mirror.m

%mirror.m
%calculates mirror geometry action for MTUAF
function main()
    %inputs, Units in inches
    b=cart2both([-0.5,-0.5]); %bottom of screen
    [th,r]=pol2cart(deg2rad(90),0.5*12); %top of screen
    a=[th,r]+b{1};
    topangle=deg2rad(40);%top inside angle
    bottomangle=deg2rad(100);%bottom inside angle
    m_dist=12;%distance down c where mirror starts
    m_angle=deg2rad(38);%angle of mirror
    
    %calculations
    afromb=cart2both(a{1}-b{1});
    aasa=asa(topangle,afromb{2}(2),bottomangle); %intermediate for finding c
    %c represents focus without mirror
    %THIS IS WRONG
    c=pol2both([bottomangle-afromb{2}(1), aasa(1)]); %length
    m_bot=cart2both((m_dist/c{2}(2))*c{1});%bottom of mirror
    m_botfromb=cart2both(m_bot{1}-b{1});
    [sass1,sass2]=sas(afromb{2}(2),bottomangle,m_botfromb{2}(2));
    [sasstheta,sassr]=pol2cart(sass2,-sass1);
    %THIS IS WRONG
    m_top=cart2both(m_bot{1} + ...
        [sasstheta,sassr] + ... %side-angle-side
        [pi+m_botfromb{2}(1),0]); %add to angle for proper orientation
    F=cart2both(refl(c{1}-m_bot{1},m_top{1}-m_bot{1})+m_bot{1});%focus using reflection formula
    
    %create some sets to plot
    %sansmirror=vertcat(a{1},b{1},c{1},a{1})
    screen=vertcat(a{1},b{1});
    oldlight=vertcat(a{1},c{1},b{1});
    mirror=vertcat(m_bot{1},m_top{1});
    lightbox=vertcat(b{1},m_bot{1},F{1},m_top{1},a{1});
    
    plot(screen(:,1),screen(:,2),'--r');
    hold on;
    plot(mirror(:,1),mirror(:,2),'--r');
    plot(oldlight(:,1),oldlight(:,2));
    %plot(lightbox(:,1),lightbox(:,2));
    hold off;
    
    
    %helpeur fxn's
    function w=refl(u,v) %thx wikipedia for equation
        %reflection of u over v
        %where u and v are of form [x,y]
        w=(2*dot(u,v)/dot(v,v))*v-u;
    end
    function x=cart2both(xcart)
        [theta,r]=cart2pol(xcart(1),xcart(2));
        x={xcart,[theta,r]};
    end
    function x=pol2both(xpol)
        [x,y]=pol2cart(xpol(1),xpol(2));
        x={[x,y],xpol};
    end
    function [a,gamma,b]=asa(alpha,c,beta)
        %ASA geometry action
        gamma=pi-alpha-beta;
        a=c*sin(alpha)/sin(gamma);
        b=c*sin(beta)/sin(gamma);
    end
    function [alpha,c,beta]=sas(a,gamma,b)
        %SAS geometry action
        c=sqrt(a^2+b^2-2*a*b*cos(gamma));
        alpha=asin((a/c)*sin(gamma));
        beta=asin((b/c)*sin(gamma));
    end
    function rad=deg2rad(deg)
        rad=deg*pi/180.0;
    end
    function deg=rad2deg(rad)
        deg=rad*180/pi;
    end
end