How to draw a perfect circle and distance calculation

Hi,

I got 2 issues:

1. to draw a perfect circle
2. to calculate a perfect distance

This is my code:

load fisheriris
rng(1); % For reproducibility
n = size(meas,1);
idx = randsample(n,1)
X = meas(~ismember(1:n,idx),3:4); % Training data
Y = meas(idx,3:4) 

MdlKDT = KDTreeSearcher(X)  % not used by mahanalobis
MdlES = ExhaustiveSearcher(X) % Prepare an exhaustive nearest neighbors searcher.

r = 0.3; % Search radius
IdxKDT = rangesearch(MdlKDT,Y,r)
IdxES = rangesearch(MdlES,Y,r)
[IdxKDT IdxES]
cellfun(@isequal,IdxKDT,IdxES)

figure;
plot(X(:,1),X(:,2),'.k');
hold on;
plot(Y(:,1),Y(:,2),'*r');
Mdl = KDTreeSearcher(X)
[n,d] = knnsearch(Mdl,Y,'k',10);
ctr = Y - d(end);
diameter = 2*d(end);
% Draw a circle around the 10 nearest neighbors.
h = rectangle('position',[ctr,diameter,diameter],...
   'curvature',[1 1]);
h.LineStyle = ':';

If i used the fisheriris data, it is works well. But if i'm using Faithful Geyser data (the data as in the attachment), the circle becomes weird. The distance calculation as shown in second picture with yellow color also effected where the data points do not lie within a circle.. This is the code to apply the faithful data:

faithfuldat = xlsread('faithful.csv');
fData = faithfuldat(:,:);
[n,dim]=size(fData);

idx = randsample(n,1)
X = fData(~ismember(1:n,idx),:); % Training data
Y = fData(idx,:)

The distance code i used from this link: https://stackoverflow.com/questions/27475978/finding-k-nearest-neighbors-and-its-implementation/27476929#27476929

I really appreciate if anyone could advice me how to improve the circle and distance.

Answer 1

[Image Analyst]

To draw a circle, you can use rectangle(), viscircles(), or the FAQ: http://matlab.wikia.com/wiki/FAQ#How_do_I_create_a_circle.3F

Add

axis equal;

to your code after you plot to make your circles look circular on the screen.

[amj]

Dear Image Analyst,

I had applied axis equal and i got this output:

I also referred to the given link but it does not work. This is the codes:

for j = 1:length(Y)
     c = Y(j,:);
     circleFun = @(x1,x2)r^2 - (x1 - c(1)).^2 - (x2 - c(2)).^2;
     %%option 1
     %%------
     %fimplicit(circleFun,[c(1) + [-1 1]*r, c(2) + [-1 1]*r]);
      %%option 2
      %%------
     %ezplot(circleFun,[c(1) + [-1 1]*r, c(2) + [-1 1]*r]);
      %%option 3
      %%------
%      radius = r; 
%     centerX = c(1);
%     centerY = c(2);
%     rectangle('Position',[centerX - radius, centerY - radius, radius*2, radius*2],...
%         'Curvature',[1,1],...
%         'FaceColor','r');
%%option 4
%%------
% c = [3, 4];
% %r = 2;
% pos = [c-r, 2*r 2*r];
% annotation('ellipse', pos );
end

All the options code yield output as above. Really appreciate if i can get any advice.

[Image Analyst]

OK. Looks right - your circle is now round after using "axis" equal. Thanks for Accepting the answer.

But you may want to get rid of so much plot along the x axis by using xlim():

xlim([0, 10]);

[amj]

Thank you Image Analyst,

Let me try

[amj]

Dear Image Analyst, It is still appears the same result.

[Image Analyst]

Looks like you didn't call axis equal on that plot so your circles still show up as ellipses on the screen, even though they are circles in the data space. Obviously if you stretch your graph one way or the other, your circles will change shape. I hope you understand this.

[amj]

Dear Image Analyst, I really do apologize. I dont get your points. Or does it mean, the min / max on axis based on the data?

[Image Analyst]

You didn't call axis equal so the scales on x and y don't match. Look at your y axis - it goes from 40 to 100, a range of 60. Now look at your x axis - it goes from 1 to 6, a range of 5. So your x axis is magnified compared to your y axis. Let's say you have a circle centered at x=2, y=60 with radius 1. So the circle goes from 1 to 3, a diameter of 2 which is 1/3 of the x axis range. But in the vertical direction, the circle goes from 59 to 61, again a range of 2. However 2 is only 1/30 of the vertical y axis size, not 1/3 so it's much, much narrower in the y direction. That's why it looks like an ellipse. Basically you're squashing your graph vertically to get it to fit in the same space as your horizontal space. So the circle gets squashed. If you do axis equal, it prevents squashing and the circle will truly be a circle.

[amj]

Yeah, it is indeed true. It is because the faithful data has different range of data compared to Iris data. I have been exploring on how to improve/combine with the range, still could not find the best solution

[Image Analyst]

If you want it to display as a circle despite the axes not being equal, you have to scale the height of the circle in rectangle() by the ratio of the two axes lengths, which you can get with xlim() and ylim().

[amj]

Dear image analsyt,if so, i would try tomorrow. i have been trying since his morning. I'm still could not fix it

[amj]

Dear Image Analyst,

I referred from his link: https://stackoverflow.com/questions/33555369/automatically-resizing-a-custom-plotting-character

I modified the code:

xx = (range(diff(X(:,1))))
yy = (range(diff(X(:,2))))
ratio = (xx / yy) /sqrt(2)
for j = 1:length(Y)
     c = Y(j,:)
     Yx = c(1);
     Yy = c(2);
     pos = [c-r (2*r) (2*r)/ratio];
     rectangle('Position',pos,'Curvature',[1 1])
end
axis([1 5.5 45 95])

Unluckily, the central points are not lie in center part. If you could advice an improvement, i would be grateful