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

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Jes 2017-1-30

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https://ww2.mathworks.cn/matlabcentral/answers/322596-how-to-plot-the-equation-x-y-z-1

评论： Walter Roberson 2017-1-30

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

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Answer 1

Benjamin Kraus 2017-1-30

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https://ww2.mathworks.cn/matlabcentral/answers/322596-how-to-plot-the-equation-x-y-z-1#answer_252676

编辑：Benjamin Kraus 2017-1-30

在 MATLAB Online 中打开

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).

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Walter Roberson 2017-1-30

Nice solution, Benjamin!

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Answer 2

John Chilleri 2017-1-30

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编辑：John Chilleri 2017-1-30

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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!

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John Chilleri 2017-1-30

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.

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