def moving_truss_cp_square(n_steps = 40):
cp = CreasePattern(n_steps = n_steps)
cp.nodes = [[ 0, 2, 0 ],
[ 0, 0, 0 ]]
cp.crease_lines = [[ 0, 1 ]]
face_z_0 = FF(Rf = z_ - 0)
face_x_0 = FF(Rf = x_ - 0)
# face_xy_135 = FF(Rf = x_ + y_ - 1.0)
# face_xy_round = FF(Rf = x_**2 + (y_)**2 - 1.0)
# face_x_1_t = FF(Rf = x_ - 1.0 + 1.99 * t_)
# argument = 2*3.14159*t_
# face_x_1_t = FF(Rf = y_ + 3 + sp.sin(argument))
face_x_1_t = FF(Rf = y_ - 1.0 * (t_ - 1) * sp.Heaviside(t_ - 1)
+ 1.0 * (t_ - 3) * sp.Heaviside(t_ - 3)
+ 1.0 * (t_ - 5) * sp.Heaviside(t_ - 5)
- 1.0 * (t_ - 7) * sp.Heaviside(t_ - 7))
face_y_1_t = FF(Rf = x_ + 1.0 * t_ * sp.Heaviside(t_)
- 1.0 * (t_ - 1) * sp.Heaviside(t_ - 1)
- 1.0 * (t_ - 3) * sp.Heaviside(t_ - 3)
+ 1.0 * (t_ - 5) * sp.Heaviside(t_ - 5)
+ 1.0 * (t_ - 7) * sp.Heaviside(t_ - 7)
- 1.0 * (t_ - 8) * sp.Heaviside(t_ - 8))
# +3.14159/2.0
# face_x_1_t = FF(Rf = y_ - 1.99 * t_)
cp.cnstr_lst = [(face_z_0, [0, 1]),
(face_x_0, [0]),
(face_x_1_t, [1]),
(face_y_1_t, [1])]
X = np.zeros((cp.n_dofs,), dtype = float)
# X[1] = 0.01
# X[0] = 0.01
print 'initial lengths\n', cp.c_lengths
print 'initial vectors\n', cp.c_vectors
print 'initial R\n', cp.get_R(X)
print 'initial dR\n', cp.get_dR(X)
X = cp.solve_ff(X)
print '========== results =============='
print 'solution X\n', X
print 'final positions\n', cp.get_new_nodes(X)
print 'final vectors\n', cp.get_new_vectors(X)
print 'final lengths\n', cp.get_new_lengths(X)
return cp
def moving_truss_cp_ff(n_steps = 10, dx = -1.99):
cp = CreasePattern(n_steps = n_steps)
cp.nodes = [[ 0, 0, 0 ],
[ 1, 0, 0 ]]
cp.crease_lines = [[ 0, 1 ]]
face_z_0 = FF(Rf = z_ - 0)
face_x_0 = FF(Rf = x_ - 0)
face_xy_135 = FF(Rf = x_ + y_ - 1.0)
face_x_1_t = FF(Rf = x_ - 1.0 + 1.99 * t_)
cp.cnstr_lst = [(face_z_0, [0, 1]),
(face_x_0, [0]),
(face_xy_135, [1]),
(face_x_1_t, [1])]
X = np.zeros((cp.n_dofs,), dtype = float)
X[1] = 0.01
print 'initial lengths\n', cp.c_lengths
print 'initial vectors\n', cp.c_vectors
print 'initial R\n', cp.get_R(X)
print 'initial dR\n', cp.get_dR(X)
X = cp.solve_ff(X)
print '========== results =============='
print 'solution X\n', X
print 'final positions\n', cp.get_new_nodes(X)
print 'final vectors\n', cp.get_new_vectors(X)
print 'final lengths\n', cp.get_new_lengths(X)
return cp
def cp_t2(self):
# ------------------------------------------------------------------------------
# test with 3 creaselines
# ------------------------------------------------------------------------------
cp = CreasePattern()
cp.nodes = [[0, 0, 0], [1, 0, 0], [1, 1, 0]]
cp.crease_lines = [[0, 1], [1, 2], [2, 0]]
cp.constraints = [[0, 0], [0, 1], [0, 2], [1, 2], [2, 2], [1, 1]]
cp.constraint_values = [0, 0, 0, 0, 0, 0.1]
X = np.zeros((cp.n_dofs,), dtype=float)
print "initial lengths\n", cp.c_lengths
print "initial vectors\n", cp.c_vectors
print "initial R\n", cp.get_R(X)
print "initial dR\n", cp.get_dR(X)
print "constrained dofs\n", cp.cnstr_dofs
print "free dofs\n", cp.free_dofs
# Newton-Raphson iteration
MAX_ITER = 150
TOLERANCE = 1e-10
for i in range(MAX_ITER):
dR = cp.get_dR(X)[:, cp.free_dofs]
R = cp.get_R(X)
if np.linalg.norm(R) < TOLERANCE:
print "==== converged in ", i, "iterations ===="
break
dX = np.linalg.solve(dR, -R)
X[cp.free_dofs] += dX
print "========== results =============="
print "solution X\n", X
print "final positions\n", cp.get_new_nodes(X)
print "final vectors\n", cp.get_new_vectors(X)
print "final lengths\n", cp.get_new_lengths(X)
def cp_t3(self):
# ------------------------------------------------------------------------------
# test 6 triangles (standard pattern)
# 7 nodes
# 12 creaselines
# 3 * 7 - 12 constrains needed
# ------------------------------------------------------------------------------
cp = CreasePattern()
cp.nodes = [[0, 0, 0], [1, 0, 0], [1, 1, 0], [-1, 1, 0], [-1, 0, 0], [-1, -1, 0], [1, -1, 0]]
cp.crease_lines = [
[0, 1],
[1, 2],
[2, 0],
[2, 3],
[3, 0],
[3, 4],
[4, 0],
[4, 5],
[5, 0],
[5, 6],
[6, 0],
[6, 1],
]
cp.constraints = [[0, 1], [0, 2], [1, 0], [1, 1], [1, 2], [4, 1], [2, 0], [6, 0], [4, 2]]
# lift node 0 in z-axes
cp.constraint_values = [0, 0.5, 0, 0, 0, 0, 0, 0, 0]
X = np.zeros((cp.n_dofs,), dtype=float)
print "initial lengths\n", cp.c_lengths
print "initial vectors\n", cp.c_vectors
print "initial R\n", cp.get_R(X)
print "initial dR\n", cp.get_dR(X)
print "constrained dofs\n", cp.cnstr_dofs
print "free dofs\n", cp.free_dofs
# Newton-Raphson iteration
MAX_ITER = 150
TOLERANCE = 1e-10
n_steps = 8
cv = np.copy(cp.constraint_values)
for k in range(n_steps):
print "step", k
cp.constraint_values = (k + 1.0) / float(n_steps) * cv
for i in range(MAX_ITER):
dR = cp.get_dR(X)[:, cp.free_dofs]
print "dR", dR.shape
R = cp.get_R(X)
if np.linalg.norm(R) < TOLERANCE:
print "==== converged in ", i, "iterations ===="
break
dX = np.linalg.solve(dR, -R)
X[cp.free_dofs] += dX
cp.set_next_node(X)
print "========== results =============="
print "solution X\n", X
print "final positions\n", cp.get_new_nodes(X)
print "final vectors\n", cp.get_new_vectors(X)
print "final lengths\n", cp.get_new_lengths(X)
# initialise View
from crease_pattern_view import CreasePatternView
my_model = CreasePatternView(data=cp)
print my_model.data.iteration_nodes.shape
my_model.configure_traits()
def get_V_du(self, u):
'''Get the gradient of potential energy with respect to the current nodal position.
'''
F = self.F_N
F_V_du = self.get_F_V_du(u)
dof_map = (3 * F[:, :, np.newaxis] + np.arange(3)[np.newaxis, np.newaxis, :])
V_du = np.bincount(dof_map.flatten(), weights=F_V_du.flatten())
return V_du
if __name__ == '__main__':
from crease_pattern import CreasePattern
cp = CreasePattern(X=[[0, 0, 0],
[1, 0, 0],
[1, 1, 0],
[0, 1, 0],
[2, 2, 1]],
L=[[0, 1], [1, 2], [3, 2], [0, 3], [0, 2], [1, 4], [2, 4], [3, 4]],
F=[[0, 1, 2], [2, 0, 3], [1, 2, 4], [2, 3, 4]])
# structural mappings
print 'nodes'
print cp.X
print 'lines'
print cp.L
print 'faces'
print cp.F
print 'faces counter-clockwise'
print cp.F_N
print 'node neighbors'
),
dock = 'tab',
resizable = True,
width = 1.0,
height = 1.0
)
#===============================================================================
# Test Pattern
#===============================================================================
if __name__ == '__main__':
# little example with all visual elements
# ToDo: suface missing
cp = CreasePattern()
cp.nodes = [[0, 0, 0],
[1, 0, 0],
[1, 1, 0],
[0, 1, 0],
[0.2, 0.2, 0],
[0.5, 0.5, 0.0]]
cp.crease_lines = [[0, 1],
[1, 2],
[2, 3],
[3, 0],
[1, 3]]
cp.facets = [[0, 1, 3],
[1, 2, 3]]
cp.grab_pts = [[4, 0]]
def triangle_cp_cnstr(n_steps = 10, dx = -1.99):
cp = CreasePattern(n_steps = n_steps)
cp.nodes = [[ 0, 0, 0 ],
[ 1, 0, 0 ],
[ 1, 1, 0]]
cp.crease_lines = [[ 0, 1 ],
[ 1, 2 ],
[ 2, 0 ]]
cp.facets = [[0, 1, 2 ]]
cp.grab_pts = [[[0.667,0.333,0],0],
[[0.1,0.05,0],0]]
cp.cnstr_lhs = [
[(0, 0, 1.0)],
[(0, 1, 1.0)],
[(0, 2, 1.0)],
[(1, 1, 1.0)],
[(1, 2, 1.0)],
[(2, 2, 1.0)],
]
cp.cnstr_rhs = [0.0, 0.0, 0.0, 0.0, 0.0, dx]
X = np.zeros((cp.n_dofs,), dtype = float)
X[1] = 0.01
print 'L ', cp.grab_pts_L
print 'initial lengths\n', cp.c_lengths
print 'initial vectors\n', cp.c_vectors
print 'initial R\n', cp.get_R(X)
print 'initial dR\n', cp.get_dR(X)
X = cp.solve(X)
print '========== results =============='
print 'solution X\n', X
print 'final positions\n', cp.get_new_nodes(X)
print 'final vectors\n', cp.get_new_vectors(X)
print 'final lengths\n', cp.get_new_lengths(X)
return cp
def rhombcp():
cp = CreasePattern()
cp.nodes = [[ 0, 0, 0 ],
[ 2, 0, 0 ],
[ 4, 0, 0 ],
[ 0, 1, 0 ],
[ 1, 1, 0 ],
[ 3, 1, 0 ],
[ 4, 1, 0]]
cp.crease_lines = [[ 0, 1 ],
[ 1, 2 ],
[ 0, 3 ],
[ 2, 6 ],
[ 0, 4 ],
[ 1, 4 ],
[ 3, 4 ],
[ 5, 4 ],
[ 1, 5 ],
[ 2, 5 ],
[ 6, 5 ],
]
cp.constraints = [[3, 2],
[3, 1],
[4, 1],
[4, 2],
[5, 1],
[5, 2],
[6, 0],
[6, 1],
[6, 2],
[0, 2]]
# lift node 0 in z-axes
cp.constraint_values = np.zeros((10,), dtype = float)
cp.constraint_values[3] = 0.4
cp.constraint_values[5] = 0.4
cp.constraint_values[8] = 0.0
cp.constraint_values[9] = 0.0
X = np.zeros((cp.n_dofs,), dtype = float)
X[3] = 0.1
X[5] = 0.1
print 'initial lengths\n', cp.c_lengths
print 'initial vectors\n', cp.c_vectors
print 'initial R\n', cp.get_R(X)
print 'initial dR\n', cp.get_dR(X)
print 'constrained dofs\n', cp.cnstr_dofs
print 'free dofs\n', cp.free_dofs
# Newton-Raphson iteration
MAX_ITER = 150
TOLERANCE = 1e-10
n_steps = 3
cv = np.copy(cp.constraint_values)
for k in range(n_steps):
print 'step', k
#cp.set_next_node(X)
cp.constraint_values = (k + 1.) / float(n_steps) * cv
i = 0
while i in range(MAX_ITER):
dR = cp.get_dR(X)[:, cp.free_dofs ]
print 'dR', dR.shape
R = cp.get_R(X)
if np.linalg.norm(R) < TOLERANCE:
print '==== converged in ', i, 'iterations ===='
cp.set_next_node(X)
break
dX = np.linalg.solve(dR, -R)
X[ cp.free_dofs ] += dX
i += 1
else:
raise ValueError
break
print '========== results =============='
print 'solution X\n', X
print 'final positions\n', cp.get_new_nodes(X)
print 'final vectors\n', cp.get_new_vectors(X)
print 'final lengths\n', cp.get_new_lengths(X)
# initialise View
my_model = CreasePatternView(data = cp)
my_model.configure_traits()
),
),
dock = 'tab',
resizable = True,
id = 'creaspatternview',
width = 1.0,
height = 1.0
)
if __name__ == '__main__':
# initialise CreasePattern
cp = CreasePattern()
cp.nodes = [[ 0, 0, 0 ],
[ 1, 0, 0 ],
[ 1, 1, 0 ]]
cp.crease_lines = [[ 0, 1 ], [1, 2]] # , [2, 0]]
X = np.zeros( ( cp.n_dofs, ), dtype = float )
cp.set_next_node( X )
# initialise View
my_model = CreasePatternView( data = cp )
my_model.configure_traits()
import matplotlib
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.widgets import Slider
from pprint import pprint
import time
from crease_pattern import CreasePattern
import matrix_utils as mu
import plot_utils as pu
from solver import Solver
if __name__ == "__main__":
# Initialize the crease pattern and solver
increments = 50
crease_pattern = CreasePattern('patterns/waterbomb.json', 30.0)
solver = Solver(num_increments=increments)
# Hide toolbars (with "save" button, etc.) and set the GUI theme
matplotlib.rcParams['toolbar'] = 'None'
matplotlib.style.use('ggplot')
# Create a 3D plot for displaying various folded configurations of the model
solve = True
print_fold_angles = False
export_keyframes = True
show_grid_in_xyz = False
show_crease_pattern_plot = False
size = 60
fig_3d = plt.figure(figsize=(8, 8))