MATLAB, How to visualize my directional beam Data - matlab

Question

I've made an experiment with directional beams and I would like to visualise it. The set-up was like this:
I've measured my values at 22, 15, 10, 5 and 0 degrees in a distance of 100, 75, 50 and 25 cm.
Now I would like to bring this Data into a 3D waterfall() diagram where the source is the highest peak and you can see that the voltage decreases in all directions.
So my first thought was to fit all distances individually and these functions I would like to put them into the waterfall(). But this doesn't work very well, because the begin and end different layers of values (have a look at the example code) after I calculate them to the x, y system was different.
So, how can I bring my data into a waterfall diagram?
clearvars
x=-1:0.1:1;
%________________________________________________________measured Values (layers)
A=[208; 256; 480; 704; 776; 752; 672; 480; 264]; % 0.25m
B=[104; 156; 304; 388; 432; 440; 340; 280; 140]; % 0.50m
C=[ 54; 104; 250; 264; 320; 270; 252; 144; 70]; % 0.75m
D=[ 32; 64; 142; 198; 228; 208; 130; 86; 46;]; % 1.00m
% plot(A)
% figure(2)
% plot(B)
% figure(3)
% plot(C)
% figure(4)
% plot(D)
%________________________________________________________to x,y System
dist1=[tand(-22)*0.25; tand(-15)*0.25; tand(-10)*0.25; tand(-5)*0.25; tand(0)*0.25; tand(5)*0.25; tand(10)*0.25; tand(15)*0.25; tand(22)*0.25;];
dist2=[tand(-22)*0.50; tand(-15)*0.50; tand(-10)*0.50; tand(-5)*0.50; tand(0)*0.50; tand(5)*0.50; tand(10)*0.50; tand(15)*0.50; tand(22)*0.50;];
dist3=[tand(-22)*0.75; tand(-15)*0.75; tand(-10)*0.75; tand(-5)*0.75; tand(0)*0.75; tand(5)*0.75; tand(10)*0.75; tand(15)*0.75; tand(22)*0.75;];
dist4=[tand(-22); tand(-15); tand(-10); tand(-5); tand(0); tand(5); tand(10); tand(15); tand(22)];
plot(dist1,A)
figure(2)
plot(dist2,B)
figure(3)
plot(dist3,C)
figure(4)
plot(dist4,D)
% func1= fit(dist1,A,'poly2')
%
% plot(dist1, func1(dist1))
Furthermore:
As a result I would like to create something like this:
http://de.mathworks.com/help/matlab/ref/waterfall.html
or maybe a surface:
http://de.mathworks.com/help/matlab/ref/surf.html
But I don't know how I can convert my current data into a format, which fits the requirements of the waterfall() or surf() function

Answer 1

It's all about organizing your data. As Daniel said, waterfall (or even surf for that matter) require a mesh as input (your data need to be matrices).
So let's build a proper mesh with your data:
%% // measured Values (layers)
A = [208; 256; 480; 704; 776; 752; 672; 480; 264] ; %// 0.25m
B = [104; 156; 304; 388; 432; 440; 340; 280; 140] ; %// 0.50m
C = [ 54; 104; 250; 264; 320; 270; 252; 144; 70] ; %// 0.75m
D = [ 32; 64; 142; 198; 228; 208; 130; 86; 46] ; %// 1.00m
%% // Building the mesh
%// primary parameters
x = (0.25:0.25:1).' ; %'// ignore that comment
angles = [-22 -15 -10 -5 0 5 10 15 22] ;
%// mesh matrices
X = x * ones(1,numel(angles)) ; %// distance to source
Y = x * tand(angles) ; %// lateral spread due to angle
V = [A B C D].' ; %'// measurements (voltages)
At this point, you have 3 matrices X,Y and V which are perfect input for most 3D graphing functions like surf or waterfall. So it becomes quite straightforward:
%% // Waterfall visualisation
hf = figure ;
hw = waterfall(X,Y,V) ;
If you want to add some refinements :
%% // refinements
shading interp
xlabel('Distance to source')
ylabel('Lateral spread')
zlabel('Voltage')
hold on
plot3(0,0,0,'or','MarkerSize',10,'LineWidth',4) %// show the source position
and/or even more information on the figure:
%% // displays the base rays
xrays = [0;x] ;
yrays = [zeros(1,numel(angles)) ; Y] ;
set(0,'DefaultAxesColorOrder',[0 0 0] , 'DefaultAxesLineStyleOrder','--|:' )
plot(xrays,yrays,'Marker','.')
At this stage, it yields the following figure, but you can keep it simple or adjust many other properties of all the graphic object to personalize your display:
You can also play with the surf function instead of waterfall, and use the same matrices as input.
Another way to better link the voltage recorded for every sensor position would be to use a stem plot. Unfortunately the stem function does not take 3D arrays as input, however, the ZData property still exist so we can instantiate the stem plot first then loop through them to set their ZData:
%% // STEM waterfall variant
hsf = figure ; hold on
hs = stem(X.',Y.',':ob') ;
for k=1:4
set(hs(k),'ZData',V(k,:))
end
With all the refinements above, it yields:
This variant doesn't color code the voltage but it shows exactly the position where it was recorded.

Answer 2

Easiest way is to mesh your data first (i.e. put them in X, Y and Z matrices):
%Z:
dist1234=[dist1 dist2 dist3 dist4];
%Y:
ABCD=[A B C D];
%X:
[n1,n2]=size(ABCD);
X=repmat(1:n2,n1,1); % or whatever your x-axis is, here it is 1, 2, 3...
% Take your pick:
figure(1)
surf(X,dist1234,ABCD);title('surf')
figure(2)
waterfall(X',dist1234',ABCD');title('waterfall')
figure(3)
mesh(X,dist1234,ABCD);title('mesh')