%% Skript zum Plot Interpolieren

close all
clear all

%Skript für Plotbasics
basics_plot

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

clf(fig_Res)

strNurbBasic = struct('p',[],'pj',[],'u',[]);

nurbs = strNurbBasic;





nurbs.u = [0,0,0,1,1,1];

nurbs.p = [2];

bsplinehyper = nurbs;

for i = 4:4
    
    switch i
        case 1
            wi = 0.2;
            lineStyle = myLineTwo;
        case 2
            wi = 0.6;
            lineStyle = myLineThree;
            lineStyle2 = myGray75;
        case 3
            wi = 1;
            lineStyle = myLineOne;
        case 4
            wi = 2;
            lineStyle = myLineFour;
            lineStyle2 = myGray25;
        case 5
            wi = 4;
            lineStyle = myLineFive;
    end
    
    
    
    nurbs.pj = [0 wi*1 1;0 wi*0 1;1 wi 1];
    bsplinehyper.pj = nurbs.pj;
    
    ui = 0:0.01:1;
    
    vek = zeros(2,numel(ui));
    vekbspline = zeros(3,numel(ui));
   
    %% Plot NURBS
    
    for j = 1:numel(ui)
        vek(:,j) = berechneAbleitungenAnPunkt(ui(j),nurbs.p,nurbs.u,nurbs.pj,0);
    end
    
    plot3(vek(1,:),vek(2,:),ones(size(vek(1,:))),'Color',lineStyle)
    hold on 
    %% Plot BSpline
    
    for j = 1:numel(ui)
        vekbspline(:,j) = berechneAbleitungBSplineAnPunkt(ui(j),bsplinehyper.p,bsplinehyper.u,bsplinehyper.pj,0);
    
    end
    
    plot3(vekbspline(1,:),vekbspline(2,:),vekbspline(3,:),'Color',myLineSix)
    

    
    
    
end

plot3(nurbs.pj(1,1:end)./nurbs.pj(end,1:end),nurbs.pj(2,1:end)./nurbs.pj(end,1:end),ones(size(nurbs.pj(2,1:end))),'LineStyle','none','Marker','x','MarkerSize',8,'Color',myLineOne,'LineWidth',1.1)

plot3(bsplinehyper.pj(1,1:end),bsplinehyper.pj(2,1:end),bsplinehyper.pj(3,1:end),'LineStyle','none','Marker','x','MarkerSize',5,'Color',myLineSix,'LineWidth',0.9)

for k = 1:numel(nurbs.pj(1,1:end))

    text(bsplinehyper.pj(1,k)-0.2,bsplinehyper.pj(2,k)+0.05,bsplinehyper.pj(3,k)+0.00,['$\tilde{\mv{p}}_' num2str(k-1) '$'],'Interpreter','none')
    text(nurbs.pj(1,k)./nurbs.pj(end,k)-0.05,nurbs.pj(2,k)./nurbs.pj(end,k)-0.05,1+0.02,['$\cp{' num2str(k-1) '}$'],'Interpreter','none')
end
    
    for n = 1:2:11
        plot3([0 vek(1,10*(n-1)+1),vekbspline(1,10*(n-1)+1)],[0 vek(2,10*(n-1)+1),vekbspline(2,10*(n-1)+1)],[0 1,vekbspline(3,10*(n-1)+1)],'Color',lineStyle2,'LineStyle','--','Marker','.','MarkerSize',4)
    end
    plot3([0 vek(1,end),vekbspline(1,end)],[0 vek(2,end),vekbspline(2,end)],[0 1,vekbspline(3,end)],'Color',lineStyle2,'LineStyle','--','Marker','.','MarkerSize',4)
    plot3([0, nurbs.pj(1,2)./nurbs.pj(end,2),bsplinehyper.pj(1,2)],[0, nurbs.pj(2,2)./nurbs.pj(end,2),bsplinehyper.pj(2,2)],[0, nurbs.pj(3,2)./nurbs.pj(end,2),bsplinehyper.pj(3,2)],'Color',lineStyle2,'LineStyle','--','Marker','.','MarkerSize',4)
    

pat = fill3([1 1 0 0],[0 1 1 0],[1 1 1 1],myGray50,'LineStyle','none');

alpha(pat,0.2);

text(0.1,0.95,1,'$w=1$')

grid on


xlabel('\figureXLabel')
ylabel('\figureYLabel')
zlabel('\figureZLabel')
% 
% set(gca,'XLim',[0,1])
% set(gca,'YLim',[0,1])

%
% % scatter(P(1,:),P(2,:),'x','MarkerEdgeColor','black','LineWidth',1.5,'SizeData',400)
%
% % axis off
%
% axis equal
% hold on
%
% text(P(1,1)+0.2,P(2,1)+0.1,'$\mv{p}_{i-1}$','Interpreter','none')
% text(P(1,2)+0.1,P(2,2)+0.4,'$\mv{p}_i$','Interpreter','none')
% text(P(1,3)+0.1,P(2,3)-0.3,'$\mv{p}_{i+1}$','Interpreter','none')
% text(P(1,4)-0.9,P(2,4)+0.3,'$\mv{p}_{i+2}$','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_nurbshyperebene.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