def get_geometry(self):
if self.mode == 'CURVE':
curves = self.inputs['Curves'].sv_get()
if isinstance(curves[0], (list, tuple)):
curves = sum(curves, [])
container = multi.CurveContainer()
for i, curve in enumerate(curves):
if not isinstance(curve, SvNurbsCurve):
if hasattr(curve, 'to_nurbs'):
curve = curve.to_nurbs(
implementation=SvNurbsCurve.GEOMDL)
else:
raise TypeError(
"Provided object #%s is not a NURBS curve, but %s!"
% (i, type(curve)))
container.append(SvGeomdlCurve.from_any_nurbs(curve).curve)
return container
else: # SURFACE
surfaces = self.inputs['Surfaces'].sv_get()
if isinstance(surfaces[0], (list, tuple)):
surfaces = sum(surfaces, [])
container = multi.SurfaceContainer()
for i, surface in enumerate(surfaces):
if not isinstance(surface, SvNurbsSurface):
if hasattr(surface, 'to_nurbs'):
surface = surface.to_nurbs(
implementation=SvNurbsCurve.GEOMDL)
else:
raise TypeError(
"Provided object #%s is not a NURBS surface, but %s!"
% (i, type(surface)))
container.append(
SvGeomdlSurface.from_any_nurbs(surface).surface)
return container
def test_deriv_curve_fig(bspline_curve2d):
fname = "test-derivative_curve.png"
data = operations.derivative_curve(bspline_curve2d)
multi_shape = multi.CurveContainer(data)
multi_shape.vis = VisMPL.VisCurve2D()
multi_shape.render(filename=fname, plot=False)
assert os.path.isfile(fname)
assert os.path.getsize(fname) > 0
# Clean up temporary file if exists
if os.path.isfile(fname):
os.remove(fname)
def test_curve3d_multi_fig_nowindow(bspline_curve3d):
conf = VisMPL.VisConfig()
vis = VisMPL.VisCurve3D(config=conf)
data = operations.decompose_curve(bspline_curve3d)
multi_shape = multi.CurveContainer(data)
multi_shape.vis = vis
multi_shape.render(plot=False)
assert os.path.isfile(conf.figure_image_filename)
assert os.path.getsize(conf.figure_image_filename) > 0
# Clean up temporary file if exists
if os.path.isfile(conf.figure_image_filename):
os.remove(conf.figure_image_filename)
def test_curve3d_multi_fig_save(bspline_curve3d):
conf = VisMPL.VisConfig()
vis = VisMPL.VisCurve3D(config=conf)
fname = "test-multi_curve.png"
data = operations.decompose_curve(bspline_curve3d)
multi_shape = multi.CurveContainer(data)
multi_shape.vis = vis
multi_shape.render(filename=fname, plot=False)
assert os.path.isfile(fname)
assert os.path.getsize(fname) > 0
# Clean up temporary file if exists
if os.path.isfile(fname):
os.remove(fname)
def get_geometry(self):
if self.mode == 'CURVE':
curves = self.inputs['Curves'].sv_get()
if isinstance(curves[0], (list, tuple)):
curves = sum(curves, [])
container = multi.CurveContainer()
for i, curve in enumerate(curves):
if not isinstance(curve, SvExGeomdlCurve):
raise TypeError("Provided object #%s is not a NURBS curve, but %s!" % (i, type(curve)))
container.append(curve.curve)
return container
else: # SURFACE
surfaces = self.inputs['Surfaces'].sv_get()
if isinstance(surfaces[0], (list, tuple)):
surfaces = sum(surfaces, [])
container = multi.SurfaceContainer()
for i, surface in enumerate(surfaces):
if not isinstance(surface, SvExGeomdlSurface):
raise TypeError("Provided object #%s is not a NURBS surface, but %s!" % (i, type(surface)))
container.append(surface.surface)
return container
def generate_nurbs_from_file(file_name, delta, shape_idx, file_type=''):
"""Generates NURBS objects from supported file formats"""
# Fix input types
delta = float(delta)
shape_idx = int(shape_idx)
# Try to find file type from its extension
if not file_type:
fname, fext = os.path.splitext(file_name)
file_type = fext[1:]
ftype = file_type.lower()
if ftype in CLI_FILE_IMPORT_TYPES:
# Build NURBS object
nurbs_objs = CLI_FILE_IMPORT_TYPES[ftype](file_name,
delta=delta,
jinja2=True)
# Return the shape
if len(nurbs_objs) == 1:
return nurbs_objs[0]
if isinstance(nurbs_objs[0], NURBS.Curve):
result = multi.CurveContainer(nurbs_objs)
elif isinstance(nurbs_objs[0], NURBS.Surface):
result = multi.SurfaceContainer(nurbs_objs)
else:
result = multi.VolumeContainer(nurbs_objs)
# Set the delta for multi shape objects
if 0.0 < delta < 1.0:
result.delta = delta
if shape_idx >= 0:
return result[shape_idx]
return result
else:
raise RuntimeError("The input file type '" + str(file_type) +
"' is not supported")
# Fix file path
os.chdir(os.path.dirname(os.path.realpath(__file__)))
# Create a BSpline curve instance
curve = BSpline.Curve()
# Set degree
curve.degree = 3
# Read control points from a file
curve.ctrlpts = exchange.import_txt("ex_curve03.cpt")
# Set knot vector
curve.knotvector = [0, 0, 0, 0, 0.25, 0.25, 0.5, 0.75, 0.75, 1, 1, 1, 1]
# Decompose the curve
curve_list = operations.decompose_curve(curve)
curve_decomposed = multi.CurveContainer(curve_list)
# Set sample size for the decomposed curve
curve_decomposed.sample_size = 25
# Plot the decomposed curve
vis_comp = vis.VisCurve2D()
curve_decomposed.vis = vis_comp
curve_decomposed.render()
# Good to have something here to put a breakpoint
pass
from geomdl import operations
from geomdl import multi
from geomdl.visualization import VisMPL
# Fix file path
os.chdir(os.path.dirname(os.path.realpath(__file__)))
# Create a B-Spline curve instance
curve = BSpline.Curve()
# Set up the curve
curve.degree = 4
curve.ctrlpts = exchange.import_txt("ex_curve01.cpt")
# Auto-generate knot vector
curve.knotvector = utilities.generate_knot_vector(curve.degree, len(curve.ctrlpts))
# Decompose the curve into Bezier curve segments
bezier_curves = operations.decompose_curve(curve)
bezier = multi.CurveContainer(bezier_curves)
# Plot the curves using the curve container
bezier.sample_size = 40
vis_comp = VisMPL.VisCurve2D()
bezier.vis = vis_comp
bezier.render()
# Good to have something here to put a breakpoint
pass
def get_cm_from_interpolation_length(pts, interpolation_factor, center_circle,
radius): # 0 is circ
center = center_circle
cm = multi.CurveContainer()
cm.vis = VisMPL.VisCurve2D(axes=False,
labels=False,
ctrlpts=False,
legend=False)
circle_length = 2 * math.pi * radius
tangents = []
curve_lengths = []
for i in range(len(pts)):
p1 = pts[(i - 1) % len(pts)]
p2 = pts[(i + 1) % len(pts)]
pr = (p2[0] - p1[0], p2[1] - p1[1])
alpha = math.atan2(pr[1], pr[0]) % math.pi
tangents.append(alpha)
dists = []
for i in range(len(pts)):
dist = functions.euclid_dist(pts[i], pts[(i + 1) % len(pts)])
d = dist * 0.25
dists.append(d)
for i in range(len(pts)):
c = BSpline.Curve()
c.degree = 3
d = dists[i]
p1, p2 = get_points_on_tangent(pts[i], tangents[i], d)
if functions.euclid_dist(
p1, pts[(i + 1) % len(pts)]) < functions.euclid_dist(
p2, pts[(i + 1) % len(pts)]):
p2, p1 = p1, p2
p3, p4 = get_points_on_tangent(pts[(i + 1) % len(pts)],
tangents[(i + 1) % len(pts)], d)
if functions.euclid_dist(p4, pts[i]) < functions.euclid_dist(
p3, pts[i]):
p4, p3 = p3, p4
c.ctrlpts = [pts[i], p2, p3, pts[(i + 1) % len(pts)]]
c.knotvector = [0, 0, 0, 0, 1, 1, 1, 1]
length = get_curve_length(c)
curve_lengths.append(length)
cm.add(c)
curve_lengths.reverse()
xc, yc = center_circle
pts_r = list(pts)
pts_r.reverse()
distance_factor = circle_length / sum(curve_lengths)
pts_interpolated = []
starting_point = functions.project_to_circle(pts[0], center_circle, radius)
pts_interpolated.append(starting_point)
starting_angle = math.atan2(starting_point[1] - yc, starting_point[0] - xc)
alpha = curve_lengths[0] * distance_factor / radius
xp = xc + radius * math.cos(alpha)
yp = yc + radius * math.sin(alpha)
angle_sum = starting_angle
for i in range(len(pts) - 1):
alpha = curve_lengths[i] * distance_factor / radius
angle_sum += alpha
xp = xc + radius * math.cos(angle_sum)
yp = yc + radius * math.sin(angle_sum)
pts_interpolated.append((xp, yp))
pts_interpolated.reverse()
pts_interpolated.insert(0, pts_interpolated.pop())
tangents_interpolated = []
for i in range(len(pts_interpolated)):
x, y = pts_interpolated[i]
alpha = math.atan2(y - center_circle[1], x - center_circle[0])
alpha -= 0.5 * math.pi
alpha = alpha % math.pi
tangents_interpolated.append(alpha)
dists_interpolated = []
for i in range(len(pts_interpolated)):
x1, y1 = pts_interpolated[i]
x4, y4 = pts_interpolated[(i + 1) % len(pts_interpolated)]
xc, yc = center_circle
axx = x1 - xc
ay = y1 - yc
bx = x4 - xc
by = y4 - yc
q1 = axx * axx + ay * ay
q2 = q1 + axx * bx + ay * by
k2 = 4 / 3 * (math.sqrt(2 * q1 * q2) - q2) / (axx * by - ay * bx)
d = math.sqrt((k2 * ay)**2 + (k2 * axx)**2)
dists_interpolated.append(d)
cm = multi.CurveContainer()
cm.vis = VisMPL.VisCurve2D(axes=False,
labels=False,
ctrlpts=False,
legend=False)
pts = [[
interpolation_factor * pp[0] + (1 - interpolation_factor) * pc[0],
interpolation_factor * pp[1] + (1 - interpolation_factor) * pc[1]
] for (pp, pc) in zip(pts, pts_interpolated)]
new_tangents = []
for tp, tc in zip(tangents, tangents_interpolated):
if abs(tp - tc) > math.pi / 2:
if tp < math.pi / 2:
t = interpolation_factor * (tp + math.pi) + (
1 - interpolation_factor) * tc
elif tc < math.pi / 2:
t = interpolation_factor * tp + (1 - interpolation_factor) * (
tc + math.pi)
else:
t = interpolation_factor * tp + (1 - interpolation_factor) * tc
new_tangents.append(t)
tangents = new_tangents
dists = [
interpolation_factor * dp + (1 - interpolation_factor) * dc
for (dp, dc) in zip(dists, dists_interpolated)
]
angle_mapping = {}
ctrlpts = []
for i in range(len(pts)):
c = BSpline.Curve()
c.degree = 3
d = dists[i]
p1, p2 = get_points_on_tangent(pts[i], tangents[i], d)
if i == 0:
print(tangents[i])
if p1[1] < p2[1] and tangents[i] < math.pi:
p1, p2 = p2, p1
elif p1[1] > p2[1] and tangents[i] > math.pi:
p1, p2 = p2, p1
else:
if math.atan2(p1[1] - center[1], p1[0] - center[0]) < math.atan2(
p2[1] - center[1], p2[0] - center[0]):
p1, p2 = p2, p1
if functions.euclid_dist(
p1, pts[(i + 1) % len(pts)]) < functions.euclid_dist(
p2, pts[(i + 1) % len(pts)]):
p2, p1 = p1, p2
xp, yp = pts[i]
if (xp, yp) in angle_mapping:
p = angle_mapping[(xp, yp)]
if p[0] > xp and p2[0] > xp or p[0] < xp and p2[0] < xp:
p1, p2 = p2, p1
angle_mapping[(xp, yp)] = p2
p3, p4 = get_points_on_tangent(pts[(i + 1) % len(pts)],
tangents[(i + 1) % len(pts)], d)
if functions.euclid_dist(p4, pts[i]) < functions.euclid_dist(
p3, pts[i]):
p4, p3 = p3, p4
xp, yp = pts[(i + 1) % len(pts)]
angle_mapping[(xp, yp)] = p3
c.ctrlpts = [pts[i], p2, p3, pts[(i + 1) % len(pts)]]
c.knotvector = [0, 0, 0, 0, 1, 1, 1, 1]
cm.add(c)
return cm
def get_cm_from_interpolation_radial(pts, interpolation_factor): # 0 is circ
center_circle = (200, 540)
center_polygon = (223, 555)
center = center_circle[0] * (
1 - interpolation_factor
) + center_polygon[0] * interpolation_factor, center_circle[1] * (
1 - interpolation_factor) + center_polygon[1] * interpolation_factor
radius = 70
tangents = []
for i in range(len(pts)):
p1 = pts[(i - 1) % len(pts)]
p2 = pts[(i + 1) % len(pts)]
pr = (p2[0] - p1[0], p2[1] - p1[1])
alpha = math.atan2(pr[1], pr[0])
tangents.append(alpha)
dists = []
for i in range(len(pts)):
dist = functions.euclid_dist(pts[i], pts[(i + 1) % len(pts)])
d = dist * 0.3
dists.append(d)
pts_interpolated = [
functions.project_to_circle(p, center_circle, radius) for p in pts
]
tangents_interpolated = []
for i in range(len(pts)):
x, y = pts[i]
alpha = math.atan2(y - center_circle[1], x - center_circle[0])
alpha -= 0.5 * math.pi
alpha = alpha % math.pi
tangents_interpolated.append(alpha)
dists_interpolated = []
for i in range(len(pts_interpolated)):
x1, y1 = pts_interpolated[i]
x4, y4 = pts_interpolated[(i + 1) % len(pts_interpolated)]
xc, yc = center_circle
axx = x1 - xc
ay = y1 - yc
bx = x4 - xc
by = y4 - yc
q1 = axx * axx + ay * ay
q2 = q1 + axx * bx + ay * by
k2 = 4 / 3 * (math.sqrt(2 * q1 * q2) - q2) / (axx * by - ay * bx)
d = math.sqrt((k2 * ay)**2 + (k2 * axx)**2)
dists_interpolated.append(d)
cm = multi.CurveContainer()
cm.vis = VisMPL.VisCurve2D(axes=False,
labels=False,
ctrlpts=False,
legend=False)
pts = [[
interpolation_factor * pp[0] + (1 - interpolation_factor) * pc[0],
interpolation_factor * pp[1] + (1 - interpolation_factor) * pc[1]
] for (pp, pc) in zip(pts, pts_interpolated)]
new_tangents = []
for tp, tc in zip(tangents, tangents_interpolated):
if abs(tp - tc) > math.pi / 2:
if tp < math.pi / 2:
t = interpolation_factor * (tp + math.pi) + (
1 - interpolation_factor) * tc
elif tc < math.pi / 2:
t = interpolation_factor * tp + (1 - interpolation_factor) * (
tc + math.pi)
else:
t = interpolation_factor * tp + (1 - interpolation_factor) * tc
new_tangents.append(t)
tangents = new_tangents
dists = [
interpolation_factor * dp + (1 - interpolation_factor) * dc
for (dp, dc) in zip(dists, dists_interpolated)
]
ctrlpts = []
for i in range(len(pts)):
c = BSpline.Curve()
c.degree = 3
d = dists[i]
p1, p2 = get_points_on_tangent(pts[i], tangents[i], d)
if math.atan2(p1[1] - center[1], p1[0] - center[0]) < math.atan2(
p2[1] - center[1], p2[0] - center[0]):
p1, p2 = p2, p1
if functions.euclid_dist(
p1, pts[(i + 1) % len(pts)]) < functions.euclid_dist(
p2, pts[(i + 1) % len(pts)]):
p2, p1 = p1, p2
p3, p4 = get_points_on_tangent(pts[(i + 1) % len(pts)],
tangents[(i + 1) % len(pts)], d)
if functions.euclid_dist(p4, pts[i]) < functions.euclid_dist(
p3, pts[i]):
p4, p3 = p3, p4
c.ctrlpts = [pts[i], p2, p3, pts[(i + 1) % len(pts)]]
c.knotvector = [0, 0, 0, 0, 1, 1, 1, 1]
cm.add(c)
return cm
bx = x4 - xc
by = y4 - yc
q1 = ax * ax + ay * ay
q2 = q1 + ax * bx + ay * by
k2 = 4 / 3 * (math.sqrt(2 * q1 * q2) - q2) / (ax * by - ay * bx)
x2 = xc + ax - k2 * ay
y2 = yc + ay + k2 * ax
x3 = xc + bx + k2 * by
y3 = yc + by - k2 * bx
return 0, (x2, y2), (x3, y3)
curve = NURBS.Curve()
mcrv_circle = multi.CurveContainer()
mcrv_circle.vis = VisMPL.VisCurve2D(axes=False,
labels=False,
ctrlpts=False,
legend=False)
center = (317, 465)
#pts = [[204, 604], [284, 612], [387, 577], [485, 475], [430, 366], [325, 231], [274, 438], [193, 436], [150, 525], [204, 604], [284, 612], [387, 577]]
pts = [[204, 604], [284, 612], [387, 577], [485, 475], [430, 366], [325, 231],
[274, 438], [193, 436], [150, 525], [204, 604]]
pts_c = [[204, 604], [284, 612], [387, 577], [485, 475], [430,
366], [325, 231],
[274, 438], [193, 436], [150, 525], [204, 604], [284, 612],
[387, 577]]
#pts = [[204, 604], [284, 612], [430, 366], [274, 438], [193, 436], [204, 604]]
#pts_c = [[204, 604], [284, 612], [430, 366], [274, 438], [193, 436], [204, 604], [284, 612], [430, 366]]
#radius = max([functions.euclid_dist(center, p) for p in pts])
curve = BSpline.Curve()
# Set up the curve
curve.degree = 3
curve.ctrlpts = exchange.import_txt("ex_curve02.cpt")
# Auto-generate knot vector
curve.knotvector = utilities.generate_knot_vector(curve.degree,
len(curve.ctrlpts))
# Split the curve
curve1, curve2 = operations.split_curve(curve, 0.2)
# Move the 1st curve a little bit far away from the 2nd curve
c2tan = curve2.tangent(0.0, normalize=True)
c2tanvec = [-1 * p for p in c2tan[1]]
operations.translate(curve1, c2tanvec, inplace=True)
# Plot the curves using the curve container
curves = multi.CurveContainer()
curves.sample_size = 40
curves.add(curve1)
curves.add(curve2)
vis_comp = VisMPL.VisCurve2D()
curves.vis = vis_comp
curves.render()
# Good to have something here to put a breakpoint
pass
q1 = ax * ax + ay * ay
q2 = q1 + ax * bx + ay * by
k2 = 4 / 3 * (math.sqrt(2 * q1 * q2) - q2) / (ax * by - ay * bx)
x2 = xc + ax - k2 * ay
y2 = yc + ay + k2 * ax
x3 = xc + bx + k2 * by
y3 = yc + by - k2 * bx
return 0, (x2, y2), (x3, y3)
#pts = [[204, 604], [284, 612], [387, 577], [485, 475], [430, 366], [325, 231], [274, 438], [193, 436], [150, 525], [204, 604], [284, 612], [387, 577]]
pts = [[485, 475], [430, 366], [325, 231], [274, 438], [193, 436], [150, 525],
[204, 604], [284, 612], [387, 577]]
cm = multi.CurveContainer()
cm.vis = VisMPL.VisCurve2D(axes=False,
labels=False,
ctrlpts=True,
legend=False)
x = [p[0] for p in pts]
y = [p[1] for p in pts]
# append the starting x,y coordinates
x = np.r_[x, x[0]]
y = np.r_[y, y[0]]
# fit splines to x=f(u) and y=g(u), treating both as periodic. also note that s=0
# is needed in order to force the spline fit to pass through all the input points.
tck, u = interpolate.splprep([x, y], s=0, per=True)
os.chdir(os.path.dirname(os.path.realpath(__file__)))
# Create a B-Spline curve instance
curve = BSpline.Curve()
# Set up curve
curve.degree = 4
curve.ctrlpts = exchange.import_txt("ex_curve3d01.cpt")
# Auto-generate knot vector
curve.knotvector = utilities.generate_knot_vector(curve.degree,
len(curve.ctrlpts))
# Split the curve
split_curves = operations.split_curve(curve, 0.3)
curves = multi.CurveContainer(split_curves)
# Move the 1st curve a little bit far away from the 2nd curve
c2tan = operations.tangent(curves[1], 0.0, normalize=True)
c2tanvec = [-1 * p for p in c2tan[1]]
operations.translate(curves[0], c2tanvec, inplace=True)
# Plot the curves using the curve container
curves.sample_size = 100
# Plot the control point polygon and the evaluated curve
vis_comp = VisPlotly.VisCurve3D()
curves.vis = vis_comp
curves.render()
# Good to have something here to put a breakpoint
from geomdl.shapes import curve2d from geomdl import operations from geomdl import multi from geomdl.visualization import VisMPL # Generate a NURBS full circle from 7 control points circle = curve2d.full_circle2(radius=5.0) circle.sample_size = 75 # Render the circle and the control points polygon vis_config = VisMPL.VisConfig(ctrlpts=True, figure_size=[9, 8]) vis_comp = VisMPL.VisCurve2D(config=vis_config) circle.vis = vis_comp circle.render() # Decompose the circle into Bezier curve segments segments = operations.decompose_curve(circle) bezier_segments = multi.CurveContainer(segments) # Set sample size (delta) bezier_segments.sample_size = 25 # Render the Bezier curve segments and their control points polygons vis_config = VisMPL.VisConfig(ctrlpts=True, figure_size=[9, 8]) vis_comp = VisMPL.VisCurve2D(config=vis_config) bezier_segments.vis = vis_comp bezier_segments.render() # Good to have something here to put a breakpoint pass
# Fix file path
os.chdir(os.path.dirname(os.path.realpath(__file__)))
# Create a NURBS curve instance (full circle)
curve = NURBS.Curve()
# Set up the curve
curve.degree = 2
curve.ctrlptsw = exchange.import_txt("ex_curve04.cptw")
# Use a specialized knot vector
curve.knotvector = [0, 0, 0, 0.25, 0.25, 0.5, 0.5, 0.75, 0.75, 1, 1, 1]
# Decompose the curve into Bezier curve segments
curve_list = operations.decompose_curve(curve)
bezier = multi.CurveContainer(curve_list)
# Set sample size of the Bezier curves
bezier.sample_size = 25
# Plot the Bezier curves
vis_config = VisMPL.VisConfig(figure_size=[8, 8])
vis_comp = VisMPL.VisCurve2D(vis_config)
bezier.vis = vis_comp
bezier.render()
# Good to have something here to put a breakpoint
pass
# Fix file path
os.chdir(os.path.dirname(os.path.realpath(__file__)))
# Create a B-Spline curve instance
curve = BSpline.Curve()
# Set up the curve
curve.degree = 4
curve.ctrlpts = exchange.import_txt("ex_curve01.cpt")
# Auto-generate knot vector
curve.knotvector = utilities.generate_knot_vector(curve.degree, len(curve.ctrlpts))
# Split the curve
curve_list = operations.split_curve(curve, 0.6)
curves = multi.CurveContainer(curve_list)
# Move the 1st curve a little bit far away from the 2nd curve
c2tan = curves[1].tangent(0.0, normalize=True)
c2tanvec = [-3 * p for p in c2tan[1]]
operations.translate(curves[0], c2tanvec, inplace=True)
# Plot the curves using the curve container
curves.sample_size = 40
# Plot the curve
vis_comp = VisMPL.VisCurve2D()
curves.vis = vis_comp
curves.render()
# Good to have something here to put a breakpoint
crv1.knotvector = knotvector.generate(crv1.degree, crv1.ctrlpts_size)
# Create the curve instance #2
crv2 = BSpline.Curve()
# Set degree
crv2.degree = 3
# Set control points
crv2.ctrlpts = [[1, 0, 0], [1, 1, 0], [2, 1, 0], [1, 1, 0]]
# Generate a uniform knot vector
crv2.knotvector = knotvector.generate(crv2.degree, crv2.ctrlpts_size)
# Create a curve container
mcrv = multi.CurveContainer(crv1, crv2)
# Import Matplotlib visualization module
from geomdl.visualization import VisMPL
# Set the visualization component of the curve container
mcrv.vis = VisMPL.VisCurve3D()
# Plot the curves in the curve container
mcrv.render()
'''
Convert non-rational to rational curve
Generates a B-Spline (non-rational) curve and converts it
into a NURBS (rational) curve.
'''
