torres16simple.m

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% Torres et al 16
% flight lines rotattion angle
% V: vertices of the polygon
% dx: distance between lines

function [Path, flra] = torres16simple(V, dx)
    [n,~] = size(V);
    optimal_dist = Inf;
    
    %for all edges in the polygon
    for i=1:n;
        max_dist_edge = 0;
        %for all vertex in the polygon
        for j=1:n;
            if distPoint2Line(V(i,:),V(increment(i,n),:),V(j,:))>max_dist_edge
                max_dist_edge = distPoint2Line(V(i,:),V(increment(i,n),:),V(j,:));
                opposed_vertex = j;
            end
        end
        
        if max_dist_edge < optimal_dist
            optimal_dist = max_dist_edge;
            angle = slopeAngle(V(i,:), V(increment(i,n),:));
        end
    end
    
    flra = angle;
    alpha = angle-pi/2; % R rotation is with respect of the east; alpha rotation is with respect of the north
    Pstart = V;
    Pend = circshift(V, -1);
    PsR = rotatePolygon(Pstart, -alpha);
    PsR = PsR';
    PeR = rotatePolygon(Pend, -alpha);
    PeR = PeR';

    [PathRotated, ~] = getPathMR([PsR PeR], dx, 1);
    Path = rotatePolygon(PathRotated, alpha);
       
    Path = Path';
end

function i_next = increment(i,n)
    i_next = mod(i,n)+1;
end

function alpha = slopeAngle(p1, p2)
    alpha = atan2(p2(2)-p1(2),p2(1)-p1(1));
end