Plotting f(x,y,z)=0?

01192023, 07:02 PM
Post: #1




Plotting f(x,y,z)=0?
Is there any way to make the Prime create a 3D plot when the equation cannot be explicitly solved for z? Specifically, the following equation has been used in 3D printing to recreate the porous internal structure of human bone:
cos(x)*sin(y) + cos(y)*sin(z) + cos(z)*sin(x) = 0 Is it possible to plot this on the Prime?  Bruce 

01192023, 11:31 PM
Post: #2




RE: Plotting f(x,y,z)=0?
Maybe you can use fsolve to solve for z like this:
p:=(x,y,n)>(fsolve((cos(x)*sin(y)+cos(y)*sin(z)+cos(z)*sin(x)) = 0,z,0 .. (2*π)))(n) That give 2 solutions between 0 and 2*pi so you can plot each one separately: FZ1(X,Y)=p(X,Y,1) and FZ2((X,Y)=p(X,Y,2) road 

01202023, 12:30 AM
(This post was last modified: 01202023 01:25 AM by Albert Chan.)
Post: #3




RE: Plotting f(x,y,z)=0?
(01192023 07:02 PM)byoung Wrote: cos(x)*sin(y) + cos(y)*sin(z) + cos(z)*sin(x) = 0 I think you can solve for z Let K = sqrt(cos(y)^2 + sin(x)^2) Let θ = asin(sin(x)/K) cos(x)*sin(y) + K*(sin(z)*cos(θ) + cos(z)*sin(θ)) = 0 sin(z + θ) = cos(x)*sin(y) / K z = asin(cos(x)*sin(y) / K)  θ Comment: I assumed y within ±pi/2, otherwise θ = atan2(sin(x), cos(y)) 

01202023, 02:58 PM
Post: #4




RE: Plotting f(x,y,z)=0?
Roadrunner and Albert, thanks for those solutions; both look like they should work. I'll probably need a few tries to get the fsolve syntax correct (syntax errors have become my nemesis as I get used to the Prime after 40 years of other HPs).
Albert, it's been too long since I've studied trig  I would never have thought of those substitutions! Thanks again to both of you.  Bruce 

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