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3D Scatterplot and Pareto Front visualization

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Apostolos Fragkalas
Apostolos Fragkalas on 11 Apr 2021
Edited: Apostolos Fragkalas on 12 Apr 2021
So first things first, I'm really new in MatLab and even though I'm trying to learn the bassics in order to do what I want and udenrstand it, it seems like it is hard when you are under schedule.
I've Uploaded an excel file with all my data ( 525 rows and 3 columns) and then I created my workspace. After that I defined my x's,y's and z's using the following commands.
numbers = xlsread(filename);
x = numbers(1:525,3);
y = numbers(1:525,2);
z = numbers(1:525,1);
I tried following this answer ( but I had no luck - the first reason was because I couldn'y understand what a,b and c were and how they were related to my data.
So my question is, how do I create a 3d scatterplot were I can also create a visible Pareto front?
Thanks in advance!

Answers (1)

Alan Weiss
Alan Weiss on 12 Apr 2021
Did you try the scatteredinterpolant code from the answer? Modify it for your data:
F = scatteredInterpolant(numbers(:,1),numbers(:,2),numbers(:,3),'linear','none');
sgr = min(f(:,1)):.01:max(f(:,1));
ygr = min(f(:,2)):.01:max(f(:,2));
[XX,YY] = meshgrid(sgr,ygr);
ZZ = F(XX,YY);
Alan Weiss
MATLAB mathematical toolbox documentation
Apostolos Fragkalas
Apostolos Fragkalas on 12 Apr 2021
So the full and revised code is this. The minor changes were made to correspond with my data
F = scatteredInterpolant(numbers(1:525,2),numbers(1:525,3),numbers(1:525,1),'linear','none');
sgr = linspace(min(numbers(1:525,2)),max(numbers(1:525,2)));
ygr = linspace(min(numbers(1:525,3)),max(numbers(1:525,3)));
[XX,YY] = meshgrid(sgr,ygr);
ZZ = F(XX,YY);
Warning: Duplicate data points have been detected and removed - corresponding values have been averaged.
If I exclude the "Warning" messege, everything else seems to be looking great to be honest!
However, I do have some followup questions. Is there a way wher I can have the data combination that give me the Pareto Front, in a more vivid color, and the rest of data combination shown too? You know, like dots. I don't know if I'm explaining what I want to say the right way.
Also, is there a way to know the optimal solution based on the formula that calucmates the distance between two points (d = ((x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2)1/2) ?
Thanks in advance!

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