MATLAB: How to draw a perfect circle and distance calculation

circledistanceknnsearchrangesearchStatistics and Machine Learning Toolbox

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.

Best Answer

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.
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