finding the distance between two points

prompt = "enter the number of elements to make";
x = input(prompt);

Unable to run the 'fevalJSON' function because it calls the 'input' function, which is not supported for this product offering.

M = 2; 
N = x/M;
r = 1; 
R = 2;
W = linspace(r,R,M);
C = linspace(0,2*pi,N);
[R,T] = meshgrid(W,C);
X = R.*cos(T);
Y = R.*sin(T);
[m,n] = size(X)

figure 
set(gcf, 'color', 'w'); 
axis equal;
axis on; 
hold on;


for i = 1:m
    plot(X(i,:), Y(i,:), '-o');
end

for j=1:n
    G = plot(X(:,j),Y(:,j), 'b', 'linewidth', 1);
end

fprintf('the x coordinates of the nodes are')
X
fprintf('the y coordinates of the nodes are')
Y

%distance b/w two nodes

How do I find the distance between two nodes? I need to find the length of each side of the sements created (4 lengths in total).

Answer 1

[Sam Chak]

Hi @Natali Petani

You can try the function: pdist2().

https://www.mathworks.com/help/stats/pdist2.html

help pdist2

 PDIST2 Pairwise distance between two sets of observations.
    D = PDIST2(X,Y) returns a matrix D containing the Euclidean distances
    between each pair of observations in the MX-by-N data matrix X and
    MY-by-N data matrix Y. Rows of X and Y correspond to observations,
    and columns correspond to variables. D is an MX-by-MY matrix, with the
    (I,J) entry equal to distance between observation I in X and
    observation J in Y.
 
    D = PDIST2(X,Y,DISTANCE) computes D using DISTANCE.  Choices are:
 
        'euclidean'        - Euclidean distance (default)
        'squaredeuclidean' - Squared Euclidean distance
        'seuclidean'       - Standardized Euclidean distance. Each
                             coordinate difference between rows in X and Y
                             is scaled by dividing by the corresponding
                             element of the standard deviation computed
                             from X, S=NANSTD(X). To specify another value
                             for S, use
                             D = PDIST2(X,Y,'seuclidean',S).
        'cityblock'        - City Block distance
        'minkowski'        - Minkowski distance. The default exponent is 2.
                             To specify a different exponent, use
                             D = PDIST2(X,Y,'minkowski',P), where the
                             exponent P is a scalar positive value.
        'chebychev'        - Chebychev distance (maximum coordinate
                             difference)
        'mahalanobis'      - Mahalanobis distance, using the sample
                             covariance of X as computed by NANCOV.  To
                             compute the distance with a different
                             covariance, use
                             D = PDIST2(X,Y,'mahalanobis',C), where the
                             matrix C is symmetric and positive definite.
        'cosine'           - One minus the cosine of the included angle
                             between observations (treated as vectors)
        'correlation'      - One minus the sample linear correlation
                             between observations (treated as sequences of
                             values).
        'spearman'         - One minus the sample Spearman's rank
                             correlation between observations (treated as
                             sequences of values)
        'hamming'          - Hamming distance, percentage of coordinates
                             that differ
        'jaccard'          - One minus the Jaccard coefficient, the
                             percentage of nonzero coordinates that differ
        function           - A distance function specified using @, for
                             example @DISTFUN
 
    A distance function must be of the form
 
          function D2 = DISTFUN(ZI,ZJ),
 
    taking as arguments a 1-by-N vector ZI containing a single observation
    from X or Y, an M2-by-N matrix ZJ containing multiple observations from
    X or Y, and returning an M2-by-1 vector of distances D2, whose Jth
    element is the distance between the observations ZI and ZJ(J,:).
 
    For built-in distance metrics, the distance between observation I in X
    and observation J in Y will be NaN if observation I in X or observation
    J in Y contains NaNs.
 
    D = PDIST2(X,Y,DISTANCE,'Smallest',K) returns a K-by-MY matrix D
    containing the K smallest pairwise distances to observations in X for
    each observation in Y. PDIST2 sorts the distances in each column of D
    in ascending order. D = PDIST2(X,Y,DISTANCE, 'Largest',K) returns the K
    largest pairwise distances sorted in descending order. If K is greater
    than MX, PDIST2 returns an MX-by-MY distance matrix. For each
    observation in Y, PDIST2 finds the K smallest or largest distances by
    computing and comparing the distance values to all the observations in
    X.
 
    [D,I] = PDIST2(X,Y,DISTANCE,'Smallest',K) returns a K-by-MY matrix I
    containing indices of the observations in X corresponding to the K
    smallest pairwise distances in D. [D,I] = PDIST2(X,Y,DISTANCE,
    'Largest',K) returns indices corresponding to the K largest pairwise
    distances.
 
    Example:
       % Compute the ordinary Euclidean distance
       X = randn(100, 5);
       Y = randn(25, 5);
       D = pdist2(X,Y,'euclidean');         % euclidean distance
 
       % Compute the Euclidean distance with each coordinate difference
       % scaled by the standard deviation
       Dstd = pdist2(X,Y,'seuclidean');
 
       % Use a function handle to compute a distance that weights each
       % coordinate contribution differently.
       Wgts = [.1 .3 .3 .2 .1];            % coordinate weights
       weuc = @(XI,XJ,W)(sqrt((XI - XJ).^2 * W'));
       Dwgt = pdist2(X,Y, @(Xi,Xj) weuc(Xi,Xj,Wgts));
 
    See also PDIST, KNNSEARCH, CREATENS, KDTreeSearcher,
             ExhaustiveSearcher.

    Documentation for pdist2
       doc pdist2

    Other uses of pdist2

       gpuArray/pdist2    tall/pdist2

Answer 2

[Star Strider]

I am not exactly certain what you want.

Calculating the perimeters of each segment appears to be straightforward —

% prompt = "enter the number of elements to make";
% x = input(prompt);
x = 16;

M = 2; 
N = x/M;
r = 1; 
R = 2;
W = linspace(r,R,M);
C = linspace(0,2*pi,N);
[R,T] = meshgrid(W,C);
X = R.*cos(T);
Y = R.*sin(T);
[m,n] = size(X)

m = 8

n = 2

figure 
set(gcf, 'color', 'w'); 
axis equal;
axis on; 
hold on;


for i = 1:m
    plot(X(i,:), Y(i,:), '-o');
end

for j=1:n
    G = plot(X(:,j),Y(:,j), 'b', 'linewidth', 1);
end

fprintf('the x coordinates of the nodes are')

the x coordinates of the nodes are

X

X = 8×2

1.0000 2.0000 0.6235 1.2470 -0.2225 -0.4450 -0.9010 -1.8019 -0.9010 -1.8019 -0.2225 -0.4450 0.6235 1.2470 1.0000 2.0000

fprintf('the y coordinates of the nodes are')

the y coordinates of the nodes are

Y

Y = 8×2

0 0 0.7818 1.5637 0.9749 1.9499 0.4339 0.8678 -0.4339 -0.8678 -0.9749 -1.9499 -0.7818 -1.5637 -0.0000 -0.0000

%distance b/w two nodes

dX = hypot(diff(X,[],2), diff(Y,[],2));             % Radial Distances

dY = hypot(diff(X), diff(Y));                       % Circumferential Distances
dY = [dY(1,:); dY];                                 % Duplicate First Row

Perimeters = sum([2*dX dY],2)                       % Perimeters Of Each Segment

Perimeters = 8×1

4.6033 4.6033 4.6033 4.6033 4.6033 4.6033 4.6033 4.6033

.

Answer 3

[Karim]

To identify the distances between the nodes of a segment you first need to identify the nodes that make up that segment. Once you have those coordinates the distance can be determined. See below for an example. I adjusted the figure a bit to highlight the segment and the node numbers.

x = 16; % user input

M = 2; % number or radii divisions 
N = x/M; % number of angluar divisions

r = 1; % bound inner radius
R = 2; % bound outer radius
W = linspace(r,R,M); % radii for the plot
C = linspace(0,2*pi,N); % angluar segments for the plot
[R,T] = meshgrid(W,C); % combined radii (R) and angle segment (T)

X = R.*cos(T); % x coordinates for the points
Y = R.*sin(T); % y coordinates for the points

[m,n] = size(X);

% reshape the points to ease the plotting
% note that we add 'nan' to disconnect the different lines
X_circ = reshape([X;NaN(1,n)],[],1);
Y_circ = reshape([Y;NaN(1,n)],[],1);

X_seg = reshape([X,NaN(m,1)]',[],1);
Y_seg = reshape([Y,NaN(m,1)]',[],1);

% create the grid for the segment highlight
SegGrid = [X(1,1) Y(1,1);
           X(1,2) Y(1,2);
           X(2,2) Y(2,2);
           X(2,1) Y(2,1)];

% evaluate the distance
Edge_12 = sqrt( (SegGrid(1,1)-SegGrid(2,1))^2 + (SegGrid(1,2)-SegGrid(2,2))^2);
Edge_23 = sqrt( (SegGrid(2,1)-SegGrid(3,1))^2 + (SegGrid(2,2)-SegGrid(3,2))^2);
Edge_34 = sqrt( (SegGrid(3,1)-SegGrid(4,1))^2 + (SegGrid(3,2)-SegGrid(4,2))^2);
Edge_41 = sqrt( (SegGrid(4,1)-SegGrid(1,1))^2 + (SegGrid(4,2)-SegGrid(1,2))^2);

figure
hold on
% plot the circles
plot(X_circ,Y_circ,'b','linewidth',1); 
% plot the inner edges
plot(X_seg ,Y_seg ,'r','Marker','o'); 
% highlight the first segment in yellow
patch('Faces',[1 2 3 4],'Vertices',SegGrid,'FaceColor','y','FaceAlpha',0.5,'EdgeColor','none')
% print text to indicate the node number
text(SegGrid(:,1),SegGrid(:,2),"  "+num2str((1:4)'))
hold off
axis equal
grid on

fprintf('Edge between nodes %i and %i has length %.3f \n',1,2,Edge_12)

Edge between nodes 1 and 2 has length 1.000 

fprintf('Edge between nodes %i and %i has length %.3f \n',2,3,Edge_23)

Edge between nodes 2 and 3 has length 1.736 

fprintf('Edge between nodes %i and %i has length %.3f \n',3,4,Edge_34)

Edge between nodes 3 and 4 has length 1.000 

fprintf('Edge between nodes %i and %i has length %.3f \n',4,1,Edge_41)

Edge between nodes 4 and 1 has length 0.868 

% EDIT: added the perimeter
SegPer = Edge_12+Edge_23+Edge_34+Edge_41;
fprintf('Perimeter of the segment is %.3f \n',SegPer)

Perimeter of the segment is 4.603