MaplePrimes - answers and comments on Question, Plot a surface on a circular domain

one way: piecewise

pagan — Tue, 01 Nov 2011 05:21:51 Z

plot3d(piecewise(x^2+y^2<=1,4*x^2-y^2,undefined),x=-2..2,y=-2..2,axes=box);

Throw in the `grid` option, to refine the resolution. Eg, toss grid=[50,50] in as another optional argument to that plot3d() call.

Cylindrical coordinates

Robert Israel — Tue, 01 Nov 2011 05:42:52 Z

I think the best way to do this is using cylindrical coordinates.

> plot3d([r,theta,4*(r*cos(theta))^2 - (r*sin(theta))^2], r = 0 .. 1, theta=0..2*Pi, 
coords=cylindrical, axes=box, labels=[x,y,z]);

A third way

pchin — Tue, 01 Nov 2011 21:28:45 Z

You can also do it this way:

plot3d(4*x^2-y^2, x=-1..1, y=-sqrt(1-x^2)..sqrt(1-x^2));

Actually, I think Robert's cylindrical-coordinates solution is a better one for this particular example; however, I wanted to show that you can use expressions in terms of x in the y range argument.

Paulina

Thank you

Melykin — Tue, 01 Nov 2011 22:52:46 Z

Thanks so much for the quick response. So far I have tried the cylindrical coordinates and it works well. I will keep the other two methods on file. I had considered trying Paulina's method before I posted my question but I wasn't sure if it would work and I was short of time. I also investigated cylindrical coordinates before posting but I kept getting strange looking, incorrect graphs. I didn't know there was a piecewise command in Maple. Good to know. In the past I've made 2d piecewise graphs using "display".

Thanks again for the help. This site is a really big help.