def SecondFundamentalForm(v, f):
from chumpy import hstack, vstack
from chumpy.linalg import Pinv
nbrs = MatVecMult(FirstEdgesMtx(v, f, want_big=True), v.ravel()).reshape(
(-1, 3))
b0 = VertNormals(f=f, v=v)
b1 = NormalizedNx3(CrossProduct(b0, nbrs - v)).reshape((-1, 3))
b2 = NormalizedNx3(CrossProduct(b0, b1)).reshape((-1, 3))
cnct = get_vert_connectivity(np.asarray(v), f)
ffs = []
for i in range(v.size / 3):
nbrs = v[np.nonzero(np.asarray(cnct[i].todense()).ravel())[0]] - row(
v[i])
us = nbrs.dot(b2[i])
vs = nbrs.dot(b1[i])
hs = nbrs.dot(b0[i])
coeffs = Pinv(
hstack((col((us * .5)**2), col(us * vs), col(
(vs * .5)**2)))).dot(hs)
ffs.append(row(coeffs))
# if i == 3586:
# import pdb; pdb.set_trace()
ffs = vstack(ffs)
return ffs
def FirstEdgesMtx(v, f, want_big=True):
cnct = get_vert_connectivity((v.r if hasattr(v, 'r') else v), f)
nbrs = [np.nonzero(np.array(cnct[:,i].todense()))[0][0] for i in range(cnct.shape[1])]
JS = np.array(nbrs)
IS = np.arange(len(JS))
data = np.ones(IS.size)
if want_big:
IS = np.concatenate((IS*3, IS*3+1, IS*3+2))
JS = np.concatenate((JS*3, JS*3+1, JS*3+2))
data = np.concatenate((data, data, data))
return sp.csc_matrix((data, (IS, JS)), shape=(JS.size, JS.size))
def SecondFundamentalForm(v, f):
from chumpy import hstack, vstack
from chumpy.linalg import Pinv
nbrs = MatVecMult(FirstEdgesMtx(v, f, want_big=True), v.ravel()).reshape((-1,3))
b0 = NormalizedNx3(VertNormalsScaled(f=f, v=v)).reshape((-1,3))
b1 = NormalizedNx3(CrossProduct(b0, nbrs-v)).reshape((-1,3))
b2 = NormalizedNx3(CrossProduct(b0, b1)).reshape((-1,3))
cnct = get_vert_connectivity(v.r, f)
ffs = []
for i in range(v.size/3):
nbrs = v[np.nonzero(np.asarray(cnct[i].todense()).ravel())[0]] - row(v[i])
us = nbrs.dot(b2[i])
vs = nbrs.dot(b1[i])
hs = nbrs.dot(b0[i])
coeffs = Pinv(hstack((col((us*.5)**2), col(us*vs), col((vs*.5)**2)))).dot(hs)
ffs.append(row(coeffs))
# if i == 3586:
# import pdb; pdb.set_trace()
ffs = vstack(ffs)
return ffs