實驗九

restart;

with(plots):

r:=sqrt(24)/3;

q1:=[0,0,sqrt(3)];

x1:=r*cos(t);

y1:=r*sin(t);

z1:=sqrt(3)/3;

q2:=[x1,y1,z1];

p:=Pi/3;

x2:=r*cos(t+p);

y2:=r*sin(t+p);

z2:=-sqrt(3)/3;

q3:=[x2,y2,z2];

q4:=[0,0,-sqrt(3)];

q12:=expand((1-u)*q1+u*q2):

q23:=expand((1-u)*q2+u*q3):

q34:=expand((1-u)*q3+u*q4):

p12:=plot3d(q12,u=0..1,t=0..4*Pi/3,scaling=constrained,color=red):

p23:=plot3d(q23,u=0..1,t=0..4*Pi/3,scaling=constrained,color=blue):

p34:=plot3d(q34,u=0..1,t=0..4*Pi/3,scaling=constrained,color=red):

restart;

with(plots):

p1:=plot3d([1,theta,phi],theta=0..Pi,phi=0..2*Pi/3,coords=spherical,scaling=constrained,style=patchnogrid):

phi:=2*Pi/3;

rho:=1;

z:=rho*cos(phi);

r:=rho*sin(phi);

x:=r*cos(theta);

y:=r*sin(theta);

q:=expand((1-u)*[0,0,-2]+u*[x,y,z]):

p2:=plot3d(q,u=0..1,theta=0..Pi,scaling=constrained,style=patchnogrid):

restart;

with(plots):

with(plottools):

p1:=display(sphere([0,0,1],1)):

p2:=display(sphere([1,1,0.3],0.3)):

p3:=display(sphere([0,2,0.5],0.5)):

pa:=display(p1,p2,p3,scaling=constrained,style=patchnogrid):

expand((1-u1)*[1,1,0.3]+u1*[0,2,0.5]);

u1:=-3/2;

expand((1-u1)*[1,1,0.3]+u1*[0,2,0.5]);

p32:=display(line([0,2,0],[5/2,-1/2,0]),thickness=3,color=red):

expand((1-u2)*[0,2,0.5]+u2*[0,0,1]);

u2:=-1;

expand((1-u2)*[0,2,0.5]+u2*[0,0,1]);

p13:=display(line([0,0,0],[0,4,0]),thickness=3,color=green):

expand((1-u3)*[1,1,0.3]+u3*[0,0,1]);

u3:=-3/7;

expand((1-u3)*[1,1,0.3]+u3*[0,0,1]);

p12:=display(line([10/7,10/7,0],[0,0,0]),thickness=3,color=blue):

pb:=display(p12,p13,p32):

pc:=reflect(pb,[[0,0,1],[1,1,0.3],[0,2,0.5]]):

pd:=display(line([0,4,0],[5/2,-1/2,0]),thickness=3,color=yellow):

restart;

q:=expand((1-v)*[cos(t),0,1]+v*[0,sin(t),-1]):

restart;

m:=[[x,0],[0,y]];

x:=cos(t);

y:=sin(t);

t:=n*2*Pi/100;

restart;

m:=[[x,y],[x,-y],[x1,-y],[x1,y],[x,y]];

x:=cos(t)-1;

y:=sin(t);

t:=n*Pi/100;

x1:=sqrt(1-(y-1)^2);