%% Skript zum Plot Poylnominterpolation

%Skript für Plotbasics
basics_plot

clf
%tatsächlich zu interpolierendes Polynom
% plot([-pi:0.01:pi],sin([-pi:0.01:pi]),'LineStyle','-','Color','black')

hold on

%Interpolation mit v=3,5,7,9 Grad
dist = 1.0;
grad = 4:2:10;

for i = 1:numel(grad)
    
    switch i
        case 1
            line=myLineOne;
        case 2
            line=myLineTwo;
        case 3
            line=myLineThree;
        case 4
            line=myLineFour;
        case 5
            line=myLineFive;
        case 6
            line=myLineSix;
        case 7
            line=myLineSeven;           
    end
    
    %Punkte generieren:
    
    uvec = -dist:(2*dist/(grad(i))):dist+0.001;
    rungefunc = @(x) 1./(1+25*x.^2);
    pvec = rungefunc(uvec);
    
    a = polyfit(uvec,pvec,grad(i));
    y = polyval(a,[-dist:0.01:dist]);
    
    plot([-dist:0.01:dist],y,'LineStyle','--','Color',line)
    
    if grad(i) == 10 %Spline interpolation
        
        xx = [-dist:0.01:dist];
        yy = spline(uvec,pvec,xx);
        plot(xx,yy,'LineStyle','-.','Color',myLineFive,'LineWidth',1.5)
    end
    
end





xlabel('\figureXLabel')
ylabel('\figureYLabel')

%%
% a2 = polyfit(P(1,:),P(2,:),4);
% y2 = polyval(a2,[-5:0.01:5]);
% plot([-5:0.01:5],y2,'LineStyle','--','Color','red')

box on

grid on

plot([-dist:0.01:dist],rungefunc([-dist:0.01:dist]),'LineStyle','-','Color','black')

matlab2tikz('filename','plot_Interpolation_Polynom.tex',...
     'height', '\figureheight', 'width', '\figurewidth', 'encoding', 'UTF8', 'showInfo', false, 'checkForUpdates', false, ...
     'parseStrings', false, ... % switch off LaTeX parsing by matlab2tikz for titles, axes labels etc. ("greater flexibility", "use straight LaTeX for your labels")
     'floatFormat', '%.4g', ... % limit precision to get smaller .tikz files
     'noSize', false);