%  knownAngleConstraint - Affine transform constraints given a known angle.
%
%  Function calculates centre and radius of the constraint
%  circle in alpha-beta space generated by having a known
%  angle between two lines in an affine image
%
%  Usage:  [c, r] = knownAngleConstraint(la, lb, theta)
%
%  Where:  la and lb are the two lines defined using homogeneous coords.
%          theta is the known angle between the lines.
%          c is the 2D coordinate of the centre of the constraint circle.
%          r is the radius of the centre of the constraint circle.

%  Peter Kovesi  April 2000
%  Department of Computer Science
%  The University of Western Australia

%  Equations from Liebowitz and Zisserman 

function [c, r] = knownAngleConstraint(la, lb, theta)

a = -la(2)/la(1);   % direction of line la
b = -lb(2)/lb(1);   % direction of line lb

c = [(a+b)/2,  (a-b)/2*cot(theta)];

r = abs( (a-b)/(2*sin(theta)) );