Polygon turning number

Calculate a polygon's turning number.

% Syntax:

% n = polyturn(poly,tol);

% n = polyturn(poly);

%

% Inputs:

%

% poly: 2-column matrix of polygon vertices ([x,y] coordinate pairs),

% size(poly,1)>=3.

%

% tol: scalar, non-negative, proximity tolerance for point equality

% testing, OPTIONAL, default = 0.

%

% Output:

%

% n: integer number of turns or nan. For a non-self-intersecting polygon,

% n is +1 for counterclockwise orientation and -1 for clockwise

% orientation. (n can be zero for a figure-8 polygon.) If any polygon

% segment has an end point within distance tol from an adjacent segment,

% n will be nan.