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Plotting Three Dimensional Curves

Curves in three dimensions are given in parametric form

which are plotted using the spacecurve command in the plots package. As an example, we plot the two curves

and

with(plots):                       load the plots package
spacecurve( { [cos(t),sin(t),sin(t), t=0..7],            Line Feed
              [5*cos(t)/6, 5*sin(t)/6, t/(t^2+1), t=0..5] } );
Move the new picture window so that it does not obscure the Maple command window. The colors on the monitor may behave strangely - activating the picture window will correct the problem. (Be sure the keyboard NumLock light is off.)

Two curves have been drawn but they seem faint. Left click the Style button, then left click the Line Width line, and then left click the Width 2 (medium) line. Next, from the Axes menu choose Boxed in a similar fashion. Now type p and the two curves are redrawn - surrounded by a box. Note the scaling on the edges of the box; they represent the x,y,z axes - but the origin is not one of the corners of the box.

The picture is not very informative due to the orientation. We remedy that by placing the arrow on a corner of the box, holding down the left button and dragging the box to the desired orientation. Notice the changes in the values of Theta and Phi in the top left corner. Then type p again. You obtain a new view of the curves. Rotate some more - a reasonable view is when . Some informative views are obtained when the box is flattened into a square; there are several such orientations - try them. Also try the options from the Color menu. To get rid of the picture type q (for quit) in the picture window.



Peter Monk
Tue Aug 29 14:41:29 EDT 1995