How to find all points that are a certain distance away from one point.

I have a large set of 10,000 points defined as A. How can I find all points in A, that are an exact distance away from a point I?

[Jala Douglas]

What is the code you used to define 'A' ?

Answer 1

[Image Analyst]

Just use the Pythagorean theorem then use logical indexing

allDistances = sqrt(Ax-ix).^2 + (Ay-iy).^2);
% Find points with 0.1 tolerance of 398.453 away from point (ix,iy)
tolerance = 0.1;
farAwayIndexes = abs(allDistances - 398.453) < tolerance;

Why did I use a tolerance when you said "exact"? Because there rarely is "exact" for floating point calculations. Why? See the FAQ: http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

Answer 2

[Matt J]

I'll assume all the points are column vectors

   distances = sqrt( sum( bsxfun(@minus,A,I).^2 ,1) );

   find(abs(distances-givendistance)<=tolerance)

Answer 3

[Star Strider]

Or, you can use the inpolygon function:

xy = rand(1E+4, 2);                         % Create Random Points

r    = 0.20;                                % Radius
xctr = 0.35;                                % Center Point ‘x’
yctr = 0.65;                                % Center Point ‘y’
th   = linspace(0, 2*pi)';
circ = [xctr + r*cos(th),  yctr + r*sin(th)];

[~,on] = inpolygon(xy(:,1), xy(:,2), circ(:,1), circ(:,2));
on_circ = nnz(on);                          % Number Of Points On Circle

figure(1)
plot(xy(:,1), xy(:,2), '.r')
hold on
plot(xctr, yctr, 'bp', 'MarkerFaceColor','b')
plot(xy(on,1), xy(on,2), 'gp', 'MarkerFaceColor','g')
hold off