calculate the perimeter of a polygon arranged in space

Hi. I need to calculate the perimeter of the geometry in the figure.

load plane_new
figure
x = plane_new(:,1);
y = plane_new(:,2);
plot(x,y,'.-r')
line(x(k),y(k))

Initially I calculated the perimeter, as the sum of each segment, in this way:

r1 = height(plane_new);
union_dist = {};
for k = 1:(r1-1)
    d1 = pdist(plane_new(k:k+1,:),'euclidean');
    union_dist = [union_dist;{d1}];
end
union_dist = cell2mat(union_dist);
    
last_first = [plane_new(r1,:); plane_new(1,:)];
d_last_first = pdist(last_first(1:2,:),'euclidean');
    
union_dist(r1) = d_last_first;
    
result_1 = sum(union_dist);  %26.1782

On the internet I saw instead that the function 'perimeter' can be used:

dataX = plane_new(:,1);
dataY = plane_new(:,2);

pgon = polyshape(dataX,dataY);
result_2 = perimeter(pgon);  %23.4138

What is the correct solution?

Answer 1

[Dyuman Joshi]

I am not sure what the idea behind that method is, but it does not give the correct result -

load plane_new
figure
x = plane_new(:,1);
y = plane_new(:,2);
plot(x,y,'.-r')

r1 = height(plane_new);
union_dist = {};
for k = 1:(r1-1)
    d1 = pdist(plane_new(k:k+1,:),'euclidean');
    union_dist = [union_dist;{d1}];
end
union_dist = cell2mat(union_dist);
    
last_first = [plane_new(r1,:); plane_new(1,:)];
d_last_first = pdist(last_first(1:2,:),'euclidean');
    
union_dist(r1) = d_last_first;

result_1 = sum(union_dist)  %26.1782

result_1 = 26.1782

pgon = polyshape(x,y);

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.

result_2 = perimeter(pgon)  %23.4138

result_2 = 23.4138

%Calculating pair-wise distance and adding it
X = [x; x(1)];
Y = [y; y(1)];
result_3 = sum(sqrt(sum([diff(X).^2 diff(Y).^2],2)))

result_3 = 23.4138

Answer 2

[Torsten]

After reading the x/y data, sum up the lengths of the line segments that constitute the circumference:

perimeter = 0;
for i = 1:numel(x)-1
  perimeter = perimeter + sqrt((x(i+1)-x(i))^2+(y(i+1)-y(i))^2);
end
perimeter = perimeter + sqrt((x(1)-x(end))^2+(y(1)-y(end))^2);
perimeter