> z:=cos(phi);
> r:=sin(phi);
> x:=r*cos(theta);
> y:=r*sin(theta);
> plot3d([x,y,z],phi=0..Pi,theta=0..2*Pi,scaling=constrained);

> restart;
> with(plots):
> z:=cos(phi);
> r:=sin(phi);
> x:=r*cos(theta);
> y:=r*sin(theta);
> p1:=plot3d([x,y,z],phi=0..Pi,theta=0..Pi/3,

    scaling=constrained,color=green,style=patchnogrid):
> theta:=0;
> z:=rho*cos(phi);
> r:=rho*sin(phi);
> x:=r*cos(theta);
> y:=r*sin(theta);
> p2:=plot3d([x,y,z],phi=0..Pi,rho=0..1,

    scaling=constrained,color=red,style=patchnogrid):
> theta:=Pi/3;
> z:=rho*cos(phi);
> r:=rho*sin(phi);
> x:=r*cos(theta);
> y:=r*sin(theta);
> p3:=plot3d([x,y,z],phi=0..Pi,rho=0..1,

    scaling=constrained,color=red,style=patchnogrid):
> display(p1,p2,p3);

> restart;
> with(plots):
> z:=cos(phi);
> r:=sin(phi);
> x:=r*cos(theta);
> y:=r*sin(theta);
> p1:=plot3d([x,y,z],phi=0..Pi,theta=0..Pi/3,scaling=constrained,color=green):
> p2:=plot3d([x,y,z],phi=0..Pi,theta=Pi/3..2*Pi/3,

    scaling=constrained,color=red):
> p3:=plot3d([x,y,z],phi=0..Pi,theta=2*Pi/3..Pi,

    scaling=constrained,color=green):
> p4:=plot3d([x,y,z],phi=0..Pi,theta=Pi..4*Pi/3,scaling=constrained,color=red):
> p5:=plot3d([x,y,z],phi=0..Pi,theta=4*Pi/3..5*Pi/3,

    scaling=constrained,color=green):
> p6:=plot3d([x,y,z],phi=0..Pi,theta=5*Pi/3..2*Pi,

    scaling=constrained,color=red):
> display(p1,p2,p3,p4,p5,p6);

> restart;
> z:=cos(phi);
> r:=sin(phi);
> x:=r*cos(theta+w);
> y:=r*sin(theta+w);
> with(plots):
> phi:=theta;
> p1:=plot3d([x,y,z],theta=0..Pi,w=0..Pi/3,

    scaling=constrained,color=red):
> p2:=plot3d([x,y,z],theta=0..Pi,w=Pi/3..2*Pi/3,

     scaling=constrained,color=green):
> p3:=plot3d([x,y,z],theta=0..Pi,w=2*Pi/3..Pi,

    scaling=constrained,color=red):
> p4:=plot3d([x,y,z],theta=0..Pi,w=Pi..4*Pi/3,

    scaling=constrained,color=green):
> p5:=plot3d([x,y,z],theta=0..Pi,w=4*Pi/3..5*Pi/3,

    scaling=constrained,color=red):
> p6:=plot3d([x,y,z],theta=0..Pi,w=5*Pi/3..2*Pi,

    scaling=constrained,color=green):
> display(p1,p2,p3,p4,p5,p6);

> restart;
> z:=cos(phi);
> r:=sin(phi);
> x:=r*cos(theta+w);
> y:=r*sin(theta+w);
> with(plots):
> phi:=theta;
> p1:=plot3d([x,y,z],theta=0..Pi,w=0..Pi,scaling=constrained,color=red):
> p2:=plot3d([x,y,z],theta=0..Pi,w=Pi..2*Pi,scaling=constrained,color=green):
> display(p1,p2);

> restart;
> z:=cos(phi);
> r:=sin(phi);
> x:=r*cos(theta);
> y:=r*sin(theta);
> with(plots):
> phi:=theta+w;
> p1:=plot3d([x,y,z],theta=0..Pi,w=0..Pi,

    scaling=constrained,color=red,style=patchnogrid):
> p2:=plot3d([x,y,z],theta=0..Pi,w=Pi..2*Pi,scaling=constrained,

    color=green,style=patchnogrid):
> display(p1,p2);

> restart;
> with(plots):
> p:=[-1,1,1]; q:=[1,-1,1]; r:=[1,1,-1];
> w:=expand((1-v)*((1-u)*p+u*q)+v*r);
> ww:=expand(w/sqrt(w[1]^2+w[2]^2+w[3]^2)):
> p1:=plot3d(ww,u=0..1,v=0..1,scaling=constrained,color=red):
> p:=[-1,-1,-1]; q:=[1,-1,1]; r:=[1,1,-1];
> w:=expand((1-v)*((1-u)*p+u*q)+v*r);
> ww:=expand(w/sqrt(w[1]^2+w[2]^2+w[3]^2)):
> p2:=plot3d(ww,u=0..1,v=0..1,scaling=constrained,color=green):
> p:=[-1,1,1]; q:=[-1,-1,-1]; r:=[1,1,-1];
> w:=expand((1-v)*((1-u)*p+u*q)+v*r);
> ww:=expand(w/sqrt(w[1]^2+w[2]^2+w[3]^2)):
> p3:=plot3d(ww,u=0..1,v=0..1,scaling=constrained,color=blue):
> p:=[-1,1,1]; q:=[1,-1,1]; r:=[-1,-1,-1];
> w:=expand((1-v)*((1-u)*p+u*q)+v*r);
> ww:=expand(w/sqrt(w[1]^2+w[2]^2+w[3]^2)):
> p4:=plot3d(ww,u=0..1,v=0..1,scaling=constrained,color=yellow):
> display(p1,p2,p3,p4);

> restart;
> with(plots):
> w:=expand([u,v,1]/sqrt(u^2+v^2+1));
> p1:=plot3d(w,u=-1..1,v=-1..1,scaling=constrained,color=red):
> w:=expand([u,v,-1]/sqrt(u^2+v^2+1));
> p2:=plot3d(w,u=-1..1,v=-1..1,scaling=constrained,color=green):
> w:=expand([u,1,v]/sqrt(u^2+v^2+1));
> p3:=plot3d(w,u=-1..1,v=-1..1,scaling=constrained,color=blue):
> w:=expand([u,-1,v]/sqrt(u^2+v^2+1));
> p4:=plot3d(w,u=-1..1,v=-1..1,scaling=constrained,color=yellow):
> w:=expand([1,v,u]/sqrt(u^2+v^2+1));
> p5:=plot3d(w,u=-1..1,v=-1..1,scaling=constrained,color=gray):
> w:=expand([-1,v,u]/sqrt(u^2+v^2+1));
> p6:=plot3d(w,u=-1..1,v=-1..1,scaling=constrained,color=cyan):
> display(p1,p2,p3,p4,p5,p6);

> restart;
> plot3d(sin(phi)*sin(2*phi),theta=0..Pi,phi=0..Pi/2,
    coords=spherical,scaling=constrained);

> restart;
> plot3d(sin(phi)*sin(2*phi),theta=0..2*Pi,phi=0..Pi,
    coords=spherical,scaling=constrained);