How to calculate the inclination angle of whole box which their 4 vertices are stored in cell array with respect to the horizontal x-axis?

How to calculate the inclination angle of whole box which their 4 vertices are stored in cell array with respect to the horizontal x-axis?

There is cell with size 1*23 , In each part of cell there are four (x,y) coordinates stored (23 Bounding boxes coordinates )as the following:

c = {{[x1 , y1], [x2, y2], [x3 , y3 ], [x4 , y4 ]}, {[x1 , y1], [x2, y2], [x3 , y3 ], [x4 , y4 ]}, ........... }

The attached file is xy coordinates of the vertices of the boxes.

The coordinates are in the order:

(left-bottom), (right-bottom), (left-top), (right-top).where each coordinate is an (x, y) pair.. i.e([x1 , y1], [x2, y2], [x3 , y3 ], [x4 , y4 ])

[Image Analyst]

Not sure all those brackets make sense. Can you attach your c in a .mat file?

If they came from regionprops why didn't you just do this:

props = regionprops(mask, 'BoundingBox');
allBB = vertcat(regionprops.BoundingBox); % Put into an N-by-4 matrix.

TUTORIAL: How to ask a question (on Answers) and get a fast answer

[M]

@Image Analyst, I have attached the file please check it.

Answer 1

[Matt J]

boxes  = cellfun(@(z) cell2mat(z(:)) ,c ,'UniformOutput' ,false)

boxes=cat(3,boxes{:});

rays=normalize(  boxes(4,:,:)-boxes(3,:,:)  ,2 ,'n');

angles= squeeze( acosd( rays(:,1,:) ) );

[M]

@Matt J, Could you please explain this answer? Which angle exactly did you calculate?

[Matt J]

The angle with the ray between vertex 3 and vertex 4

rays=normalize(  boxes(4,:,:)-boxes(3,:,:)  ,2 ,'n');

[M]

Is that angle with respect to the horizontal x_axis?

[Matt J]

Yes, it is. The angles don't vary dramatically because, as we can see from plotting your rectangles below, they are all very close to horizontal:

load xycoordinates

boxes  = cellfun(@(z) cell2mat(z(:)) ,c ,'UniformOutput' ,false);

p=cellfun(@polyshape, boxes);

plot(p); xlabel x; ylabel y

[M]

@Matt J,Thank you so much

Could you please explaine what do these arrguments mean (,2 ,'n')??

also, why did you take the cosine inverse here acosd( rays(:,1,:) ) );?

Still I didn't understand how you got the angles. and what are the rays exactly represents. Please explain.

[Matt J]

Could you please explaine what do these arrguments mean (,2 ,'n')??

This normalizes the rows of a matrix, e.g.,

X=normalize(rand(3),2,'n')

X = 3×3

0.1460 0.7145 0.6842 0.6175 0.0445 0.7853 0.8341 0.4663 0.2946

sum(X.^2,2)

ans = 3×1

1.0000 1.0000 1.0000

and what are the rays exactly represents

They are the direction vectors from vertex 3 to vertex 4, i.e., parallel to the top edge of the rectangles. Isn't that how you wanted to measure the oientation?

also, why did you take the cosine inverse here acosd( rays(:,1,:) ) );?

The elements of the rays are direction cosines. We must take acosd to convert them to angles.

[M]

@Matt J Thank you so much for the explanations.

Just one question please, are there any other documents confirm that "The elements of the rays are direction cosines".

[Matt J]

I think you could find many, imcluding the references at the wiki page.

[M]

@Matt J, Yes but I mean in the matlab code. How did you know the output angle with respect to which direction?

[Matt J]

That's what the wiki page explains. The first element of the ray is the cosine of the angle with the x-axis.

[M]

@Matt J I got it, Thank you very much .