5 replies to this topic

[TZ250]

In class we're working on solids of revolution. How do I make the CP330 draw something like that? I can rotate a 3D function, and shade the difference between two functions, but I don't know how to revolve a function.

Example: The region bounded by y=(square root of X) , y=2X+1, X=1 and X=4.

How do I draw that? (in solid form)

[ASTRO491K]

Keep in mind that unlike shading the difference between two functions in the x-y plane, solids of revolution are just that, solids. That requires that you plot the 3d surface equivalent of the solid of revolution, for example rotataing the semi-circle y=sqrt(1-x^2) about the x axis is equivalent to plotting the 3d surface x^2+y^2+z^2=1, i.e., z=+/-sqrt(1-x^2-y^2). I hope this reply is helpful because to my knowledge there is no built in function for displaying the rotated solid of revolution. Of course I could be wrong.

In class we're working on solids of revolution. How do I make the CP330 draw something like that? I can rotate a 3D function, and shade the difference between two functions, but I don't know how to revolve a function.

Example: The region bounded by y=(square root of X) , y=2X+1, X=1 and X=4.

How do I draw that? (in solid form)

[Kilburn]

Is this what you need?



In the 3D Graph app, press the "Z=" button so it turns into "Xst", that will allow you to graph 3D parametric equations. If you want to rotate a function around an axis and see what it looks like, here's the formula:

X(s,t) = cos(t) * f(s)
Y(s,t) = sin(t) * f(s)
Z(s,t) = s

Where f is the function you want to revolve. Just look at the above picture, I did that with the square root function. Just modify smin and smax in the axis properties if you want a wider range.

[ASTRO491K]

Wow, that is really nice Kilburn. Could you then plot an additional surface, say the plane z=1-x-y to show how it intersects with the paraboloid that you already have? That would be really really super!

Is this what you need?



In the 3D Graph app, press the "Z=" button so it turns into "Xst", that will allow you to graph 3D parametric equations. If you want to rotate a function around an axis and see what it looks like, here's the formula:

X(s,t) = cos(t) * f(s)
Y(s,t) = sin(t) * f(s)
Z(s,t) = s

Where f is the function you want to revolve. Just look at the above picture, I did that with the square root function. Just modify smin and smax in the axis properties if you want a wider range.

[Kilburn]

Wow, that is really nice Kilburn. Could you then plot an additional surface, say the plane z=1-x-y to show how it intersects with the paraboloid that you already have? That would be really really super!

Nope, as far as I know, you can't even draw several surfaces at once.

[ASTRO491K]

Nope, as far as I know, you can't even draw several surfaces at once.

Hi Kilburn, me again. Isn't there some way to generate and store a surface, and then generate the second surface and store it, and then simply display both? If that was possible, it would be totally awesome!