plt.plot(x, T.basis(i)(x), lw=2, label="T_%d"%i) # ... plt.legend(loc="upper left") # <matplotlib.legend.Legend object at 0x3b3ee10> plt.show()
def phi(x, i):
return T.basis(i)(x)
x = np.linspace(-1, 1, 100)
for i in range(5):
plt.plot(x, phi(x, i), lw=2)
# In[12]:
V = np.zeros((len(nodes), deg+1))
rhs = np.zeros(len(nodes))
for i in range(1,len(nodes)-1):
# interior nodes
for j in range(deg+1):
V[i, j] = T.basis(j).deriv(2)(nodes[i])
#V[i, j] += 1000 * (1 + nodes[i]**2) * T.basis(j)(nodes[i])
rhs[i] = f(nodes[i])
for j in range(deg+1):
V[0, j] = T.basis(j)(nodes[0])
rhs[0] = 0
V[-1, j] = T.basis(j)(nodes[-1])
rhs[-1] = 0
# In[13]:
figure_size = [figure_width, figure_height]
config.load_config_medium()
#fig = plt.figure(figsize=figure_size, dpi=100)
fig, axes = plt.subplots(nrows=1,
ncols=1,
sharex=True,
sharey=True,
squeeze=False,
figsize=figure_size,
dpi=100)
ax = axes[0][0]
x = np.linspace(-1, 1, 100)
for i in range(6):
ax.plot(x, T.basis(i)(x), lw=1.0, color=colors[i], label="$t_%d(x)$" % i)
#ax.plot(x, pow(x, i), lw=1.0, color=colors[i], label="$x^%d$"%i)
ax.set_xlabel(r"$x$")
ax.set_ylabel(r"$t_n(x)$", rotation=90)
ax.set_xlim(-1.1, 1.1)
ax.set_ylim(-1.1, 1.1)
ax.xaxis.labelpad = 5
ax.yaxis.labelpad = 2
# Shrink current axis's height by 10% on the bottom
#box = ax.get_position()
#ax.set_position([box.x0, box.y0 - 0.1*box.height, box.width, 0.9*box.height]) #left, bottom, width, height
plt.subplots_adjust(top=0.85, left=0.12, bottom=0.12,
right=0.98) # Legend on top
