Double Inequality 3Dplot

Is there a way to have a 3D plot on say and clearly see the bounded region?

[Walter Roberson]

Is it a solid or a surface ?

When you say "clearly see" do you mean you want the bounding planes drawn in?

[Hmm!]

I am expecting to see all eight extreme points on the polyhedron. According to the reference text, there are 8 extreme points but whenever I plot I see 4.

[John D'Errico]

Um, unless you make the polyhedron translucent, do you expect to see those in the back?

[Hmm!]

Just anything that gets the job done!

Answer 1

[John D'Errico]

Easy peasy.

lb = [1 1 1];
ub = [2 2 2];
plotregion([],[],lb,ub)
view(29,30)
grid on
box on

plotregion can be found on the file exchange for free download.

https://www.mathworks.com/matlabcentral/fileexchange/9261-plot-2d-3d-region?s_tid=srchtitle

[Hmm!]

It gets the job done. Can we also draw this manually "by hand" assuming no resources like matlab to aid us? I tried it several times on a paper with a 3-axis to represent the 3D and I can't visualize it to get all the extreme points. Generally, is there any trick or hint?

[Walter Roberson]

https://www.mathworks.com/matlabcentral/answers/752519-creating-sphere-using-cuboids-of-varying-size#answer_637781

Or you could refer to https://www.mathworks.com/matlabcentral/answers/1447449-how-to-draw-a-volxe-size#comment_1728709 where I posted code that voxelizes a volume. In particular the rV array gives corner coordinates (vertices) and the rF array gives the indices into the vertices array needed to create the faces. When I built that code, I made sure to use the consistent "counter-clockwise" ordering of vertices in building the faces, so that lighting would work correctly.

[John D'Errico]

Could this have been done in another way? Yes, Of course. That the tool I show does what it does using MATLAB itself proves that it can be done. In fact, I can think of at least 2 or 3 easy ways you could do this using other tools.

Could you have used tools like patch to plot those facets? OF COURSE. Trivially so. If you cannot see all 8 vertices, then you need to remember to make the facets of the surface translucent, otherwise you cannot see through the front facets to see those that are hidden.

But the solution I showed does exactly what you asked to do.