image processing - Rotate a Bounding Box in Matlab -

i have plotted bounding box on image:

bbox = [50 20 200 50]; figure; imshow('coins.png');  hold on;  rectangle('position', bbox, 'edgecolor','r', 'linewidth', 3); hold off; 

how can rotate bounding box bbox 30 degrees around centroid , obtain coordinates of new box, can use inpolygon?

update: please use bounding box defined [x y width height].

to rotate coordinates of bounding box need define proper rotation matrix.

start defining coordinates of 4 corners:

x = [bbox(1), bbox(1), bbox(1)+bbox(3), bbox(1)+bbox(3), bbox(1)]; y = [bbox(2), bbox(2)+bbox(4), bbox(2)+bbox(4), bbox(2), bbox(2)]; 

rotation rotates around origin (0,0), if want rotate around center of box need adjust x , y before , after rotation

cx = bbox(1)+0.5*bbox(3); cy = bbox(2)+0.5*bbox(4); 

rotating

xr = x-xc; %// subtract center yr = y-cy; xr = cosd(30)*xr-sind(30)*yr; %// rotate yr = sind(30)*xr+cosd(30)*yr; xr = xr+xc; %// add center yr = yr+yc; 

now can plot rotated box

plot( xr, yr ); 

you can use xr , yr xv , yv arguments inpolygon.

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all these algebraic manipulations can done more elegantly using homogeneous coordinates, allows translation (subtracting/adding center of rect) expressed matrix multiplication.

h = [x;y;ones(1,5)]; %// points 3d homogeneous coordinates tc = [1 0 -cx; 0 1 -cy; 0 0 1]; %// translation matrix tr = [cosd(30) -sind(30) 0; sind(30) cosd(30) 0; 0 0 1]; %// rotation hr = inv(tc) * tr * tc * h; %// transformations matrix products  plot( hr(1,:), hr(2,:) ); %// rotated rect