added anchors

Author: liminchen

2_dirichlet/simulator.py

@@ -13,7 +13,9 @@
 k = 1e3     # spring stiffness
 n_seg = 4   # num of segments per side of the square
 h = 0.02    # time step size in s
+# ANCHOR: DBC_def
 DBC = [n_seg, (n_seg + 1) * (n_seg + 1) - 1]  # fix the left and right top nodes
+# ANCHOR_END: DBC_def
 
 # initialize simulation
 [x, e] = square_mesh.generate(side_len, n_seg)  # node positions and edge node indices
@@ -25,10 +27,12 @@
     diff = x[e[i][0]] - x[e[i][1]]
     l2.append(diff.dot(diff))
 k = [k] * len(e)    # spring stiffness
+# ANCHOR: DBC_mask
 # identify whether a node is Dirichlet
 is_DBC = [False] * len(x)
 for i in DBC:
     is_DBC[i] = True
+# ANCHOR_END: DBC_mask
 # simulation with visualization
 resolution = np.array([900, 900])
 offset = resolution / 2

2_dirichlet/time_integrator.py

@@ -36,11 +36,13 @@ def step_forward(x, e, v, m, l2, k, is_DBC, h, tol):
     v = (x - x_n) / h   # implicit Euler velocity update
     return [x, v]
 
+# ANCHOR: ADDING_GRAVITY
 def IP_val(x, e, x_tilde, m, l2, k, h):
     return InertiaEnergy.val(x, x_tilde, m) + h * h * (MassSpringEnergy.val(x, e, l2, k) + GravityEnergy.val(x, m))     # implicit Euler
 
 def IP_grad(x, e, x_tilde, m, l2, k, h):
     return InertiaEnergy.grad(x, x_tilde, m) + h * h * (MassSpringEnergy.grad(x, e, l2, k) + GravityEnergy.grad(x, m))   # implicit Euler
+# ANCHOR_END: ADDING_GRAVITY
 
 def IP_hess(x, e, x_tilde, m, l2, k, h):
     IJV_In = InertiaEnergy.hess(x, x_tilde, m)
@@ -50,6 +52,7 @@ def IP_hess(x, e, x_tilde, m, l2, k, h):
     H = sparse.coo_matrix((IJV[2], (IJV[0], IJV[1])), shape=(len(x) * 2, len(x) * 2)).tocsr()
     return H
 
+# ANCHOR: search_dir
 def search_dir(x, e, x_tilde, m, l2, k, is_DBC, h):
     projected_hess = IP_hess(x, e, x_tilde, m, l2, k, h)
     reshaped_grad = IP_grad(x, e, x_tilde, m, l2, k, h).reshape(len(x) * 2, 1)
@@ -60,4 +63,5 @@ def search_dir(x, e, x_tilde, m, l2, k, is_DBC, h):
     for i in range(0, len(x)):
         if is_DBC[i]:
             reshaped_grad[i * 2] = reshaped_grad[i * 2 + 1] = 0.0
-    return spsolve(projected_hess, -reshaped_grad).reshape(len(x), 2)
+    return spsolve(projected_hess, -reshaped_grad).reshape(len(x), 2)
+#ANCHOR_END: search_dir