Polar Plot Axis is Off Center from and not Scaled with Background Image

I am trying to plot acceptable values of saturation on an HSV Color Wheel, but the polar plot is not centered on the background image. Anyone have any good ways to get the radius right and improve the plot to be centered on the background?

minS = 15;

maxS = 30;

minH = 50; %because yellow is apparently yucky

c = (-1*minS+maxS)/2;

a = maxS-c;

ellipticity = c/a;

parameter = a*(1-ellipticity^2);

theta = 0:0.1:360;

rho = parameter./(1-ellipticity.*cosd(theta - minH + 180));

rows = 500;

columns = 500;

midX = columns / 2;

midY = rows / 2;

% Construct v image as uniform.

v = ones(rows, columns);

s = zeros(size(v)); % Initialize.

h = zeros(size(v)); % Initialize.

% Construct the h image as going from 0 to 1 as the angle goes from 0 to 360.

% Construct the S image going from 0 at the center to 1 at the edge.

for c = 1 : columns

for r = 1 : rows

% Radius goes from 0 to 1 at edge, a little more in the corners.

radius = sqrt((r - midY)^2 + (c - midX)^2) / min([midX, midY]);

s(r, c) = min(1, radius); % Max out at 1

h(r, c) = atan2d((r - midY), (c - midX));

end

end

% Flip h right to left.

h = fliplr(mat2gray(h));

% Construct the hsv image.

hsv = cat(3, h, s, v);

rgbImage = hsv2rgb(hsv);

% Display the RGB image.

fig = figure;

subplot(1,1,1);

imshow(rgbImage, []);

drawnow;

polaraxes("Color","none");

hold on;

theta_radians = deg2rad(theta);

polarplot(theta_radians,rho,'black');

rlim([0, 100]);

Answer 1

[yanqi liu]

minS = 15;
maxS = 30;
minH = 50; %because yellow is apparently yucky
c = (-1*minS+maxS)/2;
a = maxS-c;
ellipticity = c/a;
parameter = a*(1-ellipticity^2);
theta = 0:0.1:360;
rho = parameter./(1-ellipticity.*cosd(theta - minH + 180));
rows = 500;
columns = 500;
midX = columns / 2;
midY = rows / 2;
% Construct v image as uniform.
v = ones(rows, columns);
s = zeros(size(v)); % Initialize.
h = zeros(size(v)); % Initialize.
% Construct the h image as going from 0 to 1 as the angle goes from 0 to 360.
% Construct the S image going from 0 at the center to 1 at the edge.
for c = 1 : columns
	for r = 1 : rows
		% Radius goes from 0 to 1 at edge, a little more in the corners.
		radius = sqrt((r - midY)^2 + (c - midX)^2) / min([midX, midY]);
		s(r, c) = min(1, radius); % Max out at 1
		h(r, c) = atan2d((r - midY), (c - midX));
	end
end
% Flip h right to left.
h = fliplr(mat2gray(h));
% Construct the hsv image.
hsv = cat(3, h, s, v);
rgbImage = hsv2rgb(hsv);
% Display the RGB image.
fig = figure;set(gca, 'units','normalized','position',[0,0,1,1])
imshow(rgbImage, []); 
drawnow;
polaraxes("Color","none");
hold on;
theta_radians = deg2rad(theta);
hp2 = polarplot(theta_radians,rho,'black');
rlim([0, 100]);