> with(plots);
(you only need to type this command once
at the beginning of each Maple session)
> spacecurve([1-3*t,t,2*t+1],t=-5..10);
To draw the coordinate axes, you can either choose "Normal" from the "Axes" menu of the 3D display window, or enter axes=normal as an option in the spacecurve command. You may also want to adjust color and thickness for a better view. The final command may look like this:
> spacecurve([1-3*t,t,2*t+1],t=-5..10,axes=normal,thickness=3,
color=black);
You can plot several curves in the same plot. For example, consider a family of lines (s-3t, st, 2t+s). For each value of s we get a different line (the line above corresponds to the value s=1). Three of these lines corresponding to s = 0, 1, 2 can be plotted simultaneously by using the command
> spacecurve({[-3*t,0,2*t],[1-3*t,t,2*t+1],[2-3*t,2*t,2*t+2]},
t=-5..10);
To explore this example further, we can now fix t and consider s as a parameter. Let us take, for example, t=0, 1, 2, and s any number between 0 and 20. To plot the three different curves simultaneously, we type
> spacecurve({[s,0,s],[s-3,s,2+s],[s-6,2*s,4+s]},s=0..20);
Maple has a command which will consider both t and s as variables, thereby plotting the parametric surface containing these lines. This command, plot3d, is used as follows:
> plot3d([s-3*t,s*t,2*t+s],t=-5..10,s=0..20);
In addition to the options discussed above, there are several other options that may be useful with commands spacecurve and plot3d, like
labels=[x,y,z] Labels the axes in a plot
numpoints=1000
Specifies the minimum number of points
to consider
when creating a plot
title="Helix" Specifies a title ( "Helix" ) for the plot
scaling=constrained Forces the scaling to be the same on all axes