def function_2_ellipse(x):
f = 0
f = np.sin(np.pi * x[0] * x[1])
f = f * weightfunction.ellipse(radius1, radius2, x)
return f
def function_1_ellipse(x):
f = 0
f = np.sin(8 * x[0]) + np.sin(7 * x[1])
f = f * weightfunction.ellipse(radius1, radius2, x)
return f
punkte = data['punkte']
dim = data['dim']
degree = data['degree']
level_x = data['level_x']
level_y = data['level_y']
# Pruefe ob Level hoch genug
if level_x and level_y < np.log2(degree+1):
print('Error: Level zu niedrig. Es muss Level >= log2(degree+1) sein ')
quit()
# Gitter fuer Kreis erzeugen und auswerten
x0 = np.linspace(0, 1, 50)
X = np.meshgrid(x0, x0)
Z = weightfunction.ellipse(radius1,radius2, X)
h_x = data['h_x']
h_y = data['h_y']
# Definiere Knotenfolge
# Not a Knot
xi = data['xi']
yi = data['yi']
# Index von Bspline auf Knotenfolge
index_Bspline_x = data['index_Bspline_x']
index_Bspline_y = data['index_Bspline_y']
index_all_Bsplines = data['index_all_Bsplines']
def NNsearch(sort, j, q):
xblock = np.arange(I_all[int(sort[q, 1]), 0],
I_all[int(sort[q, 1]), 0] + (degree + 1) * h_x, h_x)
yblock = np.arange(I_all[int(sort[q, 1]), 1],
I_all[int(sort[q, 1]), 1] + (degree + 1) * h_y, h_y)
block = np.meshgrid(xblock, yblock)
eval_block = np.zeros(((degree + 1)**2, 1))
s = 0
for i in range(degree + 1):
for t in range(degree + 1):
eval_block[s] = weightfunction.ellipse(
radius1, radius2, [block[0][t, i], block[1][t, i]])
s = s + 1
if np.all(eval_block > 0) == True:
s = 0
for i in range(degree + 1):
for t in range(degree + 1):
NN[j, s] = [block[0][t, i], block[1][t, i]]
s = s + 1
else:
xblock = np.arange(I_all[int(sort[q, 1]), 0],
I_all[int(sort[q, 1]), 0] + (degree + 1) * h_x, h_x)
yblock = np.arange(I_all[int(sort[q, 1]), 1],
I_all[int(sort[q, 1]), 1] - (degree + 1) * h_y,
-h_y)
block = np.meshgrid(xblock, yblock)
s = 0
for i in range(degree + 1):
for t in range(degree + 1):
eval_block[s] = weightfunction.ellipse(
radius1, radius2, [block[0][t, i], block[1][t, i]])
s = s + 1
if np.all(eval_block > 0) == True:
s = 0
for i in range(degree + 1):
for t in range(degree + 1):
NN[j, s] = [block[0][t, i], block[1][t, i]]
s = s + 1
else:
xblock = np.arange(I_all[int(sort[q, 1]), 0],
I_all[int(sort[q, 1]), 0] - (degree + 1) * h_x,
-h_x)
yblock = np.arange(I_all[int(sort[q, 1]), 1],
I_all[int(sort[q, 1]), 1] - (degree + 1) * h_y,
-h_y)
block = np.meshgrid(xblock, yblock)
s = 0
for i in range(degree + 1):
for t in range(degree + 1):
eval_block[s] = weightfunction.ellipse(
radius1, radius2, [block[0][t, i], block[1][t, i]])
s = s + 1
if np.all(eval_block > 0) == True:
s = 0
for i in range(degree + 1):
for t in range(degree + 1):
NN[j, s] = [block[0][t, i], block[1][t, i]]
s = s + 1
else:
xblock = np.arange(
I_all[int(sort[q, 1]), 0],
I_all[int(sort[q, 1]), 0] - (degree + 1) * h_x, -h_x)
yblock = np.arange(
I_all[int(sort[q, 1]), 1],
I_all[int(sort[q, 1]), 1] + (degree + 1) * h_y, h_y)
block = np.meshgrid(xblock, yblock)
s = 0
for i in range(degree + 1):
for t in range(degree + 1):
eval_block[s] = weightfunction.ellipse(
radius1, radius2, [block[0][t, i], block[1][t, i]])
s = s + 1
if np.all(eval_block > 0) == True:
s = 0
for i in range(degree + 1):
for t in range(degree + 1):
NN[j, s] = [block[0][t, i], block[1][t, i]]
s = s + 1
elif q == len(I_all) - 1:
print(
'Fehler: kein (n+1)x(n+1) Block im Gebiet gefunden. Erhoehe Level.'
)
quit()
else:
NNsearch(sort, j, q + 1)
return NN
dim = 2 # Dimension
radius1 = 0.45 # Radius von Kreis
radius2 = 0.1
degree = 5 # Grad von B-Splines (nur ungerade)
level_x = 4 # Level in x Richtung
level_y = 4 # Level in y Richtung
# Pruefe ob Level hoch genug
if level_x and level_y < np.log2(degree + 1):
print('Error: Level zu niedrig. Es muss Level >= log2(degree+1) sein ')
quit()
# Gitter fuer Kreis erzeugen und auswerten
x0 = np.linspace(0, 1, 100)
X = np.meshgrid(x0, x0)
Z = weightfunction.ellipse(radius1, radius2, X)
# Plot von Ellipse
plt.contour(X[0], X[1], Z, 0)
plt.axis('equal')
#plt.show()
# Gitterweite
h_x = 2**(-level_x)
h_y = 2**(-level_y)
# Definiere Knotenfolge
# Uniform
# xi = np.arange(-(degree+1)/2, 1/h_x+(degree+1)/2+1, 1)*h_x
# yi = np.arange(-(degree+1)/2, 1/h_y+(degree+1)/2+1, 1)*h_y
dim = data['dim']
degree = data['degree']
level_x = data['level_x']
level_y = data['level_y']
# Pruefe ob Level hoch genug
if level_x and level_y < np.log2(degree + 1):
print(
'Error: Level zu niedrig. Es muss Level >= log2(degree+1) sein '
)
quit()
# Gitter fuer Kreis erzeugen und auswerten
x0 = np.linspace(0, 1, 50)
X = np.meshgrid(x0, x0)
Z = weightfunction.ellipse(radius1, radius2, X)
h_x = data['h_x']
h_y = data['h_y']
# Definiere Knotenfolge
# Not a Knot
xi = data['xi']
yi = data['yi']
# Index von Bspline auf Knotenfolge
index_Bspline_x = data['index_Bspline_x']
index_Bspline_y = data['index_Bspline_y']
index_all_Bsplines = data['index_all_Bsplines']
# Index (x,y) der Bsplines mit Knotenmittelpunkt im inneren des Gebiets
