# finding the distance between two points

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Natali Petani am 12 Nov. 2022
Bearbeitet: Karim am 12 Nov. 2022
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).
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### Antworten (3)

Sam Chak am 12 Nov. 2022
You can try the function: pdist2().
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
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Star Strider am 12 Nov. 2022
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
.
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Karim am 12 Nov. 2022
Bearbeitet: Karim am 12 Nov. 2022
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
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
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