Help with Plotting the Envelope of a Scatter Plot in MATLAB

Hello everyone,

I'm trying to plot the envelope of a scatter plot in MATLAB. However, when I use the envelope function, it returns the same plot without highlighting the upper or lower bounds.

This plot was created using a scatter plot, and when I attempt to filter it to retain only the extremum values, I end up with just a single slice of the data.

Has anyone encountered a similar issue or knows how I could extract and plot the envelope correctly (in red), as shown in the reference image?

Thanks in advance!

[Zac Lee]

Dear @Star Strider, here my x,y datas. The code is simply the classical roots of a 2nd degree polinomial equation.

[Catalytic]

The sampling density is very non-uniform, and makes it hard to see why the red boundary is appropriate in certain places. Why couldn't someone assume the following boundary drawing be valid? You need to achieve denser sampling throughout the shape for any automatic boundary detector to have any hope.

Answer 1

[Matt J]

load xy

x=x(:); y=y(:);

[G,yg]=findgroups(y);

xmin=splitapply(@min,x,G);
xmax=splitapply(@max,x,G);

[yg,is]=sort(yg);
xmin=xmin(is);
xmax=xmax(flip(is));

X=[xmin;xmax]; Y=[yg;flip(yg)];

scatter(x,y,'.');hold on
plot(X,Y,'r-x'); hold off

[Zac Lee]

Dear @Matt J, thank you verymuch for your help. it seems working

Answer 2

[Star Strider]

The boundary function or related functions can probably help with this.

Since the data appear to have stepwise y-values, another option would be to get the x-values at each y-value. This could be a problem between y-values 0.02 to 0.027 since those x-values are discontinuous. Depending on how your data are presented, that could be either straightforward or somewhat difficult.

Without your data and the code you used to create that plot, I cannot experiment with either of these approaches.

EDIT -- Corrected typographical errors.

.

Answer 3

[Catalytic]

load xy

x=x(:)/1000; y=y(:);

r=median(diff(unique(y)));


shp=alphaShape([x,y],r*.8);
[~,P]=boundaryFacets(shp);

scatter(x,y,'.b'); hold on
plot(P(:,1),P(:,2),'r.--'); hold off

[Zac Lee]

Dear @Catalytic, thank you verymuch for your help

[Zac Lee]

isn't there anyway to do not scale the values? I'm trying to combine both this solution and the one from @Matt J, in order to get the right pic.

[Catalytic]

If you increase the sampling density in the region y<0.005, as I mentioned in my comment above, then there would be not need to incorporate a second method.

load xy

x=x(:); y=y(:);

r=median(diff(unique(y)));

s=1000;
shp=alphaShape([x/s,y],r*.8);
[~,P]=boundaryFacets(shp);
P(:,1)=P(:,1)*s;


scatter(x,y,'.b'); hold on
plot(P(:,1),P(:,2),'r.--'); hold off

●

[Zac Lee]

Perfect! Tnak you verymuch for your help