實驗四
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):
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=red):
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=blue):
w:=expand([1,v,u]/sqrt(u^2+v^2+1));
p5:=plot3d(w,u=-1..1,v=-1..1,scaling=constrained,color=yellow):
w:=expand([-1,v,u]/sqrt(u^2+v^2+1));
p6:=plot3d(w,u=-1..1,v=-1..1,scaling=constrained,color=yellow):
display(p1,p2,p3,p4,p5,p6);
restart;
plot3d(sin(phi)*sin(2*phi),theta=0..2*Pi,
restart;
plot3d(sin(phi)*sin(2*phi),theta=0..Pi,
phi=0..Pi/2,coords=spherical,scaling=constrained,grid=[15,19]);