def create_spb(bbox, coors, degree=3, nsg=None):
bbox = nm.array(bbox)
coors = nm.array(coors)
dim = coors.shape[1]
spbox = []
if nsg is None:
nsg = nm.ones((dim,), dtype=nm.int)
else:
nsg = nm.array(nsg)
ncpoints = 1
spbox = {'base': [None] * dim, 'uidx': [None] * dim,
'cp': [None] * dim, 'ncp': [None] * dim,
'cp_idx': [None] * dim}
for idim in range(dim):
ucoors, ucoors_idx = nm.unique(coors[:,idim], return_inverse=True)
ncp = degree + nsg[idim]
bspl = BSpline(degree, ncp=ncp)
bspl.make_knot_vector(knot_range=(bbox[idim,0], bbox[idim,1]))
knots = bspl.get_knot_vector()
cp = nm.zeros((ncp,), dtype=nm.double)
for j in range(cp.shape[0]):
cp[j] = nm.sum(knots[(j + 1):(j + degree + 1)]) / degree
spbox['base'][idim] = bspl.eval_basis(t=ucoors,
return_val=True).copy()
spbox['uidx'][idim] = ucoors_idx[:]
spbox['cp'][idim] = cp[:]
spbox['ncp'][idim] = ncp
ncpoints *= ncp
cpoints = nm.zeros((ncpoints, dim), dtype=nm.double)
ncp = spbox['ncp']
cp = spbox['cp']
if dim == 2:
idxs = nm.mgrid[0:ncp[0],0:ncp[1]]
elif dim == 3:
idxs = nm.mgrid[0:ncp[0],0:ncp[1],0:ncp[2]]
aux = [1]
for ii in range(dim - 1):
aux.append(aux[ii] * ncp[ii])
spbox['mul_cp_idx'] = nm.array(aux)
for ii in range(dim):
spbox['cp_idx'][ii] = idxs[ii].reshape(ncpoints, order='F')
cpoints[:,ii] = cp[ii][spbox['cp_idx'][ii]]
return spbox, cpoints
def create_spb(spl_bnd, coors, rho=10):
"""
Initialize SplineBox knots, control points, base functions, ...
"""
dim = 2
if coors.shape[1] != dim:
print 'Only 2D SplineBoxSBnd is supported!'
raise (ValueError)
bnd_poly = []
bnd_cp = []
for s in spl_bnd:
s.set_param_n(rho)
bnd_poly.append(s.eval()[:-1])
bnd_cp.append(s.get_control_points()[:-1, :])
bnd_poly.append(bnd_poly[0][0, :])
ncpoints = 1
base, bspl, uidx, ncp = [], [], [], []
for idim, si in enumerate([0, 1]):
s = spl_bnd[si]
bspl0 = BSpline(s.degree, ncp=s.ncp)
bspl0.set_knot_vector(s.knots)
bspl.append(bspl0)
base.append(None)
uidx.append(None)
ncp.append(s.ncp)
ncpoints *= s.ncp
cp_idx, mul_cp_idx = SplineBox.gen_cp_idxs(ncp)
cpoints = SplineRegion2D.define_control_points(nm.vstack(bnd_cp), ncp)
idxs_inside = SplineRegion2D.points_in_poly(coors, nm.vstack(bnd_poly))
return {
'base': base,
'bspl': bspl,
'uidx': uidx,
'ncp': ncp,
'cp_idx': cp_idx,
'mul_cp_idx': mul_cp_idx,
'control_points': cpoints,
'idxs_inside': idxs_inside
}
def create_spb(bbox, coors, degree=3, nsg=None):
nc, dim = coors.shape
inside = nm.ones((nc, ), dtype=nm.bool)
nsg = nm.ones((dim, ), dtype=nm.int) if nsg is None else nm.array(nsg)
for idim in range(dim):
inrange = nm.logical_and(coors[:, idim] >= bbox[idim][0],
coors[:, idim] <= bbox[idim][1])
inside = nm.logical_and(inside, inrange)
ncpoints = 1
base, uidx, ncp, cp = [], [], [], []
for idim in range(dim):
ucoors, ucoors_idx = nm.unique(coors[inside, idim],
return_inverse=True)
ncp0 = degree + nsg[idim]
bspl = BSpline(degree, ncp=ncp0)
bspl.make_knot_vector(knot_range=(bbox[idim][0], bbox[idim][1]))
knots = bspl.get_knot_vector()
cp0 = nm.zeros((ncp0, ), dtype=nm.double)
for j in range(cp0.shape[0]):
cp0[j] = nm.sum(knots[(j + 1):(j + degree + 1)]) / degree
base.append(bspl.eval_basis(t=ucoors, return_val=True))
uidx.append(ucoors_idx)
ncp.append(ncp0)
cp.append(cp0)
ncpoints *= ncp0
cpoints = nm.zeros((ncpoints, dim), dtype=nm.double)
cp_idx, mul_cp_idx = SplineBox.gen_cp_idxs(ncp)
for ii in range(dim):
cpoints[:, ii] = cp[ii][cp_idx[ii]]
return {
'base': base,
'uidx': uidx,
'ncp': ncp,
'cp_idx': cp_idx,
'mul_cp_idx': mul_cp_idx,
'control_points': cpoints,
'idxs_inside': inside
}
from bspline import BSpline
from display import display
if __name__ == "__main__":
# 2d
b = BSpline([[2, 5], [3, 4], [5, 7], [1, 2], [1, 8], [7, 5]])
display(b)
# 3d
b = BSpline([[2, 5, 5], [3, 4, 3], [5, 7, 4], [1, 2, 2], [1, 8, 3], [7, 5, 2]])
display(b)
# Surface
splines = [BSpline([[2, i, 5], [5, i, 4], [1, i, 2], [7, i, 2]]) for i in range(-5, 5)]
display(splines)
