The spacecurve function plots a curve or a set of curves in three-dimensional space.

The first argument is a space curve defined as a list of points or a list of three or more components.  An Array or rtable may be used instead of a list.

When a list of components is provided, the first three components are considered to be the parametric representations of the x, y, and z coordinates.  Each of these components is an algebraic expression in a variable t.  Additional components can include the parameter range or the numpoints option described below.

Multiple space curves may be plotted.  To do this, provide a set of space curves instead of a single curve as the parameter sc.

The second argument r is the parameter range, provided in the form t=a..b.  This argument is optional if it is provided locally within each space curve.

The third argument opts is a sequence of one or more options.  This can include the numpoints=n option, which specifies the number of points used for drawing the curve.  The default value for n is 50.  The numpoints option may be provided locally within each space curve.

Other options allowed in the opts parameter are the same as those accepted by the plot3d command.  These are described in the plot3d/option help page.  Note that some options, such as grid, are not applicable.

The result of a call to spacecurve 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.

spacecurve may be defined by with(plots) or with(plots,spacecurve). It can also be used by the name plots[spacecurve].

$\mathrm{with}\left(\mathrm{plots}\right)\:$

$\mathrm{spacecurve}\left(\left[\cos \left(t\right)\,\sin \left(t\right)\,t\right]\,t=0..4\mathrm{\pi }\right)$

$\mathrm{spacecurve}\left(\left\{\left[\cos \left(t\right)+1\,\sin \left(t\right)\,0\,\mathrm{numpoints}=10\right]\,\left[\sin \left(t\right)\,0\,\cos \left(t\right)\,t=0..2\mathrm{\pi }\right]\right\}\,t=-\mathrm{\pi }..\mathrm{\pi }\,\mathrm{axes}=\mathrm{frame}\right)$

$\mathrm{spacecurve}\left(\left\{\left[4\cos \left(t\right)\,4\sin \left(t\right)\,0\right]\,\left[t\sin \left(t\right)\,t\,t\cos \left(t\right)\right]\right\}\,t=-\mathrm{\pi }..2\mathrm{\pi }\right)$

$\mathrm{knot}≔\left[-10\cos \left(t\right)-2\cos \left(5t\right)+15\sin \left(2t\right)\,-15\cos \left(2t\right)+10\sin \left(t\right)-2\sin \left(5t\right)\,10\cos \left(3t\right)\,t=0..2\mathrm{\pi }\right]\:$

$\mathrm{spacecurve}\left(\mathrm{knot}\right)$

$\mathrm{helix\_points}≔\left[\mathrm{seq}\left(\left[10\cos \left(\frac{r}{30}\right)\,10\sin \left(\frac{r}{30}\right)\,\frac{r}{3}\right]\,r=0..240\right)\right]\:$

$\mathrm{spacecurve}\left(\mathrm{helix\_points}\right)$

$\mathrm{spacecurve}\left(\left\{\mathrm{knot}\,\mathrm{helix\_points}\right\}\right)$