tubeplot - Maple Help

Home : Support : Online Help : Graphics : 3-D : tubeplot

plots

 tubeplot
 three-dimensional tube plotting

 Calling Sequence tubeplot(C, options)

Parameters

 C - set of spacecurves

Description

 • The tubeplot function defines a tube about one or more three-dimensional space curves. A given space curve is a list of three or more components. The initial three components define parametrically the x, y, and z components. Additional components of a given space curve specify various local attributes of the curve.
 • Remaining components of an individual space curve are interpreted as local options which are specified as equations of the form option = value. These include equations of the form numpoints = n or tubepoints = m with n and m integers. These allow the user to designate the number of points evaluated on the space curve and the number of points on the tube, respectively.  The default values used by Maple are numpoints=50 and tubepoints=10.  An equation of the form radius = f, where f is some expression, defines the radius of the tube about the given space curve. If no radius is specified, then the default used is radius=1. An equation of the form t=a..b, where a and b evaluate to constants, specifies the range of the parameter of the curve.
 • Remaining arguments to tubeplot include such specifications as numpoints = n, tubepoints = m, t= a..b, and radius = f. These are to be used in the case where an individual space curve does not have the option specified.
 • Additional options are the same as those found in spacecurve (and similar to options for plot3d). For example, the option axes= boxed specifies that the tubeplot is to include a boxed axis bounding the plot.  See also plot3d/option.
 • The result of a call to tubeplot is a PLOT3D structure which can be rendered by the plotting device. You can assign a PLOT3D value to a variable, save it in a file, then read it back in for redisplay. See plot3d/structure.
 • tubeplot may be defined by with(plots) or with(plots,tubeplot). It can also be used by the name plots[tubeplot].
 • For more examples, including ones demonstrating the use of additional plot options, see examples/knots.

Examples

 > $\mathrm{with}\left(\mathrm{plots}\right):$
 > $\mathrm{tubeplot}\left(\left[\mathrm{cos}\left(t\right),\mathrm{sin}\left(t\right),0\right],t=0..2\mathrm{\pi },\mathrm{radius}=0.5\right)$
 > $\mathrm{tubeplot}\left(\left[\mathrm{cos}\left(t\right),\mathrm{sin}\left(t\right),0,t=\mathrm{\pi }..2\mathrm{\pi },\mathrm{radius}=0.25\left(t-\mathrm{\pi }\right)\right]\right)$
 > $\mathrm{tubeplot}\left(\left[3\mathrm{sin}\left(t\right),t,3\mathrm{cos}\left(t\right)\right],t=-3\mathrm{\pi }..4\mathrm{\pi },\mathrm{radius}=1.2+\mathrm{sin}\left(t\right),\mathrm{numpoints}=80\right)$
 > $\mathrm{tubeplot}\left(\left[\mathrm{sin}\left(t\right),t,\mathrm{exp}\left(t\right)\right],t=-1..1,\mathrm{radius}=\mathrm{cos}\left(t\right),\mathrm{tubepoints}=20\right)$
 > $\mathrm{tubeplot}\left(\left[-10\mathrm{cos}\left(t\right)-2\mathrm{cos}\left(5t\right)+15\mathrm{sin}\left(2t\right),-15\mathrm{cos}\left(2t\right)+10\mathrm{sin}\left(t\right)-2\mathrm{sin}\left(5t\right),10\mathrm{cos}\left(3t\right)\right],t=0..2\mathrm{\pi },\mathrm{radius}=3\mathrm{cos}\left(\frac{t\mathrm{\pi }}{3}\right)\right)$

Multiple tubeplots are also allowed.

 > $\mathrm{tubeplot}\left(\left\{\left[0,\mathrm{sin}\left(t\right)-1,\mathrm{cos}\left(t\right)\right],\left[\mathrm{cos}\left(t\right),\mathrm{sin}\left(t\right),0\right]\right\},t=0..2\mathrm{\pi },\mathrm{radius}=\frac{1}{4}\right)$
 > $\mathrm{tubeplot}\left(\left\{\left[0,\mathrm{sin}\left(t\right)-1,\mathrm{cos}\left(t\right)\right],\left[\mathrm{cos}\left(t\right),\mathrm{sin}\left(t\right),0\right]\right\},t=0..2\mathrm{\pi },\mathrm{radius}=\frac{1}{10}t\right)$

You can specify color option as a two argument procedure:

 > $F≔\left(x,y\right)↦\mathrm{sin}\left(x\right):$
 > $\mathrm{tubeplot}\left(\left\{\left[0,\mathrm{sin}\left(t\right)-1,\mathrm{cos}\left(t\right)\right],\left[\mathrm{cos}\left(t\right),\mathrm{sin}\left(t\right),0\right]\right\},t=0..2\mathrm{\pi },\mathrm{radius}=\frac{1}{4},\mathrm{color}=F\right)$

The command to create the plot from the Plotting Guide is

 > $\mathrm{tubeplot}\left(\left\{\left[0,\mathrm{cos}\left(t\right)-1,\mathrm{sin}\left(t\right),t=0..\mathrm{\pi },\mathrm{numpoints}=45,\mathrm{radius}=0.25\right],\left[\mathrm{cos}\left(t\right),\mathrm{sin}\left(t\right),0,t=\mathrm{\pi }..2\mathrm{\pi },\mathrm{numpoints}=15,\mathrm{radius}=0.25\left(t-\mathrm{\pi }\right)\right]\right\}\right)$