I want to show intersection of these two spheres. How should I do it?
19 vues (au cours des 30 derniers jours)
Afficher commentaires plus anciens
theta=linspace(0,2*pi,40);
phi=linspace(0,pi,40);
[theta,phi]=meshgrid(theta,phi);
r=1;
x=r*sin(phi).*cos(theta);
y=r*sin(phi).*sin(theta);
z=r*cos(phi);
mesh(x,y,z)
hold on
theta=linspace(0,2*pi,40);
phi=linspace(0,pi,40);
[theta,phi]=meshgrid(theta,phi);
r=1;
x=r*sin(phi).*cos(theta);
y=r*sin(phi).*sin(theta);
z=r*cos(phi);
x=x+0.25;
y=y-0.2;
z=z+0.1;
surf(x,y,z)
0 commentaires
Réponse acceptée
Kye Taylor
le 16 Avr 2013
Modifié(e) : Kye Taylor
le 16 Avr 2013
The spheres you describe have equations
1.) x^2 + y^2 + z^2 = 1
2.) (x-0.25)^2 + (y+1/5)^2 + (z-0.1)^2 = 1
Since equations 1 and 2 have same right-hand-side (equal to one), set the left-hand sides equal and you'll end up getting rid of the squared terms to be left with
3.) 5*x+4*y+2*z = 9/8
Equation 3 is the equation for the plane that contains the intersection of the two spheres. To see it add these lines of code to the end of your code above.
[X,Y] = meshgrid(linspace(-1,1,20));
Z = -5/2*X + 2*Y + 9/16;
surf(X,Y,Z)
That gives you the plane that contains the intersection. Realize that the intersection of the spheres is actually a curve that is a circle in this plane. Parametrizing that circle is more complicated.
3 commentaires
Kye Taylor
le 16 Avr 2013
My pleasure!
What do you mean by common value? As you move along the curve where the two spheres meet, the values of (x,y,z) will change.
Jelle
le 26 Avr 2013
In case you guys haven't seen it yet, there is a sign mistake in the code. Equation 3 is correct and hence the code should be:
[X,Y] = meshgrid(linspace(-1,1,20));
Z = -5/2*X + 2*Y - 9/16;
surf(X,Y,Z)
This answer is validated by plotting both unit spheres and the plane that contains the intersection.
[X,Y] = meshgrid(linspace(-1,1,20));
Z = -5/2*X + 2*Y - 9/16;
surf(X,Y,Z)
hold on
[x,y,z] = sphere;
surf(x,y,z)
surf((x-0.25),(y+0.2),(z-0.1))
daspect([1 1 1])
Plus de réponses (0)
Voir également
Catégories
En savoir plus sur Surface and Mesh Plots dans Help Center et File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!