Animating level curves in Maple

To create animations of level curves in Maple 9:

Use commands of the form:

with(plots): animate(plot3d,[x^2-y^2,x=-2..2,y=-2..2,orientation=[45-135*t,45-45*t], color=(x^2-y^2)],t=0..1,frames=64,scaling=constrained,style=patchcontour, axes=boxed,tickmarks=[5,5,0]);

Comments:

Creating (and especially exporting) animations can create high demands for memory. Reducing the number of frames reduces this demand. This will prevent crashes, but results in less smooth motion.
In earlier versions of Maple, animating the orientation required use of the display command. For example, the following code works in Maple 7:

with(plots):readlib(piecewise): A:=seq(plot3d(x^2+y^2,x=-2..2,y=-2..2,color=x^2+y^2,style=patchcontour, axes=boxed,tickmarks=[5,5,0], orientation=[45-135*piecewise(t<48,t/48,t>=48,1),45-45*piecewise(t<48,0,t>=48,(t-48)/16)]),t=0..64): display(A,insequence=true,scaling=constrained);
The use of the piecewise function in the orientation option in the preceding Maple 7 commands yields the two stage rotation (horizontal followed by vertical) displayed in the Quicktime movies on the main page. The Maple 9 command at the top of the page combines both rotations in a single movement.
The animations can be exported as animated GIFs of converted to Quicktime movies with nice slider bars.