BIVA ellipse incorrect when rotated / sizing issue

Ive generated an ellipse and successfully rotated it about a fixed point. My problem is that the resulting rotated ellipse is much too large, with the axiis being much too large

my graph vs expected graph

Furthermore, I am working off the expected given values from the expected graph

with given semi-major, and semi-minor axii given

Im unsure what i've done wrong and just want to know if its an error with the paper or with my script

clear all;
close all;

% Creates the varaibles for the average mens impedance values:
load("mens_average_impedance_20t69_19t25.mat");

% creates AD5933 data variables:
load("Test1_Data_Averages.mat");

x = 0:RH_mean;
y = (XcH_mean / RH_mean) * x;

Height = 1.778;
GF = 93.089e-9;
% calculate Z score
ZR = ((Re_mean/Height)- (R_mean/Height)) / R_sd
ZXc = ((abs(Im_mean)/Height) - (Xc_mean/Height)) / Xc_sd

% Generate Rotation Matrix
rot_major = 68.68;
rot_minor = -21.32;

rot_matrix = [cosd(rot_major), sind(rot_major); ...
    -sind(rot_major), cosd(rot_major)];


% Generate Ellipses
C = [RH_mean, XcH_mean] ;  % center 
a_95 = 161;      % major axis 
b_95 = 62;       % minor axis 
a_75 = 110;      % major axis 
b_75 = 42;       % minor axis 
a_50 = 77;       % major axis 
b_50 = 30;       % minor axis 
th = linspace(0,2*pi) ; 

% 95% tolerance Elipse
xe_95 = C(1)+a_95*sin(th) ; 
ye_95 = C(2)+b_95*cos(th) ; 
xe_95_alligned = [xe_95 - C(1); ye_95 - C(2)]';
xe_95_shift = xe_95_alligned * rot_matrix;
% 75% tolerance Elipse
xe_75= C(1)+a_75*cos(th) ; 
ye_75 = C(2)+b_75*sin(th) ; 
xe_75_alligned = [xe_75-C(1); ye_75-C(2)]';
xe_75_shift = xe_75_alligned * rot_matrix;
% 50% tolerancee Elipse
xe_50 = C(1)+a_50*cos(th) ; 
ye_50 = C(2)+b_50*sin(th) ; 
xe_50_alligned = [xe_50-C(1); ye_50-C(2)]';
xe_50_shift = xe_50_alligned * rot_matrix;

% plot
plot(xe_95_shift(:,1)+C(1),xe_95_shift(:,2)+C(2), "r")

hold on

plot(C(1), C(2), "b*")
%plot(ZR, ZXc,"b*")
% plot(xe_95, ye_95, "k")
% plot(xe_75, ye_75, "k")
% plot(xe_50, ye_50, "k")
plot(x,y, "k")
plot(xe_75_shift(:,1)+C(1), xe_75_shift(:,2)+C(2), "r")
plot(xe_50_shift(:,1)+C(1), xe_50_shift(:,2)+C(2), "r")

xlabel("R/H, Ohm/m");
ylabel("Xc/H, Ohm/m");

Please let me know your thoughts, and if you have any issues running the code

Answer 1

[Tushar]

Hi Lachlan,

I understand that you are trying to plot an ellipse with respect to the data present in the MAT-files attached along. Here are some possible reasons for the issue:

1. Inconsistency in axes alignment: The current plot doesn't match the expected figure in terms of axis scales and positioning.
2. Ellipse distortion along the y-direction: The ellipse is similar to the expected figure in the x-direction, but blown out along the y-direction.

To address the first issue, you can try using the following lines of code:

% Plot the ellipse first

% Specify axis ticks and limits as shown in the expected figure attached
xlim([0 500]);
xticks([0:100:500]);
ylim([0 70]);
yticks([0:10:70]);
xlabel("R/H, Ohm/m");
ylabel("Xc/H, Ohm/m");

Here are some observation regarding the second issue:

• It seems that variables like 'RH_mean' and 'XcH_mean' differ among different groups of people (e.g., 'Non-Hispanic white,' 'Non-Hispanic black'). However, the imported variables from the provided MAT-files are consistent across these groups. Please verify this discrepancy.
• Could you explain the 'Re_mean' variable, since it is not present in the tables attached.
• The rotation matrix appears to be correctly implemented, so there should not be any issues related to rotation.

I am attaching the following reference material/documentation to help you taking this forward -

• Specify Axis Tick Values and Labels
• Set the x-axis, y-axis limits for a plot

With these resources, I believe you can make the necessary adjustments to achieve your desired ellipse plot.

Regards,

Tushar