How to plot the equation |x|+|y|+|z|=1 ?

I have a 3D equation. Can anyone help me to plot this? Thanks

Answer 1

[Benjamin Kraus]

If you are using MATLAB R2016b you can use the new fimplicit3 command:

fimplicit3(@(x,y,z) abs(x)+abs(y)+abs(z)-1)

You may also be interested in fplot, fplot3, fsurf, fmesh, fcontour, and fimplicit (some of these have been available since R2016a, but fimplicit3 was added in R2016b).

[Walter Roberson]

Nice solution, Benjamin!

Answer 2

[John Chilleri]

Hello,

I'm certain there's a better way to do this, such as with surf, but here is a solution.

If you consider the equation, you realize that it's all planes joined by the 6 vertices {(1,0,0),(0,1,0),(0,0,1),(-1,0,0),(0,-1,0),(0,0,-1)}. These 6 vertices 'form' 8 sides.

Using the fill3 command, you can reconstruct the shape:

fill3([1 0 0],[0 1 0],[0 0 1], 'r')
hold on
fill3([1 0 0],[0 1 0],[0 0 -1], 'r')
fill3([1 0 0],[0 -1 0],[0 0 -1], 'r')
fill3([-1 0 0],[0 -1 0],[0 0 -1], 'r')
fill3([-1 0 0],[0 -1 0],[0 0 1], 'r')
fill3([-1 0 0],[0 1 0],[0 0 1], 'r')
fill3([-1 0 0],[0 1 0],[0 0 -1], 'r')
fill3([1 0 0],[0 -1 0],[0 0 1], 'r')

which results in the following image:

(This is just an angle I chose to show.)

Hope this helps!

[John Chilleri]

If you are running R2016b, Benjamin Kraus has the smart solution! I'm running R2015b, and I would encourage my solution only if you are running an older release.