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sdf.py
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1import math
2import numpy as np
3
4# SDF Indenter
5
6# Negative level set represents interior of the indenter.
7# This normal points outside of the indenter.
8
9
10
11# Functions for MoFEM
12def sdf(delta_t, t, x, y, z, tx, ty, tz, block_id):
13 return list_indenters[0].sDF(x,y,z)
14
15
16def grad_sdf(delta_t, t, x, y, z, tx, ty, tz, block_id):
17 return list_indenters[0].gradSdf(x,y,z)
18
19
20def hess_sdf(delta_t, t, x, y, z, tx, ty, tz, block_id):
21 return list_indenters[0].hessSdf(x,y,z)
22
23# Example Indenters
24
25class NoIndenter:
26
27 def sDF(self, x, y, z):
28 return np.ones_like(x)
29
30 def gradSdf(self,x, y,z):
31 zeros = np.zeros_like(x)
32 zeros = zeros.reshape((-1,1))
33
34 grad_array = np.hstack([zeros, zeros, zeros])
35 return grad_array
36
37 def hessSdf(self,x, y,z):
38 zeros = np.zeros_like(x)
39 zeros = zeros.reshape((-1,1))
40
41 hess_array = np.hstack([zeros, zeros, zeros, zeros, zeros, zeros])
42
43 # xx, yx, zx, yy, zy, zz
44 return hess_array
45
46class yPlane:
47 def __init__(self,Xc,Yc,Zc,shift):
48 # Initial Centroid
49 self.Xc = Xc
50 self.Yc = Yc
51 self.Zc = Zc
52
53 # Current Centroid
54 self.xc = Xc
55 self.yc = Yc
56 self.zc = Zc
57
58 # Indenter Dimensions
59 self.shift = shift
60
61
62 def sDF(self, x, y, z):
63 return np.subtract(y,self.shift)
64
65 def gradSdf(self,x, y,z):
66 dx = np.zeros_like(x)
67 dy = np.ones_like(y)
68 dz = np.zeros_like(z)
69 dx = dx.reshape((-1,1))
70 dy = dy.reshape((-1,1))
71 dz = dz.reshape((-1,1))
72 grad_array = np.hstack([dx, dy, dz])
73 return grad_array
74
75 def hessSdf(self,x, y,z):
76 zeros = np.zeros_like(x)
77 zeros = zeros.reshape((-1,1))
78
79 hess_array = np.hstack([zeros, zeros, zeros, zeros, zeros, zeros])
80
81 # xx, yx, zx, yy, zy, zz
82 return hess_array
83
84class CylinderZ:
85 def __init__(self, Xc, Yc, Zc, diameter):
86 # Initial Centroid
87 self.Xc = Xc
88 self.Yc = Yc
89 self.Zc = Zc
90
91 # Current Centroid
92 self.xc = Xc
93 self.yc = Yc
94 self.zc = Zc
95
96 # Indenter Dimensions
97 self.radius = diameter/2
98
99 def sDF(self, x, y, z):
100 a = (x-self.xc)**2 + (y-self.yc)**2
101 gap = np.sqrt(a)-self.radius
102
103 self.normal = self.gradSdf(x,y,z)
104 self.dNormal = self.hessSdf(x,y,z)
105
106 return gap
107
108 def gradSdf(self, x, y, z):
109 a = (x-self.xc)**2 + (y-self.yc)**2
110 c_val = np.sqrt(a)
111 c_val_A = 1./c_val
112 c_val_dx = c_val_A * (x-self.xc)
113 c_val_dy = c_val_A * (y-self.yc)
114 c_val_dz = np.zeros_like(c_val_dy)
115 # x, y, z
116 c_val_dx = c_val_dx.reshape((-1,1))
117 c_val_dy = c_val_dy.reshape((-1,1))
118 c_val_dz = c_val_dz.reshape((-1,1))
119 grad_array = np.hstack([c_val_dx,c_val_dy,c_val_dz])
120 return grad_array
121
122 def hessSdf(self, x, y, z):
123 a = (x-self.xc)**2 + (y-self.yc)**2
124 c_val = np.sqrt(a)
125 c_val_A = 1./c_val
126 c_val_B = 1./(a**(3./2.))
127 Hxx = c_val_A - c_val_B * (x-self.xc)**2
128 Hxy = -c_val_B * (x-self.xc)*(y-self.yc)
129 Hyy = c_val_A - c_val_B * (y-self.yc)**2
130
131 Hxx = Hxx.reshape((-1,1))
132 Hzx = np.zeros_like(Hxx)
133 Hxy = Hxy.reshape((-1,1))
134 Hyy = Hyy.reshape((-1,1))
135 Hzy = np.zeros_like(Hxx)
136 Hzz = np.zeros_like(Hxx)
137 hess_array = np.hstack([Hxx, Hxy, Hzx, Hyy, Hzy, Hzz])
138
139 return hess_array
140
141class Sphere:
142 def __init__(self, Xc, Yc, Zc, diameter):
143 # Initial Centroid
144 self.Xc = Xc
145 self.Yc = Yc
146 self.Zc = Zc
147
148 # Current Centroid
149 self.xc = Xc
150 self.yc = Yc
151 self.zc = Zc
152
153 # Indenter Dimensions
154 self.radius = diameter/2
155
156 def sDF(self, x, y, z):
157 dx = np.subtract(x, self.xc)
158 dy = np.subtract(y, self.yc)
159 dz = np.subtract(z, self.zc)
160 a = (dx)**2+(dy)**2 + (dz)**2
161 gap = np.sqrt(a) - self.radius
162
163 return gap
164
165 def gradSdf(self,x, y, z):
166 a = (x-self.xc)**2 + (y-self.yc)**2 + (z-self.zc)**2
167 c_val = np.sqrt(a)
168 c_val_A = 1./c_val
169 c_val_dx = c_val_A * (x-self.xc)
170 c_val_dy = c_val_A * (y-self.yc)
171 c_val_dz = c_val_A * (z-self.zc)
172 # x, y, z
173 #size = np.size(x)
174 #grad_array = np.empty([size,3])
175 c_val_dx = c_val_dx.reshape((-1,1))
176 c_val_dy = c_val_dy.reshape((-1,1))
177 c_val_dz = c_val_dz.reshape((-1,1))
178 grad_array = np.hstack([c_val_dx,c_val_dy,c_val_dz])
179 return grad_array
180
181 def hessSdf(self,x, y, z):
182 x = x-self.xc
183 y = y-self.yc
184 z = z-self.zc
185 Hxx = -x**2/(x**2 + y**2 + z**2)**(3/2) + 1/np.sqrt(x**2 + y**2 + z**2)
186 Hzx = -x*z/(x**2 + y**2 + z**2)**(3/2)
187 Hxy = -x*y/(x**2 + y**2 + z**2)**(3/2)
188 Hyy = -y**2/(x**2 + y**2 + z**2)**(3/2) + 1/np.sqrt(x**2 + y**2 + z**2)
189 Hzy = -y*z/(x**2 + y**2 + z**2)**(3/2)
190 Hzz = -z**2/(x**2 + y**2 + z**2)**(3/2) + 1/np.sqrt(x**2 + y**2 + z**2)
191 # xx, yx, zx, yy, zy, zz
192 Hxx = Hxx.reshape((-1,1))
193 Hzx = Hzx.reshape((-1,1))
194 Hxy = Hxy.reshape((-1,1))
195 Hyy = Hyy.reshape((-1,1))
196 Hzy = Hzy.reshape((-1,1))
197 Hzz = Hzz.reshape((-1,1))
198 hess_array = np.hstack([Hxx, Hxy, Hzx, Hyy, Hzy, Hzz])
199
200 return hess_array
201
202
203
204# Define Indenters below
205r = 1
206
207list_indenters = []
208list_indenters.append(NoIndenter())
sdf
Definition sdf.py:1
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