def get_c0_mesh(self):
# Create the C0-mesh
nx, ny, nz = self.n
X = self.raw.get_c0_avg()
b1 = BSplineBasis(2, [0] + [i/nx for i in range(nx+1)] + [1])
b2 = BSplineBasis(2, [0] + [i/ny for i in range(ny+1)] + [1])
b3 = BSplineBasis(2, [0] + [i/nz for i in range(nz+1)] + [1])
c0_vol = volume_factory.interpolate(X, [b1, b2, b3])
return c0_vol
def test_lower_order(self):
b = BSplineBasis(4, [0, 0, 0, 0, .2, .3, .3, .6, .9, 1, 1, 1, 1])
t = b.greville()
Y, X, Z = np.meshgrid(t, t, t)
cp = np.zeros((len(t), len(t), len(t), 3))
cp[..., 0] = X * (1 - Y)
cp[..., 1] = X * X
cp[..., 2] = Z**2 + 2
vol = vf.interpolate(cp, [b, b, b])
vol2 = vol.lower_order(1) # still in space, vol2 is *also* exact
u = np.linspace(0, 1, 5)
v = np.linspace(0, 1, 6)
w = np.linspace(0, 1, 7)
self.assertTrue(np.allclose(vol(u, v, w), vol2(u, v, w)))
self.assertTupleEqual(vol.order(), (4, 4, 4))
self.assertTupleEqual(vol2.order(), (3, 3, 3))
def test_lower_order(self):
b = BSplineBasis(4, [0,0,0,0,.2, .3, .3, .6, .9, 1,1,1,1])
t = b.greville()
Y, X, Z = np.meshgrid(t,t,t)
cp = np.zeros((len(t), len(t), len(t), 3))
cp[...,0] = X*(1-Y)
cp[...,1] = X*X
cp[...,2] = Z**2 + 2
vol = VolumeFactory.interpolate(cp, [b,b,b])
vol2 = vol.lower_order(1) # still in space, vol2 is *also* exact
u = np.linspace(0,1, 5)
v = np.linspace(0,1, 6)
w = np.linspace(0,1, 7)
self.assertTrue(np.allclose( vol(u,v,w), vol2(u,v,w) ))
self.assertTupleEqual(vol.order(), (4,4,4))
self.assertTupleEqual(vol2.order(), (3,3,3))
def test_interpolate(self):
t = np.linspace(0, 1, 5)
V,U,W = np.meshgrid(t,t,t)
x = np.zeros((5,5,5,3))
x[:,:,:,0] = U*U + V*V
x[:,:,:,1] = U*U*W
x[:,:,:,2] = W*W*W + U*V
b1 = BSplineBasis(3, [0,0,0,.33,.66,1,1,1])
b2 = BSplineBasis(4, [0,0,0,0,.5,1,1,1,1])
b3 = BSplineBasis(4, [0,0,0,0,.2,1,1,1,1])
vol = VolumeFactory.interpolate(x, [b1,b2,b3], [t,t,t])
t = np.linspace(0, 1, 7)
V,U,W = np.meshgrid(t,t,t)
x = vol(t,t,t)
self.assertTrue(np.allclose(x[:,:,:,0], U*U + V*V))
self.assertTrue(np.allclose(x[:,:,:,1], U*U*W))
self.assertTrue(np.allclose(x[:,:,:,2], W*W*W + U*V))
def test_interpolate(self):
t = np.linspace(0, 1, 5)
V,U,W = np.meshgrid(t,t,t)
x = np.zeros((5,5,5,3))
x[:,:,:,0] = U*U + V*V
x[:,:,:,1] = U*U*W
x[:,:,:,2] = W*W*W + U*V
b1 = BSplineBasis(3, [0,0,0,.33,.66,1,1,1])
b2 = BSplineBasis(4, [0,0,0,0,.5,1,1,1,1])
b3 = BSplineBasis(4, [0,0,0,0,.2,1,1,1,1])
vol = vf.interpolate(x, [b1,b2,b3], [t,t,t])
t = np.linspace(0, 1, 7)
V,U,W = np.meshgrid(t,t,t)
x = vol(t,t,t)
self.assertTrue(np.allclose(x[:,:,:,0], U*U + V*V))
self.assertTrue(np.allclose(x[:,:,:,1], U*U*W))
self.assertTrue(np.allclose(x[:,:,:,2], W*W*W + U*V))
