How to extract points from a 3D plot that fall within a particular distance from the center coordinate?

Hello, I am a novice in matlab programmming. I am working on a computational project where I have a 3dimensional plot with thousands of points. Now I would like to fix one point having coordinate (x,y,z). At a particular distance r as a cutoff from (x,y,z), I would like to extract all the points in the plot that fall within the distance (or radius) r. I am not sure of how i can use euclidean distance formula for this. Please help me out.

Thanks in advance.

Answer 1

[Wan Ji]

If you have Coor is a n by 3 matrix as the coordinates of n points in 3d space and a fixed point (x,y,z). Then the points within the distance r can be obtained by

p = sqrt((Coor(:,1)-x).^2 + (Coor(:,2)-y).^2 + (Coor(:,3)-z).^2)<r;
Coor_withindistance_r = Coor(p,:);

[sai sai]

Thank you :)

[sai sai]

@Wan Ji I also have another doubt. If i wish to create a distribution chart (histogram) for the number of coordinates with distance r, I must create a for loop to store all values as a matrix. But I am not clear on how I can append the all the coordinates as a matrix in the matlab workspace. Please do help. Thank you.

function[] = Coordinates(X,Y,Z,Coor)
for r = 1:10
    p = sqrt((Coor(:,1)-X).^2 + (Coor(:,2)-Y).^2 + (Coor(:,3)-Z).^2)<r;
    Coor_withindistance_r = Coor(p,:);
end
Coor_withindistance_r;

[Wan Ji]

function [coor_num, neighbors_with_r] = Coordinates(X,Y,Z,Coor)
r = 1:10;
coor_num = zeros(length(r),1);
neighbors_with_r = cell(length(r),1);
for i = 1:1:length(r)
    p = sqrt((Coor(:,1)-X).^2 + (Coor(:,2)-Y).^2 + (Coor(:,3)-Z).^2)<r(i);
    Coor_withindistance_r = Coor(p,:);
    coor_num(i) = size(Coor_withindistance_r, 1);
    neighbors_with_r{i,1} = Coor_withindistance_r;
end
end

This may work, it returns the numbers of coordinates with different distance r (an array), and returns their coordinates. @sai sai

[sai sai]

Thank you so much

Answer 2

[Turlough Hughes]

The points which are within a radius, r, from the origin can be obtained as follows:

index = sum(X.^2,2) < r^2; %  X is an n by 3 array of points
Xthresh = X(index,:);

Note, squaring r is more efficient than taking the square root for ALL of the points in X.

For a starting point other than the origin, e.g. p (1 by 3), points in X within a threshold radius r from the point p can be obtained as follows:

index = sum(X.^2 - p,2) < r^2;
Xthresh = X(index,:);

[sai sai]

Thank you