contornos de superficies con matlab
DESCRIPTION
DEJO UN ARCHIVO PARA REALIZAR CONTORNOS CON EL SOFTWARE MATLAB.TRANSCRIPT
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1 DR. SORIA QUIJAITE JUAN JESÚS
MÉTODOS NUMÉRICOS CON SOFTWARE MATLAB
GRÁFICOS DE SUPERIFICIES Y CONTORNOS
%GRAFICA DE SUPERFICIE1
x1=-1:0.05:1;
y1=-1:0.05:1;
[x,y]=meshgrid(x1,y1);
f1=sin(x.*y)-x.^2+2*cos(y)
mesh(x,y,f1)
grid on
title('f(x;y)=sin(x.*y)-x.^2+2*cos(y)')
xlabel('EJE X')
ylabel('EJE Y')
zlabel('EJE Z')
%GRAFICA DE CONTORNO1
x1=-5:0.05:5;
y1=-5:0.05:5;
[x,y]=meshgrid(x1,y1);
f1=sin(x.*y);
contour(x,y,f1,[0.00 0.00],'r')
hold on
f2=x.^2+2*cos(y);
contour(x,y,f2,[0.00 0.00],'b')
grid on
title('Contorno de f1(x,y) y f2(x,y) ')
xlabel('EJE DE ABSCISAS')
ylabel('EJE DE ORDENADAS')
gtext('f1=sin(x.*y)')
gtext('f2=x.^2+2*cos(y)')
%GRAFICA DE CONTORNO2
x1=-2:0.05:4;
y1=-2:0.05:6;
[x,y]=meshgrid(x1,y1);
f1=9*x.^2+4*y.^2-18*x-16*y-11;
contour(x,y,f1,[0.00 0.00],'r')
hold on
f2=x.^2+4*y.^2-2*x-24*y+33;
contour(x,y,f2,[0.00 0.00],'b')
grid on
title('Contorno de f1(x,y) y f2(x,y) ')
xlabel('EJE DE ABSCISAS')
ylabel('EJE DE ORDENADAS')
gtext('f1=9*x.^2+4*y.^2-18*x-16*y-11')
gtext('f2=x.^2+4*y.^2-2*x-24*y+33')
%GRAFICA DE SUPERFICIE3
x1=-1:0.05:1;
y1=-1:0.05:1;
[x,y]=meshgrid(x1,y1);
f1=x.^2+x.*(y.^3)-3*(x.^2).*y+y.^3-5;
%f1=sin(x.*y)-x.^2+2*cos(y);
mesh(x,y,f1)
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2 DR. SORIA QUIJAITE JUAN JESÚS
grid on
title('x.^2+x.*(y.^3)-3*(x.^2).*y+y.^3-5')
xlabel('EJE X')
ylabel('EJE Y')
zlabel('EJE Z')
%GRAFICA DE CONTORNO3
x1=-6:0.05:6;
y1=-6:0.05:6;
[x,y]=meshgrid(x1,y1);
f1=x.^2+x.*(y.^3)-9;
contour(x,y,f1,[0.00 0.00],'k')
hold on
f2=3*(x.^2).*y-y.^3-4;
contour(x,y,f2,[0.00 0.00],'b')
grid on
xlabel('EJE DE ABSCISAS')
ylabel('EJE DE ORDENADAS')
title('Contorno de f1(x,y) y f2(x,y) ')
gtext('x.*exp(x.*y+0.8)+exp(y.^2)-3')
gtext('x.^2-y.^2-0.5*exp(x.*y)')
%GRAFICA DE CONTORNO4
x1=-6:0.05:6;
y1=-6:0.05:6;
[x,y]=meshgrid(x1,y1);
f1=x.*exp(x.*y+0.8)+exp(y.^2)-3;
contour(x,y,f1,[0.00 0.00],'k')
hold on
f2=x.^2-y.^2-0.5*exp(x.*y);
contour(x,y,f2,[0.00 0.00],'b')
grid on
xlabel('EJE DE ABSCISAS')
ylabel('EJE DE ORDENADAS')
title('Contorno de f1(x,y) y f2(x,y) ')
gtext('f1=x.*exp(x.*y+0.8)+exp(y.^2)-3')
gtext('f2=x.^2-y.^2-0.5*exp(x.*y)')
%GRAFICA DE SUPERFICIE4
x1=-1:0.05:1;
y1=-1:0.05:1;
[x,y]=meshgrid(x1,y1);
f1 = 3*(1-x).^2.*exp(-(x.^2) - (y+1).^2) ...
- 10*(x/5 - x.^3 - y.^5).*exp(-x.^2-y.^2) ...
- 1/3*exp(-(x+1).^2 - y.^2);
mesh(x,y,f1)
grid on
title('gráfica de superficies')
xlabel('EJE X')
ylabel('EJE Y')
zlabel('EJE Z')
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3 DR. SORIA QUIJAITE JUAN JESÚS
GRÁFICOS COMPLEMENTARIOS DE CONTORNOS
x1=-5:0.05:5; y1=-5:0.05:5; [x,y]=meshgrid(x1,y1); f1=2*x.^2+4*x.*y+3*y.^2-3; contour(x,y,f1,[0.00 0.00],'r') hold on f2=x.^2-2-y; contour(x,y,f2,[0.00 0.00],'b') grid on title('Contorno de f1(x,y) y f2(x,y) ') xlabel('EJE DE ABSCISAS') ylabel('EJE DE ORDENADAS')
x1=-5:0.05:5; y1=-5:0.05:5; [x,y]=meshgrid(x1,y1); f1=3*(x.^2+y.^2).^2-100*x.*y; contour(x,y,f1,[0.00 0.00],'r') hold on f2=-2*x.^2-4*x.*y+3*y.^2-2; contour(x,y,f2,[0.00 0.00],'b') grid on title('Contorno de f1(x,y) y f2(x,y) ') xlabel('EJE DE ABSCISAS') ylabel('EJE DE ORDENADAS')
x1=-5:0.05:5; y1=-5:0.05:5; [x,y]=meshgrid(x1,y1); f1=3*(x.^2+y.^2).^2-100*x.*y; contour(x,y,f1,[0.00 0.00],'r') hold on f2=2*x.^2+4*x.*y+3*y.^2-5; contour(x,y,f2,[0.00 0.00],'b') grid on title('Contorno de f1(x,y) y f2(x,y) ') xlabel('EJE DE ABSCISAS') ylabel('EJE DE ORDENADAS')
x1=-5:0.05:5; y1=-5:0.05:5; [x,y]=meshgrid(x1,y1); f1=(x.^2+y.^2).^2-8*(x.^2).*y; contour(x,y,f1,[0.00 0.00],'r') hold on f2=x.^2-y-1; contour(x,y,f2,[0.00 0.00],'b') grid on title('Contorno de f1(x,y) y f2(x,y) ') xlabel('EJE DE ABSCISAS') ylabel('EJE DE ORDENADAS')
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4 DR. SORIA QUIJAITE JUAN JESÚS
x1=-5:0.05:5; y1=-5:0.05:5; [x,y]=meshgrid(x1,y1); f1=x.^3+y.^3-6*x.*y; contour(x,y,f1,[0.00 0.00],'r') hold on f2=x.^2.*sin(x)-y.*(x.^2+y.^2)+3; contour(x,y,f2,[0.00 0.00],'b') grid on title('Contorno de f1(x,y) y f2(x,y) ') xlabel('EJE DE ABSCISAS') ylabel('EJE DE ORDENADAS')
x1=-5:0.05:5; y1=-5:0.05:5; [x,y]=meshgrid(x1,y1); f1=x.^2-3*y-4; contour(x,y,f1,[0.00 0.00],'r') hold on f2=-6*(x.^2+y.^2).^2+200*(x.*y); contour(x,y,f2,[0.00 0.00],'b') grid on title('Contorno de f1(x,y) y f2(x,y) ') xlabel('EJE DE ABSCISAS') ylabel('EJE DE ORDENADAS')
x1=-5:0.05:5; y1=-5:0.05:5; [x,y]=meshgrid(x1,y1); f1=x.^4+y.^4-2.3*(x.^2+y.^2)-exp(-x.*y); contour(x,y,f1,[0.00 0.00],'r') hold on f2=(x.^2+y.^2).^2+30*(x.*y)+sin(y); contour(x,y,f2,[0.00 0.00],'b') grid on title('Contorno de f1(x,y) y f2(x,y) ') xlabel('EJE DE ABSCISAS') ylabel('EJE DE ORDENADAS')
x1=-5:0.05:5; y1=-5:0.05:5; [x,y]=meshgrid(x1,y1); f1=1./(x.^2+y.^2+4*x-2*y+1)+0.5; contour(x,y,f1,[0.00 0.00],'r') hold on f2=x./(x.^2+y.^2+3*(x.*y))+2; contour(x,y,f2,[0.00 0.00],'b') grid on title('Contorno de f1(x,y) y f2(x,y) ') xlabel('EJE DE ABSCISAS') ylabel('EJE DE ORDENADAS')
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5 DR. SORIA QUIJAITE JUAN JESÚS
SUPERFICIES 2015
E1)
%EJEMPLO 1 clf; [x,y]=meshgrid(-8:8); r=sqrt(x.^2+y.^2); z=sin(r)./r; mesh(x,y,z,'EdgeColor','black'); xlabel('EJE ABSCISAS') ylabel('EJE ORDENADAS') zlabel('EJE Z') title('CÁLCULO III UPEU') grid on
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6 DR. SORIA QUIJAITE JUAN JESÚS
%EJEMPLO 2 %CURVA DISCONTINUA clf; [x,y]=meshgrid(-8:0.5:8); r=sqrt(x.^2+y.^2); z=sin(r)./r; surf(x,y,z,'FaceColor','red',... 'EdgeColor','none'); camlight right; lighting phong; title('CÁLCULO III UPEU') grid on
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7 DR. SORIA QUIJAITE JUAN JESÚS
%EJEMPLO 3 %CURVA CONTINUA CON eps clf; [x,y]=meshgrid(-8:0.5:8); r=sqrt(x.^2+y.^2)+eps; z=sin(r)./r; surf(x,y,z,'FaceColor','red',... 'EdgeColor','none'); camlight right; lighting phong; title('CÁLCULO III UPEU') grid on
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CÁLCULO III UPEU
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8 DR. SORIA QUIJAITE JUAN JESÚS
%EJEMPLO 4 clf; [x,y]=meshgrid(-2:0.05:2); z=x.*exp(-x.^2-y.^2); subplot(2,1,1) surf(x,y,z,'EdgeColor','none',... 'FaceColor','blue'); camlight right; lighting phong; subplot(2,1,2) contour3(x,y,z,20) grid on
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9 DR. SORIA QUIJAITE JUAN JESÚS