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function [hit_distance, hit_position, is_face_hit] = beam2face_distance(beam,face)
%% return distance to face if beam hits it or infinity otherwise
% for beams and faces structure description see face_beam_interaction.m
% defaul returning values fot the case when beam misses the face
is_face_hit = false;
hit_position = [NA, NA];
hit_distance = Inf;
k = beam.k;
% face direction or kf
kf=face.vertex2 - face.vertex1; % not a unit vector
%% simple check for intersection of two vectors
% if beam are parallel no intersection is possible
% we do this via simulated cross product calculation
angle_tolerance = 1e-15;
if ( abs( (k(1)*kf(2)-k(2)*kf(1))/norm(k)/norm(kf) ) <= angle_tolerance )
% beams never intercept
return;
end
%% let's find the intersection of lines passing through face and light beam
% we introduce parameters tb and tf
% which define distance (in arb. units) along k vectors
% we are solving
% xb_o+ k_x*tb = v1_x+ kf_x*tf
% yb_o+ k_y*tb = v1_y+ kf_y*tf
% A*t = B
A = [ k(1) , -kf(1); k(2), -kf(2)];
B= [ face.vertex1(1)-beam.origin(1); face.vertex1(2)-beam.origin(2) ];
t = A\B; tb=t(1); tf=t(2);
% beam intersects face only if 0<=tf<=1 and tb>=0
if ( (0 <= tf) && (tf<=1) && tb >=0 )
% intersection, beam hits the face
is_face_hit = true;
else
% beam misses the face
return;
end
% calculating hit position
hit_position=face.vertex1+kf*tf;
hit_distance = tb; % distance along the light beam
end
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