function res = isIntersecting_(I,S,type,varargin)
% isIntersecting_ - determines if an interval intersects a set
%
% Syntax:
%    res = isIntersecting_(I,S)
%    res = isIntersecting_(I,S,type)
%
% Inputs:
%    I - interval object
%    S - contSet object
%    type - type of check ('exact' or 'approx')
%
% Outputs:
%    res - true/false
%
% Example: 
%    I1 = interval([0;0],[2;2]);
%    I2 = interval([1;1],[3;3]);
%    I3 = interval([-3;-3],[-1;1]);
%
%    isIntersecting(I1,I2)
%    isIntersecting(I1,I3)
%
%    figure; hold on;
%    plot(I1,[1,2],'b');
%    plot(I2,[1,2],'g');
%
%    figure; hold on;
%    plot(I1,[1,2],'b');
%    plot(I3,[1,2],'r');
%
% Other m-files required: none
% Subfunctions: none
% MAT-files required: none
%
% See also: contSet/isIntersecting, zonotope/isIntersecting_

% Authors:       Matthias Althoff, Niklas Kochdumper
% Written:       22-July-2016
% Last update:   14-September-2019
%                21-November-2019 (NK, added intersection with other sets)
%                12-March-2021 (MW, add empty case)
%                04-December-2023 (MW, fix empty case)
%                24-May-2024 (TL, added interval-numeric case)
% Last revision: 27-March-2023 (MW, rename isIntersecting_)

% ------------------------------ BEGIN CODE -------------------------------
    
    if representsa_(I,'emptySet',0)
        res = false;
        return
    end

    % interval and interval intersection
    if isa(S,'interval')

        if representsa_(S,'emptySet',0)
            res = false;
            return
        end
        
        res = true;
        
        % get object properties
        sup1 = I.sup;
        inf1 = I.inf;
        sup2 = S.sup;
        inf2 = S.inf;
        
        % loop over all dimensions
        for i = 1:length(I)
           if ~aux_isIntersecting1D(inf1(i),sup1(i),inf2(i),sup2(i))
              res = false;
              return
           end
        end
        
    % interval with other set intersection
    elseif isa(S,'halfspace') || isa(S,'conHyperplane') || ...
           isa(S,'polytope') || isa(S,'ellipsoid')
        % check in their function
        res = isIntersecting_(S,I,type);

    % interval with numeric
    elseif isnumeric(S)
        % call contains
        res = contains_(I,S,type,1e-8);
        
    else
        
        % exact or over-approximative algorithm
        if strcmp(type,'exact')           
            res = isIntersecting_(S,I,type);
        else
            res = isIntersecting_(polytope(I),S,type);
        end
    end
    
end


% Auxiliary functions -----------------------------------------------------

function res = aux_isIntersecting1D(inf1,sup1,inf2,sup2)
% check if two one-dimensional intervals intersect
    res = false;

    if inf1 <= inf2
        if inf2 <= sup1
            res = true;
        end
        
    else % inf2 < inf1
        if inf1 <= sup2
            res = true;
        end
        
    end

end

% ------------------------------ END OF CODE ------------------------------
