Do the isosurfaces merely indicate a single value or do they contain information on all the value above the threshold?

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saipb 2019-9-17

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https://ww2.mathworks.cn/matlabcentral/answers/480838-do-the-isosurfaces-merely-indicate-a-single-value-or-do-they-contain-information-on-all-the-value-ab

回答： darova 2019-9-19

When I use the isosurface command with a specific value (say corresponding to 95th percentile of my data), I am interesting in viewing the regions that correspond to values equal to and greater than the 95th percentile. My question is: Using Matlab's default isosurface return (see below for portion of code), is the surface just equal to the 95th percentile? If I want Matlab to plot all the regions above the 95th percentile threshold, should I plot multiple isosurfaces of 95th, 96th...99th percentiles?

isovalue = prctile(sgs(:),95);

p = patch(isosurface(x,y,z,sgs,isovalue));

p.FaceColor = 'magenta';

p.EdgeColor = 'none';

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John D'Errico 2019-9-17

An iso-surface represents that surface where the value (here a percentile) is equal to the designated value. So if it is the 95% level, then that is what the surface represents, and nothing else.

Is it generally a truism that stuff on one side of that percentile will be above, and stuff on the other side will be below? Well, yes. Can I create a scenario where that is not true? Well, yes, I am confidant in my ability to do so. But typically, one would say the iso-surface will USUALLY represent the boundary of the region that you are interested in. Worse, the iso-surface does not even indicate on which side of the surface the part you care about lies.

saipb 2019-9-17

John,

I understand that there are different options and I certainly do not intend to question your ability to create different scenarios. I am trying to understand what the default option in Matlab is if I write the following code:

pile = 95;

isovalue = prctile(w(:),pile);

m = patch(isosurface(x,y,z,w,isovalue));

m.FaceColor = 'red';

m.EdgeColor = 'none';

m.FaceAlpha = '0.6';

And I see surfaces like: