class Srf:
'''Construct a NURB surface structure, and check the format.
The NURB surface is represented by a 4 dimensional b-spline.
INPUT:
cntrl - Control points, homogeneous coordinates (wx,wy,wz,w)
For a surface [dim,nu,nv] matrix
where nu is along the u direction and
nv is along the v direction.
dim is the dimension valid options are:
2 .... (x,y) 2D cartesian coordinates
3 .... (x,y,z) 3D cartesian coordinates
4 .... (wx,wy,wz,w) 4D homogeneous coordinates
uknots - Knot sequence along the parametric u direction.
vknots - Knot sequence along the paramteric v direction.
NOTES:
Its assumed that the input knot sequences span the
interval [0.0,1.0] and are clamped to the control
points at the end by a knot multiplicity equal to
the spline order.'''
def __init__(self, cntrl, uknots, vknots):
self._bezier = None
cntrl = numerix.asarray(cntrl, numerix.Float)
(dim, nu, nv) = cntrl.shape
if dim < 2 or dim > 4:
raise NURBSError, 'Illegal control point format'
elif dim < 4:
self.cntrl = numerix.zeros((4, nu, nv), numerix.Float)
self.cntrl[0:dim, :, :] = cntrl
self.cntrl[-1, :, :] = numerix.ones((nu, nv), numerix.Float)
else:
self.cntrl = cntrl
# Force the u knot sequence to be a vector in ascending order
# and normalise between [0.0,1.0]
uknots = numerix.sort(numerix.asarray(uknots, numerix.Float))
nku = uknots.shape[0]
uknots = (uknots - uknots[0]) / (uknots[-1] - uknots[0])
if uknots[0] == uknots[-1]:
raise NURBSError, 'Illegal uknots sequence'
self.uknots = uknots
# Force the v knot sequence to be a vector in ascending order
# and normalise between [0.0,1.0]
vknots = -numerix.sort(-numerix.asarray(vknots, numerix.Float))
nkv = vknots.shape[0]
vknots = (vknots - vknots[0]) / (vknots[-1] - vknots[0])
if vknots[0] == vknots[-1]:
raise NURBSError, 'Illegal vknots sequence'
self.vknots = vknots
# Spline Degree
self.degree = [nku - nu - 1, nkv - nv - 1]
if self.degree[0] < 0 or self.degree[1] < 0:
raise NURBSError, 'NURBS order must be a positive integer'
def trans(self, mat):
"Apply the 4D transform matrix to the NURB control points."
for v in range(self.cntrl.shape[2]):
self.cntrl[:, :, v] = numerix.dot(mat, self.cntrl[:, :, v])
def swapuv(self):
"Swap u and v parameters."
self.cntrl = numerix.transpose(self.cntrl, (0, 2, 1))
temp = self.uknots[:]
self.uknots = self.vknots[:]
self.vknots = temp
udegree, vdegree = self.degree
self.degree[0] = vdegree
self.degree[1] = udegree
def reverse(self):
"Reverse evaluation directions."
coefs = self.cntrl[:, :, ::-1]
self.cntrl = coefs[:, ::-1, :]
self.uknots = 1. - self.uknots[::-1]
self.vknots = 1. - self.vknots[::-1]
def extractV(self, u):
"Extract curve in v-direction at parameter u."
if numerix.any(u < 0.) or numerix.any(u > 1.):
raise NURBSError, 'Out of parameter range [0,1]'
if u == 0.:
cntrl = self.cntrl[:, 0, :]
knots = self.vknots[:]
elif u == 1.:
cntrl = self.cntrl[:, -1, :]
knots = self.vknots[:]
else:
uknots = numerix.repeat(
numerix.asarray([u], numerix.Float),
[self.degree[1] * (self.cntrl.shape[2] + 1)])
coefs = numerix.transpose(self.cntrl, (0, 2, 1))
coefs = numerix.resize(
coefs, (4 * self.cntrl.shape[2], self.cntrl.shape[1]))
coefs, knots = bspkntins(self.degree[0], coefs, self.uknots,
uknots)
coefs = numerix.resize(coefs,
(4, self.cntrl.shape[2], coefs.shape[1]))
cntrl = numerix.transpose(coefs, (0, 2, 1))
i = 0
j = knots[0]
for k in knots[1:]:
if k == u:
break
elif k != j:
i += 1
j = k
return Crv.Crv(cntrl[:, i, :], self.vknots[:])
def extractU(self, v):
"Extract curve in u-direction at parameter v."
if numerix.any(v < 0.) or numerix.any(v > 1.):
raise NURBSError, 'Out of parameter range [0,1]'
if v == 0.:
cntrl = self.cntrl[:, :, 0]
knots = self.uknots[:]
elif v == 1.:
cntrl = self.cntrl[:, :, -1]
knots = self.uknots[:]
else:
vknots = numerix.repeat(
numerix.asarray([v], numerix.Float),
[self.degree[0] * (self.cntrl.shape[1] + 1)])
coefs = numerix.resize(
self.cntrl, (4 * self.cntrl.shape[1], self.cntrl.shape[2]))
coefs, knots = bspkntins(self.degree[1], coefs, self.vknots,
vknots)
cntrl = numerix.resize(coefs,
(4, self.cntrl.shape[1], coefs.shape[1]))
i = 0
j = knots[0]
for k in knots[1:]:
if k == v:
break
elif k != j:
i += 1
j = k
return Crv.Crv(cntrl[:, :, i], self.uknots[:])
def kntins(self, uknots, vknots=None):
"""Insert new knots into the surface
uknots - knots to be inserted along u direction
vknots - knots to be inserted along v direction
NOTE: No knot multiplicity will be increased beyond the order of the spline"""
if len(vknots):
# Force the v knot sequence to be a vector in ascending order
vknots = numerix.sort(numerix.asarray(vknots, numerix.Float))
if numerix.any(vknots < 0.) or numerix.any(vknots > 1.):
raise NURBSError, 'Illegal vknots sequence'
coefs = numerix.resize(
self.cntrl, (4 * self.cntrl.shape[1], self.cntrl.shape[2]))
coefs, self.vknots = bspkntins(self.degree[1], coefs, self.vknots,
vknots)
self.cntrl = numerix.resize(
coefs, (4, self.cntrl.shape[1], coefs.shape[1]))
if len(uknots):
# Force the u knot sequence to be a vector in ascending order
uknots = numerix.sort(numerix.asarray(uknots, numerix.Float))
if numerix.any(uknots < 0.) or numerix.any(uknots > 1.):
raise NURBSError, 'Illegal uknots sequence'
coefs = numerix.transpose(self.cntrl, (0, 2, 1))
coefs = numerix.resize(
coefs, (4 * self.cntrl.shape[2], self.cntrl.shape[1]))
coefs, self.uknots = bspkntins(self.degree[0], coefs, self.uknots,
uknots)
coefs = numerix.resize(coefs,
(4, self.cntrl.shape[2], coefs.shape[1]))
self.cntrl = numerix.transpose(coefs, (0, 2, 1))
def degelev(self, utimes, vtimes=None):
"""Degree elevate the surface.
utimes - degree elevate utimes along u direction.
vtimes - degree elevate vtimes along v direction."""
if vtimes:
if vtimes < 0:
raise NURBSError, 'Degree must be positive'
coefs = numerix.resize(
self.cntrl, (4 * self.cntrl.shape[1], self.cntrl.shape[2]))
coefs, vknots, nh = bspdegelev(self.degree[1], coefs, self.vknots,
vtimes)
coefs = coefs[:, :nh + 1]
self.vknots = vknots[:nh + self.degree[1] + vtimes + 2]
self.degree[1] += vtimes
self.cntrl = numerix.resize(
coefs, (4, self.cntrl.shape[1], coefs.shape[1]))
if utimes:
if utimes < 0:
raise NURBSError, 'Degree must be positive'
coefs = numerix.transpose(self.cntrl, (0, 2, 1))
coefs = numerix.resize(
coefs, (4 * self.cntrl.shape[2], self.cntrl.shape[1]))
coefs, uknots, nh = bspdegelev(self.degree[0], coefs, self.uknots,
utimes)
coefs = coefs[:, :nh + 1]
self.uknots = uknots[:nh + self.degree[0] + utimes + 2]
self.degree[0] += utimes
coefs = numerix.resize(coefs,
(4, self.cntrl.shape[2], coefs.shape[1]))
self.cntrl = numerix.transpose(coefs, (0, 2, 1))
def bezier(self, update=None):
"Decompose surface to bezier patches and return overlaping control points."
if update or not self._bezier:
cntrl = numerix.resize(
self.cntrl, (4 * self.cntrl.shape[1], self.cntrl.shape[2]))
cntrl = bspbezdecom(self.degree[1], cntrl, self.vknots)
cntrl = numerix.resize(cntrl,
(4, self.cntrl.shape[1], cntrl.shape[1]))
temp1 = cntrl.shape[1]
temp2 = cntrl.shape[2]
cntrl = numerix.transpose(cntrl, (0, 2, 1))
cntrl = numerix.resize(cntrl, (4 * temp2, temp1))
cntrl = bspbezdecom(self.degree[0], cntrl, self.uknots)
cntrl = numerix.resize(cntrl, (4, temp2, cntrl.shape[1]))
self._bezier = numerix.transpose(cntrl, (0, 2, 1))
return self._bezier
def bounds(self):
"Return the bounding box for the surface."
w = self.cntrl[3, :, :]
cx = numerix.sort(numerix.ravel(self.cntrl[0, :, :] / w))
cy = numerix.sort(numerix.ravel(self.cntrl[1, :, :] / w))
cz = numerix.sort(numerix.ravel(self.cntrl[2, :, :] / w))
return numerix.asarray([cx[0], cy[0], cz[0], cx[-1], cy[-1], cz[-1]],
numerix.Float)
def pnt3D(self, ut, vt=None):
"""Evaluate parametric point[s] and return 3D cartesian coordinate[s]
If only ut is given then we will evaluate at scattered points.
ut(0,:) represents the u direction.
ut(1,:) represents the v direction.
If both parameters are given then we will evaluate over a [u,v] grid."""
val = self.pnt4D(ut, vt)
if len(val.shape) < 3:
return val[0:3, :] / numerix.resize(val[-1, :], (3, val.shape[1]))
else: #FIX!
return val[0:3, :, :] / numerix.resize(
val[-1, :, :], (3, val.shape[1], val.shape[2]))
def pnt4D(self, ut, vt=None):
"""Evaluate parametric point[s] and return 4D homogeneous coordinates.
If only ut is given then we will evaluate at scattered points.
ut(0,:) represents the u direction.
ut(1,:) represents the v direction.
If both parameters are given then we will evaluate over a [u,v] grid."""
ut = numerix.asarray(ut, numerix.Float)
if numerix.any(ut < 0.) or numerix.any(ut > 1.):
raise NURBSError, 'NURBS curve parameter out of range [0,1]'
if vt: #FIX!
# Evaluate over a [u,v] grid
vt = numerix.asarray(vt, numerix.Float)
if numerix.any(vt < 0.) or numerix.any(vt > 1.):
raise NURBSError, 'NURBS curve parameter out of range [0,1]'
val = numerix.resize(
self.cntrl, (4 * self.cntrl.shape[1], self.cntrl.shape[2]))
val = bspeval(self.degree[1], val, self.vknots, vt)
val = numerix.resize(val, (4, self.cntrl.shape[1], vt.shape[0]))
val = numerix.transpose(val, (0, 2, 1))
val = numerix.resize(self.cntrl,
(4 * vt.shape[0], self.cntrl.shape[1]))
val = bspeval(self.degree[0], val, self.uknots, ut)
val = numerix.resize(val, (4, vt.shape[0], ut.shape[0]))
return numerix.transpose(val, (0, 2, 1))
# Evaluate at scattered points
nt = ut.shape[1]
uval = numerix.resize(self.cntrl,
(4 * self.cntrl.shape[1], self.cntrl.shape[2]))
uval = bspeval(self.degree[1], uval, self.vknots, ut[1, :])
uval = numerix.resize(uval, (4, self.cntrl.shape[1], nt))
val = numerix.zeros((4, nt), numerix.Float)
for v in range(nt):
val[:, v] = bspeval(
self.degree[0],
numerix.resize(uval[:, :, v], (4, self.cntrl.shape[1])),
self.uknots, (ut[0, v], ))[:, 0]
return val
def plot(self, n=50, iso=8):
"""A simple plotting function based on dislin for debugging purpose.
n = number of subdivisions. iso = number of iso line to plot in each dir.
TODO: plot ctrl poins and knots."""
try:
import dislin
except ImportError, value:
print 'dislin plotting library not available'
return
maxminx = numerix.sort(
numerix.ravel(self.cntrl[0, :, :]) /
numerix.ravel(self.cntrl[3, :, :]))
minx = maxminx[0]
maxx = maxminx[-1]
if minx == maxx:
minx -= 1.
maxx += 1.
maxminy = numerix.sort(
numerix.ravel(self.cntrl[1, :, :]) /
numerix.ravel(self.cntrl[3, :, :]))
miny = maxminy[0]
maxy = maxminy[-1]
if miny == maxy:
miny -= 1.
maxy += 1.
maxminz = numerix.sort(
numerix.ravel(self.cntrl[2, :, :]) /
numerix.ravel(self.cntrl[3, :, :]))
minz = maxminz[0]
maxz = maxminz[-1]
if minz == maxz:
minz -= 1.
maxz += 1.
dislin.metafl('cons')
dislin.disini()
dislin.hwfont()
dislin.pagera()
dislin.name('X-axis', 'X')
dislin.name('Y-axis', 'Y')
dislin.name('Z-axis', 'Z')
dislin.graf3d(minx, maxx, 0, abs((maxx - minx) / 4.), miny, maxy, 0,
abs((maxy - miny) / 4.), minz, maxz, 0,
abs((maxz - minz) / 4.))
dislin.color('yellow')
pnts0 = self.pnt3D([
numerix.arange(n + 1, typecode=numerix.Float) / n,
numerix.zeros(n + 1, numerix.Float)
])
pnts1 = self.pnt3D([
numerix.arange(n + 1, typecode=numerix.Float) / n,
numerix.ones(n + 1, numerix.Float)
])
pnts2 = self.pnt3D([
numerix.zeros(n + 1, numerix.Float),
numerix.arange(n + 1, typecode=numerix.Float) / n
])
pnts3 = self.pnt3D([
numerix.ones(n + 1, numerix.Float),
numerix.arange(n + 1, typecode=numerix.Float) / n
])
dislin.curv3d(pnts0[0, :], pnts0[1, :], pnts0[2, :], n + 1)
dislin.curv3d(pnts1[0, :], pnts1[1, :], pnts1[2, :], n + 1)
dislin.curv3d(pnts2[0, :], pnts2[1, :], pnts2[2, :], n + 1)
dislin.curv3d(pnts3[0, :], pnts3[1, :], pnts3[2, :], n + 1)
dislin.color('red')
step = 1. / iso
for uv in numerix.arange(step, 1., step):
pnts = self.pnt3D([
numerix.arange(n + 1, typecode=numerix.Float) / n,
numerix.zeros(n + 1, numerix.Float) + uv
])
dislin.curv3d(pnts[0, :], pnts[1, :], pnts[2, :], n + 1)
pnts = self.pnt3D([
numerix.zeros(n + 1, numerix.Float) + uv,
numerix.arange(n + 1, typecode=numerix.Float) / n
])
dislin.curv3d(pnts[0, :], pnts[1, :], pnts[2, :], n + 1)
dislin.disfin()
#!/usr/bin/env python
import dislin
ctit = 'Symbols'
dislin.setpag('da4p')
dislin.metafl('cons')
dislin.disini()
dislin.pagera()
dislin.complx()
dislin.paghdr('H. Michels (', ')', 2, 0)
dislin.height(60)
nl = dislin.nlmess(ctit)
dislin.messag(ctit, (2100 - nl) / 2, 200)
dislin.height(50)
dislin.hsymbl(120)
ny = 150
for i in range(0, 22):
if (i % 4) == 0:
ny = ny + 400
nxp = 550
else:
nxp = nxp + 350
nl = dislin.nlnumb(i, -1)
dislin.number(i, -1, nxp - nl / 2, ny + 150)
class Crv:
'''Construct a NURB curve and check the format.
The NURB curve is represented by a 4 dimensional b-spline.
INPUT:
cntrl - Control points, homogeneous coordinates (wx,wy,wz,w)
[dim,nu] matrix
dim is the dimension valid options are:
2 .... (x,y) 2D cartesian coordinates
3 .... (x,y,z) 3D cartesian coordinates
4 .... (wx,wy,wz,w) 4D homogeneous coordinates
uknots - Knot sequence along the parametric u direction.
NOTES:
Its assumed that the input knot sequences span the
interval [0.0,1.0] and are clamped to the control
points at the end by a knot multiplicity equal to
the spline order.'''
def __init__(self, cntrl, uknots):
self._bezier = None
# Force the u knot sequence to be a vector in ascending order
# and normalise between [0.0,1.0]
uknots = np.sort(np.asarray(uknots, np.float))
nku = uknots.shape[0]
uknots = (uknots - uknots[0])/(uknots[-1] - uknots[0])
if uknots[0] == uknots[-1]:
raise NURBSError, 'Illegal uknots sequence'
self.uknots = uknots
cntrl = np.asarray(cntrl, np.float)
(dim, nu) = cntrl.shape
if dim < 2 or dim > 4:
raise NURBSError, 'Illegal control point format'
elif dim < 4:
self.cntrl = np.zeros((4, nu), np.float)
self.cntrl[0:dim,:] = cntrl
self.cntrl[-1,:] = np.ones((nu,))
else:
self.cntrl = cntrl
# Spline degree
self.degree = nku - nu - 1
if self.degree < 0:
raise NURBSError, 'NURBS order must be a positive integer'
def trans(self, mat):
"Apply the 4D transform matrix to the NURB control points."
self.cntrl = np.dot(mat, self.cntrl)
def reverse(self):
"Reverse evaluation direction"
self.cntrl = self.cntrl[:,::-1]
self.uknots = 1 - self.uknots[::-1]
def kntins(self, uknots):
"""Insert new knots into the curve
NOTE: No knot multiplicity will be increased beyond the order of the spline"""
if len(uknots):
uknots = np.sort(np.asarray(uknots, np.float))
if np.less(uknots, 0.) or np.greater(uknots, 1.):
raise NURBSError, 'NURBS curve parameter out of range [0,1]'
self.cntrl, self.uknots = bspkntins(self.degree, self.cntrl, self.uknots, uknots)
def degelev(self, degree):
"Degree elevate the curve"
if degree < 0:
raise NURBSError, 'degree must be a positive number'
if degree > 0:
cntrl, uknots, nh = bspdegelev(self.degree, self.cntrl, self.uknots, degree)
self.cntrl = cntrl[:,:nh + 1]
self.uknots = uknots[:nh + self.degree + degree + 2]
self.degree += degree
def bezier(self, update = None):
"Decompose curve to bezier segments and return overlaping control points"
if update or not self._bezier:
self._bezier = bspbezdecom(self.degree, self.cntrl, self.uknots)
return self._bezier
def bounds(self):
"Return the boundingbox for the curve"
ww = np.resize(self.cntrl[-1,:], (3, self.cntrl.shape[1]))
cntrl = np.sort(self.cntrl[0:3,:]/ww)
return np.asarray([cntrl[0,0], cntrl[1,0], cntrl[2,0],
cntrl[0,-1], cntrl[1,-1], cntrl[2,-1]], np.float)
def pnt3D(self, ut):
"Evaluate parametric point[s] and return 3D cartesian coordinate[s]"
val = self.pnt4D(ut)
return val[0:3,:]/np.resize(val[-1,:], (3, val.shape[1]))
def pnt4D(self, ut):
"Evaluate parametric point[s] and return 4D homogeneous coordinates"
ut = np.asarray(ut, np.float)
if np.less(ut, 0.) or np.greater(ut, 1.):
raise NURBSError, 'NURBS curve parameter out of range [0,1]'
return bspeval(self.degree, self.cntrl, self.uknots, ut)
def plot(self, n = 25):
"""A simple plotting function for debugging purpose
n = number of subdivisions.
Depends on the dislin plotting library."""
try:
import dislin
except ImportError, value:
print 'dislin plotting library not available'
return
pnts = self.pnt3D(np.arange(n + 1, typecode = np.float)/n)
knots = self.pnt3D(self.uknots)
maxminx = np.sort(self.cntrl[0,:]/self.cntrl[3,:])
minx = maxminx[0]
maxx = maxminx[-1]
if minx == maxx:
minx -= 1.
maxx += 1.
maxminy = np.sort(self.cntrl[1,:]/self.cntrl[3,:])
miny = maxminy[0]
maxy = maxminy[-1]
if miny == maxy:
miny -= 1.
maxy += 1.
maxminz = np.sort(self.cntrl[2,:]/self.cntrl[3,:])
minz = maxminz[0]
maxz = maxminz[-1]
if minz == maxz:
minz -= 1.
maxz += 1.
dislin.metafl('cons')
dislin.disini()
dislin.hwfont()
dislin.pagera()
dislin.name('X-axis', 'X')
dislin.name('Y-axis', 'Y')
dislin.name('Z-axis', 'Z')
dislin.graf3d(minx, maxx, 0 , abs((maxx-minx)/4.),
miny, maxy, 0 , abs((maxy-miny)/4.),
minz, maxz, 0 , abs((maxz-minz)/4.))
dislin.color('yellow')
dislin.curv3d(pnts[0,:], pnts[1,:], pnts[2,:], n+1)
dislin.color('red')
dislin.dashm()
dislin.curv3d(self.cntrl[0,:]/self.cntrl[3,:], self.cntrl[1,:]/self.cntrl[3,:],
self.cntrl[2,:]/self.cntrl[3,:], self.cntrl.shape[1])
dislin.color('white')
dislin.incmrk(-1)
dislin.marker(8)
dislin.curv3d(knots[0,:], knots[1,:], knots[2,:], knots.shape[1])
dislin.disfin()