%% Skript zum Plot Interpolieren

%Skript für Plotbasics
basics_plot

%Kontrollpunkte definieren:
fig_Res = figure(1); % figure handle erzeugen

clf(fig_Res)

fig_Res.Color = [1, 1, 1]; % Hintergrundfarbe weiß
fig_Res.Units = 'centimeters'; % figure Einheit in cm 
fig_Res.Position(3) = 16.49765; % hier kann man in cm die richtige Breite des Texts in LaTeX angeben ...
fig_Res.Position(4) = 16; % und hier die Höhe der figure

P = [-5 -2 0.5 5;-2 4 -1 2];



% scatter(P(1,:),P(2,:),'x','MarkerEdgeColor','black','LineWidth',1.5,'SizeData',400)

% axis off

axis equal
hold on
grid on

text(P(1,1)+0.2,P(2,1)+0.1,'$\mv{r}_{i-1}$','Interpreter','none')
text(P(1,2)+0.1,P(2,2)+0.4,'$\mv{r}_i$','Interpreter','none')
text(P(1,3)+0.1,P(2,3)-0.3,'$\mv{r}_{i+1}$','Interpreter','none')
text(P(1,4)-0.9,P(2,4)+0.3,'$\mv{r}_{i+2}$','Interpreter','none')



%% Polynomfit
% 
% a = polyfit(P(1,:),P(2,:),3);
% y = polyval(a,[-5:0.01:5]);
% plot([-5:0.01:5],y,'LineStyle','--','Color',myLineThree)


%% Lineare Interpolation mit zirkularer Blende

% Winkelhalbierende berechnen


delta = [0,1.2,0.7,0];

for i = 2:size(P,2)-1
    
    n1 = (P(:,i-1)-P(:,i))/norm(P(:,i-1)-P(:,i));
    n2 = (P(:,i+1)-P(:,i))/norm(P(:,i+1)-P(:,i));
    
    nWH = (n1+n2)/norm(n1+n2);  %Richtungsvektor der Winkelhalbierenden
    
    % WH plotten
    
    WH = P(:,i)+[-1:0.01:4].*nWH;
    plot(WH(1,:),WH(2,:),'LineStyle','-.','Color',myGray50)
      
    
    % Kreimittelpunkt berechnen
    
    
    SP1 = P(:,i)+delta(i).*n1;
    SP2 = P(:,i)+delta(i).*n2;
    
    nSenk1 = [0 1;-1 0]*n1;
    nSenk2 = [0 1;-1 0]*n2;
    
    lambda = [-nSenk1 nSenk2]\(SP1-SP2);
    
    MP = SP1+lambda(1).*nSenk1;
    MP2 = SP2+lambda(2).*nSenk2;
    
%     plot(SP1(1),SP1(2),'Marker','o','Color',myLineOne,'MarkerEdgeColor','black','MarkerFaceColor','black')
%     plot(SP2(1),SP2(2),'Marker','o','Color',myLineOne,'MarkerEdgeColor','black','MarkerFaceColor','black')  
    
    %Kreis Plotten
    plot(MP(1),MP(2),'Marker','o','Color',myLineOne,'MarkerEdgeColor','black','MarkerFaceColor','black')
    
    xval = SP1(1);
    yval = SP1(2);
    x = xval;
    y = yval;
    while xval < SP2(1)
        xval = xval + 0.01;
        if yval > MP(1)
            yval = +sqrt(lambda(1)^2-(xval-MP(1))^2)+MP(2);
        else
            yval = -sqrt(lambda(1)^2-(xval-MP(1))^2)+MP(2);
        end
        
        if imag(yval) == 0
            x = [x, xval];
            y = [y, yval];
        end
    end
    x = [x,SP2(1)];
    y = [y,SP2(2)];
    
    plot(x,y,'LineStyle','-','Color',myLineTwo)
    
    
            
            
%     plot(MP2(1),MP2(2),'Marker','o','Color',myLineOne,'MarkerEdgeColor','black','MarkerFaceColor','black')
    
end

text(P(1,2)-0.7,P(2,2)-0.2,'$\delta_i$','Interpreter','none')
text(P(1,3)-1.1,P(2,3)+0.3,'$\delta_{i+1}$','Interpreter','none')

plot(P(1,:),P(2,:),'LineStyle','-','Marker','o','Color',myLineOne,'MarkerEdgeColor','black','MarkerFaceColor','black','LineWidth',1,'MarkerSize',5)

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

matlab2tikz('filename','plot_Interpolation.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);



hold off
% box off % Box um die figure herum ausblenden