def test_edge_surfaces(self):
# test 3D surface vs 2D rational surface
# more or less random 3D surface with p=[2,2] and n=[3,4]
controlpoints = [[0, 0, 1], [-1, 1, 1], [0, 2, 1], [1, -1, 1], [1, 0, .5], [1, 1, 1],
[2, 1, 1], [2, 2, .5], [2, 3, 1], [3, 0, 1], [4, 1, 1], [3, 2, 1]]
basis1 = BSplineBasis(3, [0, 0, 0, 1, 1, 1])
basis2 = BSplineBasis(3, [0, 0, 0, .64, 2, 2, 2])
top = Surface(basis1, basis2, controlpoints)
# more or less random 2D rational surface with p=[1,2] and n=[3,4]
controlpoints = [[0, 0, 1], [-1, 1, .96], [0, 2, 1], [1, -1, 1], [1, 0, .8], [1, 1, 1],
[2, 1, .89], [2, 2, .9], [2, 3, 1], [3, 0, 1], [4, 1, 1], [3, 2, 1]]
basis1 = BSplineBasis(3, [0, 0, 0, 1, 1, 1])
basis2 = BSplineBasis(2, [0, 0, .4, .44, 1, 1])
bottom = Surface(basis1, basis2, controlpoints, True)
vol = VolumeFactory.edge_surfaces(bottom, top)
# set parametric domain to [0,1]^2 for easier comparison
top.reparam()
bottom.reparam()
# verify on 7x7x2 evaluation grid
for u in np.linspace(0, 1, 7):
for v in np.linspace(0, 1, 7):
for w in np.linspace(0, 1, 2): # rational basis, not linear in w-direction
self.assertAlmostEqual(
vol(u, v, w)[0], bottom(u, v)[0] *
(1 - w) + top(u, v)[0] * w) # x-coordinate
self.assertAlmostEqual(
vol(u, v, w)[1], bottom(u, v)[1] *
(1 - w) + top(u, v)[1] * w) # y-coordinate
self.assertAlmostEqual(
vol(u, v, w)[2], 0 * (1 - w) + top(u, v)[2] * w) # z-coordinate
# test 3D surface vs 2D surface
controlpoints = [[0, 0], [-1, 1], [0, 2], [1, -1], [1, 0], [1, 1], [2, 1], [2, 2], [2, 3],
[3, 0], [4, 1], [3, 2]]
basis1 = BSplineBasis(3, [0, 0, 0, 1, 1, 1])
basis2 = BSplineBasis(2, [0, 0, .4, .44, 1, 1])
bottom = Surface(basis1, basis2, controlpoints) # non-rational!
vol = VolumeFactory.edge_surfaces(bottom, top) # also non-rational!
# verify on 5x5x7 evaluation grid
for u in np.linspace(0, 1, 5):
for v in np.linspace(0, 1, 5):
for w in np.linspace(0, 1, 7): # include inner evaluation points
self.assertAlmostEqual(
vol(u, v, w)[0], bottom(u, v)[0] *
(1 - w) + top(u, v)[0] * w) # x-coordinate
self.assertAlmostEqual(
vol(u, v, w)[1], bottom(u, v)[1] *
(1 - w) + top(u, v)[1] * w) # y-coordinate
self.assertAlmostEqual(
vol(u, v, w)[2], 0 * (1 - w) + top(u, v)[2] * w) # z-coordinate
def test_edge_surfaces(self):
# test 3D surface vs 2D rational surface
# more or less random 3D surface with p=[2,2] and n=[3,4]
controlpoints = [[0, 0, 1], [-1, 1, 1], [0, 2, 1], [1, -1, 1], [1, 0, .5], [1, 1, 1],
[2, 1, 1], [2, 2, .5], [2, 3, 1], [3, 0, 1], [4, 1, 1], [3, 2, 1]]
basis1 = BSplineBasis(3, [0, 0, 0, 1, 1, 1])
basis2 = BSplineBasis(3, [0, 0, 0, .64, 2, 2, 2])
top = Surface(basis1, basis2, controlpoints)
# more or less random 2D rational surface with p=[1,2] and n=[3,4]
controlpoints = [[0, 0, 1], [-1, 1, .96], [0, 2, 1], [1, -1, 1], [1, 0, .8], [1, 1, 1],
[2, 1, .89], [2, 2, .9], [2, 3, 1], [3, 0, 1], [4, 1, 1], [3, 2, 1]]
basis1 = BSplineBasis(3, [0, 0, 0, 1, 1, 1])
basis2 = BSplineBasis(2, [0, 0, .4, .44, 1, 1])
bottom = Surface(basis1, basis2, controlpoints, True)
vol = vf.edge_surfaces(bottom, top)
# set parametric domain to [0,1]^2 for easier comparison
top.reparam()
bottom.reparam()
# verify on 7x7x2 evaluation grid
for u in np.linspace(0, 1, 7):
for v in np.linspace(0, 1, 7):
for w in np.linspace(0, 1, 2): # rational basis, not linear in w-direction
self.assertAlmostEqual(
vol(u, v, w)[0], bottom(u, v)[0] *
(1 - w) + top(u, v)[0] * w) # x-coordinate
self.assertAlmostEqual(
vol(u, v, w)[1], bottom(u, v)[1] *
(1 - w) + top(u, v)[1] * w) # y-coordinate
self.assertAlmostEqual(
vol(u, v, w)[2], 0 * (1 - w) + top(u, v)[2] * w) # z-coordinate
# test 3D surface vs 2D surface
controlpoints = [[0, 0], [-1, 1], [0, 2], [1, -1], [1, 0], [1, 1], [2, 1], [2, 2], [2, 3],
[3, 0], [4, 1], [3, 2]]
basis1 = BSplineBasis(3, [0, 0, 0, 1, 1, 1])
basis2 = BSplineBasis(2, [0, 0, .4, .44, 1, 1])
bottom = Surface(basis1, basis2, controlpoints) # non-rational!
vol = vf.edge_surfaces(bottom, top) # also non-rational!
# verify on 5x5x7 evaluation grid
for u in np.linspace(0, 1, 5):
for v in np.linspace(0, 1, 5):
for w in np.linspace(0, 1, 7): # include inner evaluation points
self.assertAlmostEqual(
vol(u, v, w)[0], bottom(u, v)[0] *
(1 - w) + top(u, v)[0] * w) # x-coordinate
self.assertAlmostEqual(
vol(u, v, w)[1], bottom(u, v)[1] *
(1 - w) + top(u, v)[1] * w) # y-coordinate
self.assertAlmostEqual(
vol(u, v, w)[2], 0 * (1 - w) + top(u, v)[2] * w) # z-coordinate
def test_edge_surfaces_six_sides(self):
# create the unit cube
vol = Volume()
vol.raise_order(2,2,2)
vol.refine(3)
edges = vol.faces()
# edge_surface should give back the same unit cube
vol2 = VolumeFactory.edge_surfaces(edges)
# check discretization
self.assertEqual(vol2.order(0), 4)
self.assertEqual(vol2.order(1), 4)
self.assertEqual(vol2.order(2), 4)
self.assertEqual(len(vol2.knots(0)), 5) # [0,.25,.5,.75,1]
self.assertEqual(len(vol2.knots(1)), 5)
self.assertEqual(len(vol2.knots(2)), 5)
# check a 5x5x5 evaluation grid
u = np.linspace(0,1,5)
v = np.linspace(0,1,5)
w = np.linspace(0,1,5)
pt = vol( u,v,w)
pt2 = vol2(u,v,w)
self.assertAlmostEqual(np.linalg.norm(pt-pt2), 0.0)
def test_edge_surfaces_six_sides_issue_141(self):
# create the unit cube
vol = Volume()
# modify slightly one edge: umin(w=0) is now a parabola instead of a line
vol.raise_order(0,1,0)
vol.controlpoints[-1, 1, 0, 0] += 1
faces = vol.faces()
# edge_surface should give back the same modified unit cube
vol2 = vf.edge_surfaces(faces)
# check discretization
self.assertEqual(vol2.order(0),2)
self.assertEqual(vol2.order(1),3)
self.assertEqual(vol2.order(2),2)
self.assertEqual(len(vol2.knots(0)),2) # [0, 1]
self.assertEqual(len(vol2.knots(1)),2)
self.assertEqual(len(vol2.knots(2)),2)
# check a 5x5x5 evaluation grid
u = np.linspace(0,1,5)
v = np.linspace(0,1,5)
w = np.linspace(0,1,5)
pt = vol( u,v,w)
pt2 = vol2(u,v,w)
self.assertTrue(np.allclose(pt, pt2))
def test_edge_surfaces_six_sides(self):
# create the unit cube
vol = Volume()
vol.raise_order(2,2,2)
vol.refine(3)
edges = vol.faces()
# edge_surface should give back the same unit cube
vol2 = vf.edge_surfaces(edges)
# check discretization
self.assertEqual(vol2.order(0), 4)
self.assertEqual(vol2.order(1), 4)
self.assertEqual(vol2.order(2), 4)
self.assertEqual(len(vol2.knots(0)), 5) # [0,.25,.5,.75,1]
self.assertEqual(len(vol2.knots(1)), 5)
self.assertEqual(len(vol2.knots(2)), 5)
# check a 5x5x5 evaluation grid
u = np.linspace(0,1,5)
v = np.linspace(0,1,5)
w = np.linspace(0,1,5)
pt = vol( u,v,w)
pt2 = vol2(u,v,w)
self.assertAlmostEqual(np.linalg.norm(pt-pt2), 0.0)
def texture(self, p, ngeom, ntexture, method='full', irange=[None,None], jrange=[None,None]):
# Set the dimensions of geometry and texture map
# ngeom = np.floor(self.n / (p-1))
# ntexture = np.floor(self.n * n)
# ngeom = ngeom.astype(np.int32)
# ntexture = ntexture.astype(np.int32)
ngeom = ensure_listlike(ngeom, 3)
ntexture = ensure_listlike(ntexture, 3)
p = ensure_listlike(p, 3)
# Create the geometry
ngx, ngy, ngz = ngeom
b1 = BSplineBasis(p[0], [0]*(p[0]-1) + [i/ngx for i in range(ngx+1)] + [1]*(p[0]-1))
b2 = BSplineBasis(p[1], [0]*(p[1]-1) + [i/ngy for i in range(ngy+1)] + [1]*(p[1]-1))
b3 = BSplineBasis(p[2], [0]*(p[2]-1) + [i/ngz for i in range(ngz+1)] + [1]*(p[2]-1))
l2_fit = surface_factory.least_square_fit
vol = self.get_c0_mesh()
i = slice(irange[0], irange[1], None)
j = slice(jrange[0], jrange[1], None)
# special case number of evaluation points for full domain
if irange[1] == None: irange[1] = vol.shape[0]
if jrange[1] == None: jrange[1] = vol.shape[1]
if irange[0] == None: irange[0] = 0
if jrange[0] == None: jrange[0] = 0
nu = np.diff(irange)
nv = np.diff(jrange)
nw = vol.shape[2]
u = np.linspace(0, 1, nu)
v = np.linspace(0, 1, nv)
w = np.linspace(0, 1, nw)
crvs = []
crvs.append(curve_factory.polygon(vol[i ,jrange[0] , 0,:].squeeze()))
crvs.append(curve_factory.polygon(vol[i ,jrange[0] ,-1,:].squeeze()))
crvs.append(curve_factory.polygon(vol[i ,jrange[1]-1, 0,:].squeeze()))
crvs.append(curve_factory.polygon(vol[i ,jrange[1]-1,-1,:].squeeze()))
crvs.append(curve_factory.polygon(vol[irange[0] ,j , 0,:].squeeze()))
crvs.append(curve_factory.polygon(vol[irange[0] ,j ,-1,:].squeeze()))
crvs.append(curve_factory.polygon(vol[irange[1]-1,j , 0,:].squeeze()))
crvs.append(curve_factory.polygon(vol[irange[1]-1,j ,-1,:].squeeze()))
crvs.append(curve_factory.polygon(vol[irange[0] ,jrange[0] , :,:].squeeze()))
crvs.append(curve_factory.polygon(vol[irange[0] ,jrange[1]-1, :,:].squeeze()))
crvs.append(curve_factory.polygon(vol[irange[1]-1,jrange[0] , :,:].squeeze()))
crvs.append(curve_factory.polygon(vol[irange[1]-1,jrange[1]-1, :,:].squeeze()))
# with G2('curves.g2') as myfile:
# myfile.write(crvs)
# print('Written curve.g2')
if method == 'full':
bottom = l2_fit(vol[i, j, 0,:].squeeze(), [b1, b2], [u, v])
top = l2_fit(vol[i, j, -1,:].squeeze(), [b1, b2], [u, v])
left = l2_fit(vol[irange[0] ,j, :,:].squeeze(), [b2, b3], [v, w])
right = l2_fit(vol[irange[1]-1,j, :,:].squeeze(), [b2, b3], [v, w])
front = l2_fit(vol[i, jrange[0], :,:].squeeze(), [b1, b3], [u, w])
back = l2_fit(vol[i, jrange[1]-1,:,:].squeeze(), [b1, b3], [u, w])
volume = volume_factory.edge_surfaces([left, right, front, back, bottom, top])
elif method == 'z':
bottom = l2_fit(vol[i,j, 0,:].squeeze(), [b1, b2], [u, v])
top = l2_fit(vol[i,j,-1,:].squeeze(), [b1, b2], [u, v])
volume = volume_factory.edge_surfaces([bottom, top])
volume.set_order(*p)
volume.refine(ngz - 1, direction='w')
volume.reverse(direction=2)
# Point-to-cell mapping
# TODO: Optimize more
eps = 1e-2
u = [np.linspace(eps, 1-eps, n) for n in ntexture]
points = volume(*u).reshape(-1, 3)
cellids = np.zeros(points.shape[:-1], dtype=int)
cell = None
nx, ny, nz = self.n
for ptid, point in enumerate(tqdm(points, desc='Inverse mapping')):
i, j, k = cell = self.raw.cell_at(point) # , guess=cell)
cellid = i*ny*nz + j*nz + k
cellids[ptid] = cellid
cellids = cellids.reshape(tuple(ntexture))
all_textures = {}
for name in self.attribute:
data = self.attribute[name][cellids]
# TODO: This flattens the image if it happens to be 3D (or higher...)
# do we need a way to communicate the structure back to the caller?
# data = data.reshape(-1, data.shape[-1])
# TODO: This normalizes the image,
# but we need a way to communicate the ranges back to the caller
# a, b = min(data.flat), max(data.flat)
# data = ((data - a) / (b - a) * 255).astype(np.uint8)
all_textures[name] = data
all_textures['cellids'] = cellids
return volume, all_textures