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tubeplot3d function in sage ?

asked 2010-12-16 06:08:54 -0500

Wizard gravatar image

Is there a function equivalent to the function tubeplot as appended below ? If not, how to use the script below in sage ? Or could such a function be defined in sage in the future ? Thanks for any reply ! @mfunction("varargout") def tubeplot(x=None, y=None, z=None, *varargin):

# TUBEPLOT - plots a tube r along the space curve x,y,z.
# tubeplot(x,y,z) plots the basic tube with radius 1
# tubeplot(x,y,z,r) plots the basic tube with variable radius r (either a vector or a value)
# tubeplot(x,y,z,r,v) plots the basic tube with coloring dependent on the values in the vector v
# tubeplot(x,y,z,r,v,s) plots the tube with s tangential subdivisions (default is 6)
# [X,Y,Z]=tubeplot(x,y,z) returns [Nx3] matrices suitable for mesh or surf
# Note that the tube may pinch at points where the normal and binormal 
# misbehaves. It is suitable for general space curves, not ones that 
# contain straight sections. Normally the tube is calculated using the
# Frenet frame, making the tube minimally twisted except at inflexion points.
# To deal with this problem there is an alternative frame:
# tubeplot(x,y,z,r,v,s,vec) calculates the tube by setting the normal to
# the cross product of the tangent and the vector vec. If it is chosen so 
# that it is always far from the tangent vector the frame will not twist unduly
# Example:
#  t=0:(2*pi/100):(2*pi);
#  x=cos(t*2).*(2+sin(t*3)*.3);
#  y=sin(t*2).*(2+sin(t*3)*.3);
#  z=cos(t*3)*.3;
#  tubeplot(x,y,z,0.14*sin(t*5)+.29,t,10)
# Written by Anders Sandberg,, 2005

subdivs = 6

N = size(x, 1)
if (N == 1):
    x = x.cT
    y = y.cT
    z = z.cT
    N = size(x, 1)

if (nargin == 3):
    r = x * 0 + 1
    r = varargin(1)
    if (size(r, 1) == logical_and(1, size(r, 2) == 1)):
        r = r * ones(N, 1)
if (nargin > 5):
    subdivs = varargin(3) + 1
if (nargin > 6):
    vec = varargin(4)
    [t, n, b] = frame(x, y, z, vec)
    [t, n, b] = frenet(x, y, z)

X = zeros(N, subdivs)
Y = zeros(N, subdivs)
Z = zeros(N, subdivs)

theta = mslice[0:(2 * pi / (subdivs - 1)):(2 * pi)]

for i in mslice[1:N]:
    X(i, mslice[:]).lvalue = x(i) + r(i) * (n(i, 1) * cos(theta) + b(i, 1) * sin(theta))
    Y(i, mslice[:]).lvalue = y(i) + r(i) * (n(i, 2) * cos(theta) + b(i, 2) * sin(theta))
    Z(i, mslice[:]).lvalue = z(i) + r(i) * (n(i, 3) * cos(theta) + b(i, 3) * sin(theta))

if (nargout == 0):
    if (nargin > 4):
        V = varargin(2)
        if (size(V, 1) == 1):
            V = V.cT
        V = V * ones(1, subdivs)
        surf(X, Y, Z, V)
        surf(X, Y, Z)
    varargout(1).lvalue = mcellarray([X ...
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3 answers

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answered 2010-12-21 20:32:34 -0500

Jason Grout gravatar image

You might be able to just use line3d and thicken it a bit. What exactly do you want to plot?

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answered 2010-12-30 20:32:18 -0500

pangard gravatar image

Well, you sure can't use that script, that's not python. The tubular neighborhood of radius R can be plotted easily with a parametric_surface3d plot, if you can write its parametric equations. Parametric equations for a tubular neighborhood require a Frenet frame for the curve which might be problematic, but you seem to know about that. I don't know of anyone who has worked the equations already, although there is some people working in diff geometry in Sage right now, so I might be wrong. Doens't seem too hard, anyway, does it?

Alternatively, if you can find the implicit equations for the tubular neighborhood, you can use implicit_plot3d (though I don't see how this can be done in some generality).

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answered 2010-12-16 06:54:54 -0500

niles gravatar image

I don't know of a function which does exactly this, but you could look through the 3D Graphics section of the reference manual. In particular, you may be able to modify the script fairly easily by using either parametric_plot3d or implicit_plot3d.

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Asked: 2010-12-16 06:08:54 -0500

Seen: 305 times

Last updated: Dec 30 '10