How can I write matlab program for the following sample region selection from image?

I have a point V. I have created some imaginary rays (r1,r2,r3,.....rn) from that point. How can I select two neighboring regions (like A1 and A2) on either side of the ith ray. How can I get the points of that region and the points on the ith ray? Please see the picture: In the picture r1...r3 are imaginary rays created from point V. now I need the region A1 and A2 and points on the ith ray (e.g. r2 ray) N.B. Angle between each ray is equal.

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[[e-mail]]

what about building a function that you can call whenever you need to know if a point P stands inside the wanted areas.

% 
% You know V and you know the point P that you want to know if it
% stands close to R2 (between R1 and R3)
%
% Output inside = 0 means that P is on R2
%                -1 you are outside of the areas A1 and A2
%                 1 you are inside the areas
%
function inside =tellMeWhereAmI(Vx, Vy, Px, Py, angleR2, deltaAngle)
  % what is the angle between V and P, here atan2 works between +/-Pi
  angle =atan2(Py-Vy, Px-Vx);
  % to avoid confusion around +/-Pi
  if angle < 0
    angle = 2*pi+angle;
  end
  if angleR2 < 0
    angleR2 = 2*pi+angleR2;
  end
  % to avoid confusion around 0/2Pi
  if angle <= angleR2+deltaAngle-2*pi
    angle = angle+2*pi;
  end
  % now we compare
  if angle == angleR2
    inside = 0;      % we are on the line
  elseif (angle > angleR2+deltaAngle) | (angle < angleR2-deltaAngle)
    inside = -1;     % we are outside of the areas
  else
    inside = 1;      % we are inside of the areas
  end
end

Do you think it could do the job?

MEK

[K M Ibrahim Khalilullah]

Thanks for your answer. sorry MEK my thinking is different. I want the points between two end points of the line and the region like A1 and A2. However , I have already my work.

Answer 1

[[e-mail]]

Sorry I have forgotten a little correction, here is the final

% 
% You know V and you know the point P that you want to know if it
% stands close to R2 (between R1 and R3)
%
% Output inside = 0 means that P is on R2
%                -1 you are outside of the areas A1 and A2
%                 1 you are inside the areas
%
function inside =tellMeWhereAmI(Vx, Vy, Px, Py, angleR2, deltaAngle)
  % what is the angle between V and P, here atan2 works between +/-Pi
  angle =atan2(Py-Vy, Px-Vx);
  % to avoid confusion around +/-Pi
  if angle < 0
    angle = 2*pi+angle;
  end
  if angleR2 < 0
    angleR2 = 2*pi+angleR2;
  end
  % to avoid confusion around 0/2Pi
  if angle <= angleR2+deltaAngle-2*pi
    angle = angle+2*pi;
  elseif angle-2*pi > angleR2-deltaAngle  % I had forgotten this!!!
    angle = angle-2*pi;
  end
  % now we compare
  if angle == angleR2
    inside = 0;      % we are on the line
  elseif (angle > angleR2+deltaAngle) | (angle < angleR2-deltaAngle)
    inside = -1;     % we are outside of the areas
  else
    inside = 1;      % we are inside of the areas
  end
end