plot the 2d and 3d c-planes of a light distribution curve in matlab

Question

I would like to plot the C-planes that describe the light distribution curve (ldc) of a light source in 2D and 3D space respectively. Usually the manufacturers provide the details of the ldc in polar coordinates. An example can be seen below:

together with the graph (the red lines solid/dashed represent the C-planes)

the above 2D plot can be plotted in simulation software quite nicely as you can see in the images below:

Now if it is possible I would like to plot the same graphs/plots in matlab as well. However, I am not sure how to do it. For the 2D graph I had a look at the polarplot() function but I am not sure what my input should be based on my matrix. Regarding the 3D plot, totally no clue how I could get the plot in 3D space. Therefore, if someone could provide me with some hints or a solution it would be really helpful. Below are the values of the above matrix in case someone wants to experiment with it.

Many thanks in advance.

---

Update:

Ok plotting the 2D polar diagram can be achieved with the following code:

ldc = [426.0060  426.0060  426.0060  426.0060  426.0060  426.0060  426.0060
  424.7540  425.0980  425.5810  425.9940  425.6490  425.1670  424.7540
  421.8600  422.2040  422.7550  423.1690  422.6860  422.2040  421.8600
  415.5200  416.0020  416.1400  416.8980  416.6910  416.2780  415.7960
  408.6290  406.9060  407.0440  408.0090  409.0420  407.3890  406.5620
  394.1580  394.2960  394.5030  395.1920  395.0540  394.5720  394.5720
  374.5880  375.8290  376.9310  376.6550  374.6570  376.3800  377.4820
  349.7810  351.3660  352.8130  351.9170  350.7460  352.1930  353.9150
  317.8070  316.2910  318.2210  316.2910  316.8420  317.1870  319.8750
  267.2280  269.4330  264.4720  267.9170  267.9170  269.6400  266.1260
  200.4280  162.1010  174.1260  163.2380  199.5320  163.8650  174.8770
  111.4940  118.7160  150.0280  118.3780  112.6450  116.1870  151.6540
   73.5810   78.4390   99.5180   80.3960   75.7450   78.4250  100.4280
   49.7660   69.2120   54.2240   71.2930   52.1980   71.8860   56.8360
   35.5290   49.5180   46.4930   48.3810   35.8390   47.2780   48.2220
   34.3720   37.9410   35.3290   38.5750   33.9930   39.9950   35.4050
   24.1730   24.9380   28.9690   25.8750   24.7800   24.6350   28.5140
   14.3050   15.9870   19.6670   16.4830   15.1460   15.9450   19.7770
    6.0920    6.5390    7.0420    7.2350    6.9940    6.8220    6.6840
    4.7550    4.9550    5.2780    5.2160    5.2090    5.4780    5.6640
    3.8590    3.8520    3.8930    3.9000    3.8870    4.3210    4.4380
    3.1150    3.1420    2.9350    2.8530    3.0870    3.4660    3.5970
    2.8670    2.6670    2.4740    2.3500    2.5700    2.9290    3.1700
    2.4120    2.4050    2.3360    2.0330    2.3500    2.6050    2.7840
    1.6540    1.6670    1.9090    1.8880    1.7300    1.5920    1.6810
    1.1300    1.1990    1.2680    1.4880    1.2270    1.1580    1.1300
    1.0470    1.0400    1.0400    1.1440    1.0750    1.0540    1.0470
    1.1300    1.1640    1.2060    1.1850    1.2130    1.1850    1.1710
         0         0         0         0         0         0         0
         0         0         0         0         0         0         0
         0         0         0         0         0         0         0
         0         0         0         0         0         0         0
         0         0         0         0         0         0         0
         0         0         0         0         0         0         0
         0         0         0         0         0         0         0
         0         0         0         0         0         0         0
         0         0         0         0         0         0         0];

color = 'r';
line = '-';
% plotting only the first and the last C-planes, i.e. 0 and 90 degrees respectively
for i = 1:6:size(ldc,2)
    polarplot(degtorad(theta),ldc(:,i), 'Color', color, 'LineStyle', line, 'LineWidth', 1.5)
    hold on
    polarplot(-degtorad(theta),ldc(:,i), 'Color' ,color, 'LineStyle', line, 'LineWidth', 1.5)
    line = ':';
end

ax = gca;
ax.ThetaZeroLocation = 'bottom';
ax.RAxisLocation = 0;
ax.ThetaTickLabel = {'0'; '30'; '60'; '90'; '120'; '150'; '180'; '150'; '120'; '90'; '60'; '30';};

Answer 1

I have not tried this but you could convert your polar coordinates into cartesian ones using pol2cart, then add the third dimension and use fill3 to render the surface.

Ok, I'm procrastinating and implemented it here:

% range of angles
angles = 0:0.01:(2*pi);

% light intensity example (insert values from table)
r = 1 + sin(angles);

% convert to cartesian coordinates
[p1, p2] = pol2cart(angles, r);

% plot on x-axis (x=0)
X = zeros(size(p1));
Y = p1;
Z = p2;
C = ones(size(Z)); % color input needed
fill3(X,Y,Z,C)
hold on

% plot on y-axis (y=0)
X = p1;
Y = zeros(size(p1));
Z = p2;
C = ones(size(Z))+1;
fill3(p1,zeros(size(p1)),p2,C)

xlabel('x')
ylabel('y')
zlabel('z')
grid on

For your specific dataset, you can do the following

% angles around x-axis, need to turn by 90 degree right pol2cart output
anglesX = (0:5:360)/180*pi+pi/2;

% angles around z-axis
anglesZ = 0:15:90; 

% loop over columns
for i = 1:size(ldc,2)

    % you need to create a closed contour for fill3
    ldcJoined = [ldc(:,i);ldc((end-1):-1:1,i)];

    % plot for positive and negative angle around z, i as color-index
    plotPlane(anglesX, ldcJoined, anglesZ(i), i)
    hold on
    plotPlane(anglesX, ldcJoined, -anglesZ(i), i)
end

xlabel('x')
ylabel('y')
zlabel('z')

function [] = plotPlane(anglesX, r, angleZ, c)

    % convert to cartesian coordinates
    [p1, p2] = pol2cart(anglesX, r');

    % plot on x-axis (x=0)
    X = zeros(size(p1));
    Y = p1;
    Z = p2;
    C = ones(size(Z)) .* c; % color input needed, you could e.g. C=sin(angles);
    h = fill3(X,Y,Z,C);
    rotate(h, [0,0,1], angleZ)

end

Which gives