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+--- Thread: Plotting f(x,y,z)=0? (/thread-19450.html)
Plotting f(x,y,z)=0? - byoung - 01-19-2023 07:02 PM
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?
RE: Plotting f(x,y,z)=0? - roadrunner - 01-19-2023 11:31 PM
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
RE: Plotting f(x,y,z)=0? - Albert Chan - 01-20-2023 12:30 AM
(01-19-2023 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))
RE: Plotting f(x,y,z)=0? - byoung - 01-20-2023 02:58 PM
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.