MATLAB exercise program (finding convex hull, Graham scanning)

I am not sure how this convex bag will be used in image processing, because it seems to be more about computing ry or graphics. However, as an algorithm, I feel it is necessary to study it. My main reference material is 33.3 of Introduction to algorithms and this blog.

Here, I only write the main process, and the judgment of excessive details is omitted. Here is the search counter-clockwise:

Main. m

Clear all; close all; clc; IMG = ones (256,256 );
Imshow (IMG); [x y] = ginput (); X = round (x); y = round (y); n = length (x); P = []; for I = 1: n img (Y (I)-1: Y (I) + 1, x (I)-1: X (I) + 1) = 0; P = [P; X (I) y (I)]; % endimshow (IMG ); % The following convex hull [t Index] = max (P (:, 2); % locate the index of the largest vertex of y, when there are multiple such points, tmp_p = P (index, :); % finds the largest point of Y tmp_heng = [tmp_p (1) + 30, tmp_p (2)]; % set a point parallel to Y's largest point for I = 1: N %. The angle is not determined here. When the angle is the same, you can determine the distance between the current vertex and P0 vertex. Jiao (I) = multi_jiao (tmp_heng, P (I, :), tmp_p); % calculate the angle between each vertex and Y's largest vertex, and the angle between yourself and yourself is nanendjiao = Jiao '; P = [p Jiao]; P = sortrows (p, 3); % is sorted by the third column, and the third column is the angle degree re {1} = P (n ); % RE is equivalent to stack re {2} = P (1, 1: 2); Re {3} = P (2, 1: 2); Top = 3; % pointer to stack top for I = 3: n-1 while multi (P (I,), Re {top-1}, re {top})> = 0% if it is positive Top = Top-1; end Top = Top + 1; re {top} = P (I ); end % below is the dot link found on the convex bag for I = 2: Top IMG = drawline (IMG, re {I-1} (1), Re {I-1} (2 ), re {I} (1), Re {I} (2); endimg = drawline (IMG, re {1} (1), Re {1} (2 ), re {top} (1), Re {top} (2); figure; imshow (IMG)

The angle of the multi_jiao.m vector, 0-degrees.

Function Re = multi_jiao (P1, P2, P0) % judge the <P10, P20> angle, prepare for sorting x = 1; y = 2; vec1 = p1-p0; vec2 = p2-p0; re = ACOs (dot (vec1, vec2)/(norm (vec1) * norm (vec2) * 180/PI; End

Multi. m cross product to determine the symbol of the returned value

Function Re = multi (P1, P2, P0) % P10, P20 cross product, get positive and negative, the value at the top of the regular stack is not a vertex on the convex bag, if it is negative, x = 1; y = 2; Re = (p1 (x)-P0 (x) * (P2 (y) -P0 (y)-(p1 (y)-P0 (y) * (P2 (x)-P0 (x); End

Drawline. m draw line function, Matlab does not seem to have, do it yourself, full of clothes

Function IMG = drawline (IMG, X1, Y1, X2, Y2) % because the orientation of the image coordinate is opposite to that of the Y axis of the mathematical function, the inverse Number of all Y variables is Y1 =-Y1; y2 =-Y2; k = (y2-y1)/(x2-x1); B = y1-k * x1; MI = min (x1, x2); MA = max (x1, x2 ); for I = mi: Ma IMG (-round (I * k + B), I) = 0; end Mi = min (Y1, Y2); MA = max (Y1, y2); for I = mi: Ma IMG (-I, round (I-B)/K) = 0; endend

The following is a result. The biggest benefit of MATLAB is that the algorithm result is displayed intuitively: