% ==========
% Apartado I
% ==========
%
% * * * Ejemplo 1 * * *
% Generación de la malla no equiespaciada con los datos
clear all
close all
t=[-3,-2,-0.5,0,0.75,1.75,3];
[x,y]=meshgrid(t);
z=peaks(x,y);
% Generación de la malla fina para la interpolación
[xi,yi]=meshgrid(-3:0.25:3);
% Interpolación y comparación de resultados
zi1=interp2(x,y,z,xi,yi,'nearest'); % usando vecinos más próximos
zi2=interp2(x,y,z,xi,yi,'linear'); % usando bilinear
zi3=interp2(x,y,z,xi,yi,'cubic'); % usando bicúbica
figure(1);surfc(xi,yi,zi1);title('cercano');
hold on;plot3(x,y,z,'b.','markersize',20);hold off
figure(2);surfc(xi,yi,zi2);title('bilineal');
hold on;plot3(x,y,z,'b.','markersize',20);hold off
figure(3);surfc(xi,yi,zi3);title('bicubica')
hold on;plot3(x,y,z,'b.','markersize',20);hold off
figure(4);surfc(xi,yi,peaks(xi,yi));title('funcion')
hold on;plot3(x,y,z,'b.','markersize',20);hold off
figure(5);
subplot(2,2,1);surfc(xi,yi,zi1);title('cercano');
subplot(2,2,2);surfc(xi,yi,zi2);title('bilineal');
subplot(2,2,3);surfc(xi,yi,zi3);title('bicubica')
subplot(2,2,4);surfc(xi,yi,peaks(xi,yi));title('funcion')
%
%% * * * EJERCICIO 1 * * *
%
clear all
close all
a=pi;
f=inline('exp(-(x.^2+y.^2)/4).*cos(x.^2+y.^2)');
[x,y]=meshgrid(linspace(-a,a,9));
z=f(x,y);
% Generación de la malla fina para la interpolación
[xi,yi]=meshgrid(linspace(-a,a));
% Interpolación y comparación de resultados
zi1=interp2(x,y,z,xi,yi,'nearest'); % usando vecinos más próximos
zi2=interp2(x,y,z,xi,yi,'linear'); % usando bilinear
zi3=interp2(x,y,z,xi,yi,'cubic'); % usando bicúbica
figure(1);surfc(xi,yi,zi1);title('cercano');
hold on;plot3(x,y,z,'b.','markersize',20);hold off
figure(2);surfc(xi,yi,zi2);title('bilineal');
hold on;plot3(x,y,z,'b.','markersize',20);hold off
figure(3);surfc(xi,yi,zi3);title('bicubica')
hold on;plot3(x,y,z,'b.','markersize',20);hold off
figure(4);surfc(xi,yi,f(xi,yi));title('funcion')
hold on;plot3(x,y,z,'b.','markersize',20);hold off
figure(5);
subplot(2,2,1);surfc(xi,yi,zi1);title('cercano');
subplot(2,2,2);surfc(xi,yi,zi2);title('bilineal');
subplot(2,2,3);surfc(xi,yi,zi3);title('bicubica')
subplot(2,2,4);surfc(xi,yi,f(xi,yi));title('funcion')
%
%% * * * EJERCICIO 2 * * *
%
clear all
close all
a=50;
[x,y]=meshgrid(-50:25:50);
z=[2.2256 11.2256 14.670 12.5589 4.8922;
   5.8256 14.8256 18.2700 16.1589 8.4922;
   7.4256 16.4256 19.8700 17.7589 10.0922;
   7.0256 16.0256 19.4700 17.3589 9.6922;
   4.6256 13.6256 17.0700 14.9589 7.2922];
f=inline('20-(x/15-0.2).^2-(y/25-0.3).^2');
%[x,y]=meshgrid(linspace(-a,a,5))
%z=f(x,y);

% Generación de la malla fina para la interpolación
[xi,yi]=meshgrid(linspace(-a,a));
% Interpolación y comparación de resultados
zi1=interp2(x,y,z,xi,yi,'nearest'); % usando vecinos más próximos
zi2=interp2(x,y,z,xi,yi,'linear'); % usando bilinear
zi3=interp2(x,y,z,xi,yi,'cubic'); % usando bicúbica
figure(1);surfc(xi,yi,zi1,'LineWidth',0.1);title('cercano');
hold on;plot3(x,y,z,'b.','markersize',20);hold off
figure(2);surfc(xi,yi,zi2);title('bilineal');
hold on;plot3(x,y,z,'b.','markersize',20);hold off
figure(3);surfc(xi,yi,zi3);title('bicubica')
hold on;plot3(x,y,z,'b.','markersize',20);hold off
figure(4);surfc(xi,yi,f(xi,yi));title('funcion')
hold on;plot3(x,y,z,'b.','markersize',20);hold off
figure(5);
subplot(2,2,1);surfc(xi,yi,zi1);title('cercano');
subplot(2,2,2);surfc(xi,yi,zi2);title('bilineal');
subplot(2,2,3);surfc(xi,yi,zi3);title('bicubica')
subplot(2,2,4);surfc(xi,yi,f(xi,yi));title('funcion')
%
% ============
% Apartado 1.2
% ============
%
% * * * Ejemplo 1 * * *
f=inline('20-(x/15-0.2).^2-(y/25-0.3).^2');
% Generación de n puntos aleatorios en [-3,3]
N=20;rand('state', 0);T=rand(2,N)*6-3;
x=T(1,:);y=T(2,:);
plot(x,y,'.','markersize',10)
k = convhull(x,y);
hold on, plot(x(k),y(k),'-r'), hold off
grid on

plot(x,y,'.','markersize',10)
tri = delaunay(x,y);
hold on, triplot(tri,x,y), hold off

figure
hidden on
z=f(x,y);
trimesh(tri,x,y,z)
grid on
zlabel('Altura')

figure
hidden on
z=f(x,y);
trisurf(tri,x,y,z)
grid on
zlabel('Altura')

[xi,yi] = meshgrid(linspace(-3,3,51));
zi = griddata(x,y,z,xi,yi,'cubic');
[c,h] = contour(xi,yi,zi,'b-');
clabel(c,h)
xlabel('Longitude'), ylabel('Latitude')

figure;surfc(xi,yi,zi);

hold on;plot3(x,y,z,'b.','markersize',20);hold off
voronoi(x,y)
grid on
xlabel('Longitude'), ylabel('Latitude')