add anchors

Author: liminchen

4_friction/BarrierEnergy.py

@@ -1,3 +1,4 @@
+# ANCHOR: slope_barrier
 import math
 import numpy as np
 
@@ -34,20 +35,25 @@ def hess(x, n, o, contact_area):
                     IJV[1].append(i * 2 + c)
                     IJV[2] = np.append(IJV[2], local_hess[r, c])
     return IJV
+# ANCHOR_END: slope_barrier
 
+# ANCHOR: init_step_size
 def init_step_size(x, n, o, p):
     alpha = 1
     for i in range(0, len(x)):
         p_n = p[i].dot(n)
         if p_n < 0:
             alpha = min(alpha, 0.9 * n.dot(x[i] - o) / -p_n)
     return alpha
+# ANCHOR_END: init_step_size
 
+# ANCHOR: compute_mu_lambda
 def compute_mu_lambda(x, n, o, contact_area, mu):
     mu_lambda = np.array([0.0] * len(x))
     for i in range(0, len(x)):
         d = n.dot(x[i] - o)
         if d < dhat:
             s = d / dhat
             mu_lambda[i] = mu * -contact_area[i] * dhat * (kappa / 2 * (math.log(s) / dhat + (s - 1) / d))
-    return mu_lambda
+    return mu_lambda
+# ANCHOR_END: compute_mu_lambda

4_friction/FrictionEnergy.py

@@ -1,3 +1,4 @@
+# ANCHOR: f_terms
 import numpy as np
 import utils
 
@@ -22,7 +23,9 @@ def f_hess_term(vbarnorm, epsv):
         return -1.0 / (vbarnorm * vbarnorm)
     else:
         return -1.0 / (epsv * epsv)
+# ANCHOR_END: f_terms
 
+# ANCHOR: val_grad_hess
 def val(v, mu_lambda, hhat, n):
     sum = 0.0
     T = np.identity(2) - np.outer(n, n) # tangent of slope is constant
@@ -57,4 +60,5 @@ def hess(v, mu_lambda, hhat, n):
                     IJV[0].append(i * 2 + r)
                     IJV[1].append(i * 2 + c)
                     IJV[2] = np.append(IJV[2], local_hess[r, c])
-    return IJV
+    return IJV
+# ANCHOR_END: val_grad_hess

4_friction/simulator.py

@@ -14,10 +14,14 @@
 n_seg = 4       # num of segments per side of the square
 h = 0.01        # time step size in s
 DBC = []        # no nodes need to be fixed
+# ANCHOR: slope_setup
 ground_n = np.array([0.1, 1.0])     # normal of the slope
 ground_n /= np.linalg.norm(ground_n)    # normalize ground normal vector just in case
 ground_o = np.array([0.0, -1.0])    # a point on the slope  
+# ANCHOR_END: slope_setup
+# ANCHOR: set_mu
 mu = 0.11        # friction coefficient of the slope
+# ANCHOR_END: set_mu
 
 # initialize simulation
 [x, e] = square_mesh.generate(side_len, n_seg)  # node positions and edge node indices
@@ -56,8 +60,10 @@ def screen_projection(x):
 
     # fill the background and draw the square
     screen.fill((255, 255, 255))
+    # ANCHOR: slope_vis
     pygame.draw.aaline(screen, (0, 0, 255), screen_projection([ground_o[0] - 3.0 * ground_n[1], ground_o[1] + 3.0 * ground_n[0]]), 
         screen_projection([ground_o[0] + 3.0 * ground_n[1], ground_o[1] - 3.0 * ground_n[0]]))   # slope
+    # ANCHOR_END: slope_vis
     for eI in e:
         pygame.draw.aaline(screen, (0, 0, 255), screen_projection(x[eI[0]]), screen_projection(x[eI[1]]))
     for xI in x:

4_friction/time_integrator.py

@@ -12,12 +12,14 @@
 import BarrierEnergy
 import FrictionEnergy
 
+# ANCHOR: mu_lambda
 def step_forward(x, e, v, m, l2, k, n, o, contact_area, mu, is_DBC, h, tol):
     x_tilde = x + v * h     # implicit Euler predictive position
     x_n = copy.deepcopy(x)
     mu_lambda = BarrierEnergy.compute_mu_lambda(x, n, o, contact_area, mu)  # compute mu * lambda for each node using x^n
 
     # Newton loop
+# ANCHOR_END: mu_lambda
     iter = 0
     E_last = IP_val(x, e, x_tilde, m, l2, k, n, o, contact_area, (x - x_n) / h, mu_lambda, h)
     p = search_dir(x, e, x_tilde, m, l2, k, n, o, contact_area, (x - x_n) / h, mu_lambda, is_DBC, h)