# Problem with plotting a 3d Bezier curve

I have a problem with plotting a Bezier spline in 3d.

In 2d this simply works:

p2d = [[(3.0,0.0),(3.0,0.13),(2.94,0.25),(2.8,0.35)],
[(2.7,0.44),(2.6,0.5),(2.5,0.5)],
[(2.36,0.5),(2.24,0.44),(2.14,0.35)],
[(2.05,0.25),(2.0,0.13),(2.0,6.1e-17)]]

bezier_path(p2d)


But when I want to plot it in 3d, this line

bezier_path(p2d).plot3d()


or

p3d = [[(3.0,0.0,0.0),(3.0,0.13,0.0),(2.94,0.25,0.0),(2.8,0.35,0.0)],
[(2.7,0.44,0.0),(2.6,0.5,0.0),(2.5,0.5,0.0)],
[(2.36,0.5,0.0),(2.24,0.44,0.0),(2.14,0.35,0.0)],
[(2.05,0.25,0.0),(2.0,0.13,0.0),(2.0,6.1e-17,0.0)]]

bezier3d(p3d)


both give me the following error: TypeError: unable to convert -(t - 1)^3 to an integer.

What am I doing wrong?

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This looks like a bug and I opened the ticket #31640 to track the issue. Thanks for your report!

The issue turns out to be a missing vector conversion in the code. I posted a fix and should hopefully make it for a later release.

As a work around you can use the following function (that contains the fix I provided in the ticket)

def bezier3d(path, **options):
from . import parametric_plot3d as P3D
from sage.modules.free_module_element import vector
from sage.symbolic.ring import SR

p0 = vector(path[0][-1])
t = SR.var('t')
if len(path[0]) > 2:
B = (1-t)**3*vector(path[0][0])+3*t*(1-t)**2*vector(path[0][1])+3*t**2*(1-t)*vector(path[0][-2])+t**3*p0
G = P3D.parametric_plot3d(list(B), (0, 1), **options)
else:
G = line3d([path[0][0], p0], **options)

for curve in path[1:]:
if len(curve) > 1:
p1 = vector(curve[0])
p2 = vector(curve[-2])
p3 = vector(curve[-1])
B = (1-t)**3*p0+3*t*(1-t)**2*p1+3*t**2*(1-t)*p2+t**3*p3
G += P3D.parametric_plot3d(list(B), (0, 1), **options)
else:
G += line3d([p0,curve[0]], **options)
p0 = vector(curve[-1])   # this was the wrong line!
return G

more

The fix is incorporated in sage 9.3!

( 2021-06-09 23:09:03 +0200 )edit