How to detect the critical points on the boundary..?

Hello, I want to detect the critical pints on the object boundary, i am not getting how to code it in the MATLAB, My algorithm is given below let ....x-3,x-2,x-1,x,x+1,x+2,x+3... are the points on the boundary if the perpendicular distance from the x and straight line joining x-1 & x+1, is greater than the threshold then x-1 and x+1 will be our critical points and if it is less than the threshold then we progressively examine the neighbors, like x-2,x-1,x,x+1,x+2,x+3 again if it is greater than the threshold then x-2 and x+2 will be critical points and if it is less then then follow the same process, let our first set of critical points on the boundary are X+5 and X-5. Then for finding out next critical points i have to check the perpendicular distance between x+6 and straight line joining the x+5 and x+7,and again if it is less than the threshold i have to continue the process.

i would like to know how code it with the less number of for loops,i Also like to know how to save the co-ordinates of critical points after finding it. If possible please help i am beginner in MATLAB programming, Thanks in advance

[Image Analyst]

What perpendicular distance? This is a 1-D problem. There is no y, is there? So how can anything be perpendicular when everything lies along a 1-D number line? Can you provide a diagram of this?

[harshal j]

Thanks for the comment, this program is not 1-D program,This is 2-D programming each point is having x and y co-ordinates,

 for your reference consider the points b-3,b-2,b-1,b,b+1,b+2,b+3. Where b is the point on the boundary with coordinate (x,y. each point on the boundary is 2-D. for your reference i have included the figure of the object.

Answer 1

[Image Analyst]

Hint: https://en.wikipedia.org/wiki/Distance_from_a_point_to_a_line

I'd just put that into a for loop - nothing wrong with for loops for tiny amounts of data like this.

[harshal j]

Thanks for the answer, I know how to calculate the perpendicular distance, but i don't know how to save the co-ordinates of the obtain critical points and how to continue the process after obtaining the first set of critical points.

[Image Analyst]

Have a separate loop counter

numCritical = 1;
for k = 1 : length(X)
    % Code...
    if itsACriticalPoint
       % Save x and y values of this point into the criticalPoints array.
       criticalPoints(numCritical, 1) = X(k);
       criticalPoints(numCritical, 2) = Y(k);
       numCritical = numCritical + 1;
    end
end

[harshal j]

Thank u so much for the answer it will solve my problem.