def getWDerivativeAt(self,u,v,w):
""" Compute point at (u,v,w) """
udeg = self.udegree
uspan = sg.NurbsCurve.findSpan(u,udeg,self.uknots)
Nu = sg.NurbsCurve.basisFunctions(uspan, u, udeg, self.uknots)
vdeg = self.vdegree
vspan = sg.NurbsCurve.findSpan(v,vdeg,self.vknots)
Nv = sg.NurbsCurve.basisFunctions(vspan, v, vdeg, self.vknots)
wdeg = self.wdegree
wspan = sg.NurbsCurve.findSpan(w,wdeg,self.wknots)
Nw = sg.NurbsCurve.derivatesBasisFunctions(1, w, wspan, wdeg, self.wknots)
tmp = [[None for i in range(vdeg+1)] for j in range(wdeg+1)]
for i in range(0,wdeg+1):
for j in range(0,vdeg+1):
tmpVec = Vector4(0,0,0,0)
for k in range(0,udeg+1):
tmpVec += self.points[uspan-udeg+k][vspan-vdeg+j][wspan-wdeg+i] * Nu[k]
tmp[i][j] = tmpVec
tmp2 = [None for i in range(self.wdegree+1)]
for i in range(0,wdeg+1):
tmpVec = Vector4(0,0,0,0)
for j in range(0,vdeg+1):
tmpVec += tmp[i][j] * Nv[j]
tmp2[i] = tmpVec
res = [Vector4() for i in range(2)]
for j in range(2):
for i in range(0,wdeg+1):
res[j] += tmp2[i] * Nw[j,i]
return res[1]
def setPoint(self, index, npoint):
crv = self.curve
pi = crv.ctrlPointList[index]
crv.ctrlPointList[index] = Vector4(npoint[0], npoint[1], pi[2], 1)
if self.profile is not None and \
crv is not None and \
self.position in self.profile:
self.profile[
self.position] = interpolated_profile.CrossSection(
*crv.ctrlPointList)
def getUPatch(self,u):
udeg = self.udegree
uspan = sg.NurbsCurve.findSpan(u,udeg,self.uknots)
Nu = sg.NurbsCurve.basisFunctions(uspan, u, udeg, self.uknots)
tmp = [[None for j in range(self.wdim)] for i in range(self.vdim)]
for i in range(0,self.vdim):
for j in range(0,self.wdim):
tmpVec = Vector4(0,0,0,0)
for k in range(0,udeg+1):
tmpVec += self.points[uspan-udeg+k][i][j] * Nu[k]
tmp[i][j] = tmpVec
return sg.NurbsPatch(tmp,self.vknots,self.wknots,self.vdegree,self.wdegree,self.vstride,self.wstride)
def getWPatch(self,w):
wdeg = self.wdegree
wspan = sg.NurbsCurve.findSpan(w,wdeg,self.wknots)
Nw = sg.NurbsCurve.basisFunctions(wspan, w, wdeg, self.wknots)
tmp = [[None for j in range(self.vdim)] for i in range(self.udim)]
for i in range(0,self.udim):
for j in range(0,self.vdim):
tmpVec = Vector4(0,0,0,0)
for k in range(0,wdeg+1):
tmpVec += self.points[i][j][wspan-wdeg+k] * Nw[k]
tmp[i][j] = tmpVec
return sg.NurbsPatch(tmp,self.uknots,self.vknots,self.udegree,self.vdegree,self.ustride,self.vstride)
def getPointAt(self, u, v, w):
""" Compute point at (u,v,w) """
udeg = self.udegree
uspan = sg.NurbsCurve.findSpan(u, udeg, self.uknots)
Nu = sg.NurbsCurve.basisFunctions(uspan, u, udeg, self.uknots)
vdeg = self.vdegree
vspan = sg.NurbsCurve.findSpan(v, vdeg, self.vknots)
Nv = sg.NurbsCurve.basisFunctions(vspan, v, vdeg, self.vknots)
wdeg = self.wdegree
wspan = sg.NurbsCurve.findSpan(w, wdeg, self.wknots)
Nw = sg.NurbsCurve.basisFunctions(wspan, w, wdeg, self.wknots)
tmp = [[None for i in xrange(vdeg + 1)] for j in xrange(wdeg + 1)]
for i in xrange(0, wdeg + 1):
for j in xrange(0, vdeg + 1):
tmpVec = Vector4(0, 0, 0, 0)
for k in xrange(0, udeg + 1):
tmpVec += self.points[uspan - udeg + k][vspan - vdeg +
j][wspan - wdeg +
i] * Nu[k]
tmp[i][j] = tmpVec
tmp2 = [None for i in xrange(wdeg + 1)]
for i in xrange(0, wdeg + 1):
tmpVec = Vector4(0, 0, 0, 0)
for j in xrange(0, vdeg + 1):
tmpVec += tmp[i][j] * Nv[j]
tmp2[i] = tmpVec
res = Vector4(0, 0, 0, 0)
for i in xrange(0, wdeg + 1):
res += tmp2[i] * Nw[i]
if res.w != 0:
return res.project()
else:
return Vector3(res.x, res.y, res.z)
def getVPatch(self,v):
vdeg = self.vdegree
vspan = sg.NurbsCurve.findSpan(v,vdeg,self.vknots)
Nv = sg.NurbsCurve.basisFunctions(vspan, v, vdeg, self.vknots)
tmp = [[None for j in range(self.wdim)] for i in range(self.udim)]
for i in range(0,self.udim):
for j in range(0,self.wdim):
tmpVec = Vector4(0,0,0,0)
for k in range(0,vdeg+1):
tmpVec += self.points[i][vspan-vdeg+k][j] * Nv[k]
tmp[i][j] = tmpVec
return sg.NurbsPatch(tmp,self.uknots,self.wknots,self.udegree,self.wdegree,self.ustride,self.wstride)
def cubic_bezier3D(ctrl_points, uniform=False, stride=60):
"""Construct a nurbs from a set of ctrl_points
ctrl_points are control points in space that
define a cubic bezier nurbs as proposed in svg norm
http://www.w3.org/TR/SVG/paths.html#PathDataCurveCommands
An arc `i` of the resulting curve will interpolate
points 4 * i, 4 * i +1, 4 * i + 2, 4 * i + 3.
:Parameters:
- `ctrl_points` (list of Vector) - a list
of control points
- `uniform` (bool) - if True, the parameterization
of the curve will be chosen such that each
segment will be of length 1 in u space, wathever
its real geometrical size.
- `stride` (int) - number of points to discretize
the curve
:Returns Type: :class:NurbsCurve
"""
degree = 3
ctrl_points = [Vector3(*vec) for vec in ctrl_points]
nb_pts = len(ctrl_points)
nb_arc = (nb_pts - 1) / degree
nb_knots = degree + nb_pts
p = 0.
param = [p]
for i in xrange(nb_arc):
if uniform:
p += 1
else:
p += norm(ctrl_points[degree * i] \
- ctrl_points[degree * (i + 1)])
param.append(p)
kv = [param[0]]
for p in param:
for j in xrange(degree):
kv.append(p)
kv.append(param[-1])
#curve
return NurbsCurve([Vector4(v, 1.) for v in ctrl_points], kv, degree,
stride)
def create_control_point(self, abscissa):
"""Inserts an interpolated control point
to every defining section at position = abscissa.
The abscissa is expressed in the get_abscissa_range() range.
"""
abscissa = self.normalised_abscissa(abscissa)
if abscissa == 1.0 or abscissa == 0.0:
return
if self.__patch:
rows = self.itervalues()
afterId = InterpolatedProfile.__find_index_in_polyline(
abscissa, self.itervalues().next(), is_abscissa=True)
beforeId = afterId - 1
ptPairs = [(c[afterId], c[beforeId]) for c in rows]
ptList = [ Vector4(abscissa, self.__lin_interpolation(abscissa, before, after), after[2], 1) \
for after, before in ptPairs ]
self.insert_column_before(afterId, ptList)
def __init__(self, *pointTuples):
list.__init__(self, (Vector4(x[0], x[1], -1., 1) for x in pointTuples))
