def test_bending():
random.seed(7218414)
stiffness = 7
damping = 3
for d in 2,3:
mesh = SegmentSoup([[0,1],[1,2]]) if d==2 else TriangleSoup([[0,2,1],[1,2,3]])
X = random.randn(d+1,d)
dX = .1*random.randn(d+1,d)
for bend in linear_bending_elements(mesh,X,stiffness,damping),cubic_hinges(mesh,X,stiffness,damping):
print '\n',type(bend).__name__
if 'CubicHinges' in type(bend).__name__: # Compare energy with slow_energy
angles = bend.angles(mesh.bending_tuples(),X)
for theta in random.randn(20):
iX = concatenate([X[:-1],[X[1]+(Rotation.from_angle(theta) if d==2 else Rotation.from_angle_axis(theta,X[2]-X[1]))*(X[-1]-X[1])]])
bend.update_position(iX,False)
energy = bend.elastic_energy()
slow_energy = bend.slow_elastic_energy(angles,X,iX)
error = relative_error(energy,slow_energy)
print 'slow energy error = %g (slow %g vs. %g, theta = %g)'%(error,slow_energy,energy,theta)
assert error<1e-8
force_test(bend,X+dX,verbose=1)
# Test against exact sphere energies. We don't actually compute the correct answers in 3D, since hinge based energies are fundamentally mesh dependent.
radius = 78
analytics = [('S_1',circle_mesh(1000,radius=radius),pi/radius,1,1e-5),
('S_2',sphere_mesh(3,radius=radius),2*pi,4,.015),
('S_1 x [0,e]',open_cylinder_mesh((0,0,0),(0,0,e),radius=radius,na=100),pi*e/radius,3,2e-4)]
for name,(mesh,X),known,fudge,tolerance in analytics:
flat = zeros(len(mesh.bending_tuples()))
bend = cubic_hinges(mesh,X,stiffness,damping,angles=flat)
energy = bend.slow_elastic_energy(flat,X,X)/stiffness/fudge
error = relative_error(energy,known)
print '%s: known %g, energy %g, ratio %r, error %g'%(name,known,energy,energy/known,error)
assert error<tolerance
def test_fvm_3d():
random.seed(12873)
model = neo_hookean()
X = random.randn(4, 3)
dX = .1 * random.randn(4, 3)
fvm = finite_volume([(0, 1, 2, 3)], 1000, X, model)
force_test(fvm, X + dX, verbose=1)
def test_fvm_3d(): random.seed(12873) model = neo_hookean() X = random.randn(4,3) dX = .1*random.randn(4,3) fvm = finite_volume([(0,1,2,3)],1000,X,model) force_test(fvm,X+dX,verbose=1)
def test_linear_fvm_hex():
random.seed(12873)
X = [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 1, 1], [1, 0, 0], [1, 0, 1],
[1, 1, 0], [1, 1, 1]] + .1 * random.randn(8, 3)
dX = .1 * random.randn(8, 3)
fvm = linear_finite_volume([arange(8)], X, 1000)
force_test(fvm, X + dX, verbose=1)
def test_springs():
random.seed(12871)
X0 = random.randn(2, 3)
X = random.randn(2, 3)
springs = Springs([[0, 1]], [1.1, 1.2], X0, 5, 7)
force_test(springs, X, verbose=1)
springs = Springs([[0, 1]], [1.1, 1.2], X0, [5], [7])
force_test(springs, X, verbose=1)
def test_springs(): random.seed(12871) X0 = random.randn(2,3) X = random.randn(2,3) springs = Springs([[0,1]],[1.1,1.2],X0,5,7) force_test(springs,X,verbose=1) springs = Springs([[0,1]],[1.1,1.2],X0,[5],[7]) force_test(springs,X,verbose=1)
def test_pins():
random.seed(17310)
X = random.randn(5, 3)
nodes = [1, 3]
mass = random.randn(len(X))**2
targets = random.randn(len(nodes), 3)
pins = Pins(nodes, mass, targets, 3.5, 1.1)
force_test(pins, X, verbose=1)
def test_pins(): random.seed(17310) X = random.randn(5,3) nodes = [1,3] mass = random.randn(len(X))**2 targets = random.randn(len(nodes),3) pins = Pins(nodes,mass,targets,3.5,1.1) force_test(pins,X,verbose=1)
def test_simple_shell():
for i in 0,1,3,4,7:
print '\ni = %d'%i
random.seed(12872+i)
X = random.randn(3,2)
X2 = .1*random.randn(3,3)
X2[:,:2] += X
shell = simple_shell([(0,1,2)],1000,X=X,stretch=(7,6),shear=3)
shell.F_threshold = 1e-7
force_test(shell,X2,verbose=1)
def test_simple_shell():
for i in 0, 1, 3, 4, 7:
print '\ni = %d' % i
random.seed(12872 + i)
X = random.randn(3, 2)
X2 = .1 * random.randn(3, 3)
X2[:, :2] += X
shell = simple_shell([(0, 1, 2)], 1000, X=X, stretch=(7, 6), shear=3)
shell.F_threshold = 1e-7
force_test(shell, X2, verbose=1)
def test_binding_springs():
random.seed(73210)
for k in 2, 3:
nodes = [1, 2]
X = random.randn(20, 3)
parents = {2: [[5, 6], [8, 9]], 3: [[5, 6, 7], [10, 11, 12]]}[k]
weights = random.uniform(1, 2, (2, k))
weights /= weights.sum(axis=1).reshape(-1, 1)
mass = absolute(random.randn(len(X)))
springs = binding_springs(nodes, parents, weights, mass, 7, 1.2)
force_test(springs, X, verbose=1)
def test_air_pressure():
random.seed(2813)
mesh, X = icosahedron_mesh()
if 1:
X = vstack([random.randn(3), X, random.randn(3)])
mesh = TriangleSoup(mesh.elements + 1)
X2 = X + random.randn(*X.shape) / 10
for closed in 0, 1:
for side in 1, -1:
print '\nclosed %d, side %d' % (closed, side)
air = AirPressure(mesh, X, closed, side)
force_test(air, X2, verbose=1)
def test_binding_springs():
random.seed(73210)
for k in 2,3:
nodes = [1,2]
X = random.randn(20,3)
parents = {2:[[5,6],[8,9]],
3:[[5,6,7],[10,11,12]]}[k]
weights = random.uniform(1,2,(2,k))
weights /= weights.sum(axis=1).reshape(-1,1)
mass = absolute(random.randn(len(X)))
springs = binding_springs(nodes,parents,weights,mass,7,1.2)
force_test(springs,X,verbose=1)
def test_air_pressure():
random.seed(2813)
mesh,X = icosahedron_mesh()
if 1:
X = vstack([random.randn(3),X,random.randn(3)])
mesh = TriangleSoup(mesh.elements+1)
X2 = X + random.randn(*X.shape)/10
for closed in 0,1:
for side in 1,-1:
print '\nclosed %d, side %d'%(closed,side)
air = AirPressure(mesh,X,closed,side)
force_test(air,X2,verbose=1)
def test_bending():
random.seed(7218414)
stiffness = 7
damping = 3
for d in 2, 3:
mesh = SegmentSoup([[0, 1], [1, 2]]) if d == 2 else TriangleSoup(
[[0, 2, 1], [1, 2, 3]])
X = random.randn(d + 1, d)
dX = .1 * random.randn(d + 1, d)
for bend in linear_bending_elements(mesh, X, stiffness,
damping), cubic_hinges(
mesh, X, stiffness, damping):
print '\n', type(bend).__name__
if 'CubicHinges' in type(
bend).__name__: # Compare energy with slow_energy
angles = bend.angles(mesh.bending_tuples(), X)
for theta in random.randn(20):
iX = concatenate([
X[:-1],
[
X[1] +
(Rotation.from_angle(theta) if d == 2 else
Rotation.from_angle_axis(theta, X[2] - X[1])) *
(X[-1] - X[1])
]
])
bend.update_position(iX, False)
energy = bend.elastic_energy()
slow_energy = bend.slow_elastic_energy(angles, X, iX)
error = relative_error(energy, slow_energy)
print 'slow energy error = %g (slow %g vs. %g, theta = %g)' % (
error, slow_energy, energy, theta)
assert error < 1e-8
force_test(bend, X + dX, verbose=1)
# Test against exact sphere energies. We don't actually compute the correct answers in 3D, since hinge based energies are fundamentally mesh dependent.
radius = 78
analytics = [('S_1', circle_mesh(1000,
radius=radius), pi / radius, 1, 1e-5),
('S_2', sphere_mesh(3, radius=radius), 2 * pi, 4, .015),
('S_1 x [0,e]',
open_cylinder_mesh((0, 0, 0), (0, 0, e),
radius=radius,
na=100), pi * e / radius, 3, 2e-4)]
for name, (mesh, X), known, fudge, tolerance in analytics:
flat = zeros(len(mesh.bending_tuples()))
bend = cubic_hinges(mesh, X, stiffness, damping, angles=flat)
energy = bend.slow_elastic_energy(flat, X, X) / stiffness / fudge
error = relative_error(energy, known)
print '%s: known %g, energy %g, ratio %r, error %g' % (
name, known, energy, energy / known, error)
assert error < tolerance
def test_surface_pins(): random.seed(127130) # Test a sphere mesh ignoring errors in the Hessian target_mesh,target_X = sphere_mesh(0) X = random.randn(100,3) mass = absolute(random.randn(len(X))) nodes = unique(random.randint(len(X),size=50).astype(int32)) pins = SurfacePins(nodes,mass,target_mesh,target_X,7,1.1) force_test(pins,X,verbose=1,ignore_hessian=1) # Hessian should be correct if the closest points are all on faces target_mesh = TriangleSoup([[0,1,2]]) target_X = 100*eye(3) pins = SurfacePins(nodes,mass,target_mesh,target_X,7,1.1) force_test(pins,X,verbose=1)
def test_surface_pins():
random.seed(127130)
# Test a sphere mesh ignoring errors in the Hessian
target_mesh, target_X = sphere_mesh(0)
X = random.randn(100, 3)
mass = absolute(random.randn(len(X)))
nodes = unique(random.randint(len(X), size=50).astype(int32))
pins = SurfacePins(nodes, mass, target_mesh, target_X, 7, 1.1)
force_test(pins, X, verbose=1, ignore_hessian=1)
# Hessian should be correct if the closest points are all on faces
target_mesh = TriangleSoup([[0, 1, 2]])
target_X = 100 * eye(3)
pins = SurfacePins(nodes, mass, target_mesh, target_X, 7, 1.1)
force_test(pins, X, verbose=1)
def test_particle_binding_springs():
random.seed(73210)
X = random.randn(4, 3)
mass = absolute(random.randn(len(X)))
springs = particle_binding_springs([[1, 2]], mass, 7, 1.2)
force_test(springs, X, verbose=1)
def test_ether_drag(): random.seed(12871) X = random.randn(1,3) drag = EtherDrag([1.2],7) force_test(drag,X,verbose=1)
def test_ether_drag():
random.seed(12871)
X = random.randn(1, 3)
drag = EtherDrag([1.2], 7)
force_test(drag, X, verbose=1)
def test_particle_binding_springs(): random.seed(73210) X = random.randn(4,3) mass = absolute(random.randn(len(X))) springs = particle_binding_springs([[1,2]],mass,7,1.2) force_test(springs,X,verbose=1)
def test_linear_fvm_hex(): random.seed(12873) X = [[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]+.1*random.randn(8,3) dX = .1*random.randn(8,3) fvm = linear_finite_volume([arange(8)],X,1000) force_test(fvm,X+dX,verbose=1)
def test_linear_fvm_3d():
random.seed(12873)
X = random.randn(4, 3)
dX = .1 * random.randn(4, 3)
fvm = linear_finite_volume([(0, 1, 2, 3)], X, 1000)
force_test(fvm, X + dX, verbose=1)
def test_linear_fvm_2d():
random.seed(12872)
X = random.randn(3, 2)
dX = .1 * random.randn(3, 2)
fvm = linear_finite_volume([(0, 1, 2)], X, 1000)
force_test(fvm, X + dX, verbose=1)
def test_linear_fvm_2d(): random.seed(12872) X = random.randn(3,2) dX = .1*random.randn(3,2) fvm = linear_finite_volume([(0,1,2)],X,1000) force_test(fvm,X+dX,verbose=1)
def test_linear_fvm_3d(): random.seed(12873) X = random.randn(4,3) dX = .1*random.randn(4,3) fvm = linear_finite_volume([(0,1,2,3)],X,1000) force_test(fvm,X+dX,verbose=1)
def test_gravity():
random.seed(12871)
X = random.randn(1, 3)
gravity = Gravity([1])
force_test(gravity, X, verbose=1)
def test_gravity(): random.seed(12871) X = random.randn(1,3) gravity = Gravity([1]) force_test(gravity,X,verbose=1)