-fmesh- face and edge color different for neg, 0, pos Z values

Hi folks!

I am making a 3-D plot using -fmesh-.

I would like to make the face and edge colors different for negative, zero, and positive Z values.

I have tried the following so far:

s=fmesh(@(X,Y) X./(Y.*(1-X)-1));
s.FaceColor = 'interp';
s.EdgeColor = 'white';
EC = s.EdgeColor;
FC = s.FaceColor;

But, I am not sure how to creat the conditional statement to access 1x1 FunctionSurface to make these changes.

I tried something like below, which did not work, but the idea was to possibly plot only positive ZData values.

s.ZData = s.ZData(s.ZData >= 0);

What I want to obtain are:

1. Have three distinct -s.EdgeColor- and -s.FaceColor- for negative, zero, and positive Z values.
2. Draw three separate -fmesh- plots only for negative, zero, and positive Z values all separately.

Thanks in advance!

Answer 1

[Walter Roberson]

You can color by z by creating a colormap that divides the range up into segments, and setting the first half to the color for negative, the last half to the color for positive, and the middle to the color for zero.

Note that this will end up plotting a range of values with the zero color, rather than the values that are exactly zero.

FunctionSurface objects do not have the ability to set the color for individual locations.

s=fmesh(@(X,Y) X./(Y.*(1-X)-1));
s.FaceColor = 'interp';
s.EdgeColor = [0 .3 0];

[minz, maxz] = bounds(s.ZData(:));
zrange = max(abs([minz, maxz]));

negcol = [0 0 0.7];
zcol = [.8 .8 .8];
poscol = [.7 0 0];
cmap = repelem( [negcol; zcol; poscol], [127 1 128], 1);
caxis([-zrange zrange]);
colormap(cmap)

[Tatte Berklee]

Hey Walter, thanks a lot for your help. It makes a lot more sense how you access my three category criteria with -abs- and -bounds-.

Just a quick question on your actual plot. If you tilt what you coded and see from the bird's eye-view (i.e. XY-axis contour plot), you see a lot of zigzags.

Does this mean the contour map of is not smooth or is it just that our grid points are too coarse that we see these unsmooth parts? In your colored definitions, we see a lot of cusps on the contour map.

For instance, see by adding this domain lims:

ylim([0 1]);

xlim([-1 1]);

[Walter Roberson]

syms X Y real;
Z = X./(Y.*(1-X)-1);
fsurf(Z, [-1 1 0 1])

Consider Y(1-X)-1 . If the expression comes out as 0, then you would have a division by 0, and so not a smooth contour.

We can solve:

[N, D] = numden(Z);
solve(D == 0, Y)

ans = 

So if Y = -1/(X-1) then you will have a division by 0

[Tatte Berklee]

Hi Walter, this is super helpful. Thanks a lot! The analytic solution part using solve also helped me to see it through!

[Tatte Berklee]

Walter, just the last bit here,

1. do you know what might be the best way to put the legend to indicate what I originally tried to achieve which is to have three distinct colors for negative, zero, and positive? What might be the best way to incorporate this information compactly on a legend with the plot?
2. In the analytic solution approach, given the domain of Y is [0,1] and X is [-1, 1], is there a way to analytically or plot-wise show which values satisfy ? I would like to show in both ways to show that in the given domain, this expression is satisfied in a certain set of pairs (X,Y) that the expression is satisfied thus have a division by 0.
3. Is there a way that I can indicate the demarcation line where Z=0? Before, I tried the following when I used -contourf-, but I am not sure what would be the relevant Levelist for -fmesh-:

[C, h]=contourf(X,Y,Z);

Lvls = h.LevelList;

clabel(C,h, Lvls(Lvls = 0));

[Walter Roberson]

Unfortunately there is no easy way to have multiple legends for the same object. You end up having to create dummy objects off-screen that have the legend properties you want.

Boundary has been marked in the plot below.

s=fmesh(@(X,Y) X./(Y.*(1-X)-1));
s.FaceColor = 'interp';
s.EdgeColor = [0 .3 0];

xd = s.XData;
yd = s.YData;
zd = s.ZData;

[minz, maxz] = bounds(zd(:));
zrange = max(abs([minz, maxz]));
caxis([-zrange zrange]);

negcol = [0 0 0.7];
zcol = [.8 .8 .8];
poscol = [.7 0 0];
cmap = repelem( [negcol; zcol; poscol], [127 1 128], 1);

colormap(cmap)

hold on
nan2 = nan(2,2);
h(1) = surf(nan2,nan2,nan2, 'facecolor', negcol);
h(2) = surf(nan2, nan2, nan2, 'facecolor', zcol);
h(3) = surf(nan2, nan2, nan2, 'facecolor', poscol);

tolerance = 1e-2;
mask = abs(yd .* (xd - 1) + 1) < tolerance;
bx = xd(mask);
by = yd(mask);
bz = zeros(size(bx));

scatter3(bx, by, bz, 50, 'g+');

hold off

legend(h, {'Negative', 'Zero', 'Positive'})

[Walter Roberson]

[C, h]=contourf(X,Y,Z);

You cannot do that directly. fmesh() gives you vectors of XData and YData and ZData, but for contourf() you need to have 2D arrays of data.

You could switch out of using fmesh() into creating your own grids and using contour3(), but if you wanted to proceed with fmesh() you would have to use scattered interpolant techniques to create the data to contour

[Tatte Berklee]

This was super helpful, thanks a lot, Walter!