function Angles = AnglesBetweenSuccessiveNorms( normals )
% --------------------------------------
% Angles = AnglesBetweenSuccessiveNorms( normals )
%
% Find angle between each pair of segments
%
% Note: Normals must be unit-length, stacked on top of each other.
% Note2 Angle between the last vector and no-vector is zero.


A = normals(1:end-1, : );
B = normals(2:end, : );

% angle = acos(dot(A',B'))'; % Note dot() goes down columns first, but we have rows.
%angle = mod(   atan2(A(:,1).*B(:,2)-B(:,1).*A(:,2),  A(:,1).*B(:,1)+A(:,2).*B(:,2)),    2*pi);
angle = atan2(A(:,1).*B(:,2)-B(:,1).*A(:,2),  A(:,1).*B(:,1)+A(:,2).*B(:,2));
% Explanation of finding angle between 2 normalized vec's:
% dot(A,B) = 1*1*cos(theta), so theta = acos( dot(A,B) )
%  BUT
% atan is considered safer than acos when cos(theta) is near 1;
% try it: a = pi*(1-1/10^8); atan2(sin(a), cos(a)) -    acos(cos(a))    != 0
% SO
% tan(a) = sin(a) / cos(a), so a = atan( sin, cos ):
% cos = dot product, as above,
% sin: cross(A,B) = |A||B| . sin(a) . n, where n = unit vector perpendicular to both A and B.
%       here, just need to pad A and B with z=0 to make 3-vectors.
%
% FINALLY,
% 'atan2' function gives between-angle [-pi, +pi], and the 'mod' changes this to [0, 2*pi]
% --------------------------------------
Angles = [angle;0]; % The angle between the last vector and no-vector is zero.