My son has just started into Calculus III at a community college. He needed help visualizing the 3D surfaces and so I started exploring some of the cheap and free math packages I could find. IIt took me most of an evening to start getting it right but I have now started having success using this program to plot surfaces of revolution so that we can visualize volumes for Calculus II. Specifically - the problem I was trying to solve was integrating the region enclosed by the curves y=cos(x) on top, y=sin(x) on the bottom, and the y axis on the left. This region is then rotated around the X axis. To plot this I had to do some mental substitutions. My vertical axis is now referred to as Z instead of Y. And I can now rotate the region about either the X or the Y axis - same result by symmetry.

Solution is as follows - plot 2 functions

function 1 is the inner surface of this concave object (in cartesian form)
X: sin(v)*cos(u)
Y: v
Z: sin(v)*sin(u)
u goes from 0 to 6.28 (2*pi)
v goes from 0 to 0.785 (pi/4)
turn face color on - I chose green
That paints the lower curve

Similarly
function 2 - the outer surface is plotted as follows:
X: cos(v)*cos(u)
Y: v
Z: cos(v)*sin(u)
u goes from 0 to 6.28 (2*pi)
v goes from 0 to 0.785 (pi/4)

Object plotted successfully!

Maxima could not tackle this piecewise function in 3D - it could only plot one of the surfaces at a time
Archimedes 3DGeo - seemed too complicated and my trial ran out before I could figure out a solution
MultiGraphix only allows single parameter and could not seem to tackle the job either.
I have a copy of MathCad12 and it loks like it can also do the job but we can't afford two copies - so I wanted a cheep or free solution for my son's laptop.

With this tool I was able to animate a plane slicing thru the object so that we could figure out what our washers looked like.

I think this will be a useful tool for the remainder of calc II and also for calc III.

The trick to success here is to set one cartesian coordinate to 0 to plot in a plane
Play with the other two coord (Y & Z) until you plot the appropraite graph in two dimensions. Then play with how to rotate around a given axis by multiplying the other two axies by either sin(u) or cos(u). With practice it can work.

The trickier problem is rotate around a line NOT on the axis. This requires translating the region so it can be rotated around either X or Y or Z and then translating who graph back to its original location. Took another couple of hours to figure this out but it works too.

Nice program for doing this kind of work

I just want to disprove previus review. That guy just can`t figure out that if he will put u and v to X and Y fields and a function f(u,v) to Z, he`ll get exactly what he needed, like I did :). The program is very easy and more than functional for

this program makes no sense. I can't just write an eqation for z in terms of x and y, I have to write what x and y and z equal in terms of u and v. I don't want to write a parametric equation. What genius moron made this program??? You people have made a practical idea of 3 dimensional graphing into an agonizing endeveror of frustration!