def estimate_hermite(data, gdata, v0, v1, res, res_fine, coarse_level):
data_v0 = is_inside(data, tuple(v0))
data_v1 = is_inside(data, tuple(v1))
if coarse_level:
res_min = res_fine
else:
res_min = res
x0 = .5*(v0 + v1)
while res != res_min:
data_x0 = is_inside(data, tuple(x0))
if data_v0 != data_x0:
v1 = x0
elif data_v1 != data_x0:
v0 = x0
else:
print "ERROR!"
quit()
x0 = .5*(v0 + v1)
res /= 2.0
dfdx = (np.array(gdata[tuple(v0)]) + np.array(gdata[tuple(v1)]))
dfdx = dfdx / np.linalg.norm(dfdx)
#print str(dfdx) + "@" + str(x0) + "\t FROM:"+str(gdata[tuple(v0)])+ " and "+str(gdata[tuple(v1)])
return x0, dfdx
def estimate_hermite(data, v0, v1, res, res_fine, coarse_level):
data_v0 = is_inside(data, tuple(v0))
data_v1 = is_inside(data, tuple(v1))
if coarse_level:
res_min = res_fine
else:
res_min = res
x0 = .5*(v0 + v1)
while res != res_min:
data_x0 = is_inside(data, tuple(x0))
if data_v0 != data_x0:
v1 = x0
elif data_v1 != data_x0:
v0 = x0
else:
print "ERROR!"
quit()
x0 = .5*(v0 + v1)
res /= 2.0
if coarse_level:
print x0
return x0
def dual_contour(data, gdata, res, res_fine, dims, coarse_level):
# Compute vertices
dc_verts = []
vindex = {}
dc_manifold_nodes = []
manifold_index = {}
for x, y in it.product(np.arange(dims['xmin'], dims['xmax'], res), np.arange(dims['ymin'], dims['ymax'], res)):
o = np.array([float(x), float(y)])
quad_signs=[]
quad_sign_keys=[]
# Get signs for cube
for v in quad_verts:
position = (o + v*res)
quad_sign_keys.append(tuple(position))
for key in quad_sign_keys:
c = is_inside(data, key)
quad_signs.append(c)
if all(quad_signs) or not any(quad_signs):
continue
# #this checks for certain problematic cases and introduces manifold nodes, if necessary
# if coarse_level:
# if quad_signs == [False, True, False, True] or quad_signs == [True, False, True, False]:
# key = tuple(o)
# manifold_index[key] = len(dc_manifold_nodes)
# dc_manifold_nodes.append(ManifoldNode(o, quad_sign_keys, data, res))
# Estimate hermite data
h_data = []
for e in quad_edges:
if quad_signs[e[0]] != quad_signs[e[1]]:
v0 = o + quad_verts[e[0]]*res
v1 = o + quad_verts[e[1]]*res
x, dx = estimate_hermite(data, gdata, v0, v1, res, res_fine, coarse_level)
#h_data.append(x)
h_data.append(tuple([x,dx]))
print "zero crossing from node "+str(v0)+" to "+str(v1)
print "\tx:\t"+str(x)
print "\tdx:\t"+str(dx)
#Solve qef to get vertex
A = [n for p, n in h_data]
b = [np.dot(p, n) for p, n in h_data]
print A
print b
#quit()
v, residue, rank, s = la.lstsq(A, b)
# counter = 0
# v = np.array([0.0, 0.0])
#
# for p in h_data:
# v += np.array(p)
# counter += 1
#
# v /= 1.0 * counter
#Throw out failed solutions
if la.norm(v-o) > 2 * res:
continue
# Emit one vertex per every cube that crosses
key = tuple(o)
vindex[key] = len(dc_verts)
dc_verts.append(v)
# Construct faces
dc_edges = []
for x, y in it.product(np.arange(dims['xmin'], dims['xmax'], res), np.arange(dims['ymin'], dims['ymax'], res)):
# Emit one edge per each edge that crosses
if (x, y) in vindex:
o = np.array([float(x), float(y)])
for i in range(2):
if tuple(o + res*dirs[i]) in vindex:
if (data[tuple(o+res*dirs[i]+res*dirs[int(not i)])] > 0) != (data[tuple(o+res*dirs[i])] > 0):
dc_edges.append([vindex[tuple(o)], vindex[tuple(o + np.array(dirs[i])*res)]])
else:
continue
if coarse_level: # if we are working on coarse scale we want to resolve non manifold vertices
dc_verts, dc_edges = resolve_manifold_nodes(dc_edges, dc_verts, vindex, dc_manifold_nodes, manifold_index, res, dims)
return np.array(dc_verts), np.array(dc_edges)