Distance of a point to the middle of a polygon

I currently have a oval shaped polygon with 18 points plotted within the area. All were determined using latitudinal and longitudinal coordinates.

I was wondering if there is anyway of either:

a) Reorientating the points so I can subtract the middle of the field coordinates (lat,long). This will mean I can observe the points with respect to their deviation to either the left or right of centre. Ideally getting a relative position of the points. or

b) Calculate the perpendicular distance from the widest points of the field.

Attached above is a picture of the polygonal area and the points inside for which I want to calculate their relative positions.

Answer 1

[KSSV]

x = rand(10,1) ; y = rand(10,1) ;  
mx = mean(x) ; my = mean(y) ;  
plot(x,y,'.r') ;  
hold on
plot(x-mx,y-my,'.b') ;  
legend({'original', 'shifted'})

[William Sheehan]

This would be okay if the oval shape was always perfectly orientated with the latitude and longitude axis. However, this won't be as accurate if the oval is disorientated in relation to the latitudinal and longitudinal axis.

Answer 2

[Image Analyst]

If you want to do it numerically/digitally instead of analytically, you can easily do this in a few lines of code. Just use poly2mask to make a digital image from your coordinates. Then call regionprops to get the center of the oval. Then use Pythagorean theorem to get the distance from the centroid to all of the other points.

mask = poly2mask(xOval, yOval, rows, columns);
props = regionprops(mask, 'Centroid');
xCentroid = props.Centroid(1);
yCentroid = props.Centroid(2);
% Find distance from centroid to other points.
distances = sqrt((x-xCentroid).^2 + (y-yCentroid).^2)

[William Sheehan]

Is there a way i can distingush whether or not an individual is specifically to one side?

I.e. if a marker is in the bottom half of the polygon it is negative or if the polygon is in the upper half it is positive? Likewise with the left and right portions of the polygon?

[Image Analyst]

Yes, take the y coordinate of the pixel and see if it is higher or lower than yCentroid. Same for xCentroid.