實驗一 環面、Villarceaux圓、環面上之圖案
實驗二 圓柱面上之曲線、環面上之曲線、鞍面、Monkey's Saddle
實驗三 球面上之曲線、球面上之圖案
實驗四 旋轉曲面、結
實驗五 微積分所探討的立體模型  曲率
實驗六 動態生成
實驗七 微積分所探討的立體模型
實驗八 球面上相切的圓
實驗九 球面與正多面體之設計
實驗十 動態圖形animate gif之製作

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實驗五 微積分所探討的立體模型  曲率

with(plots);

animate([cos(r)*cos(t),cos(r)*sin(t),t=0..2*Pi],r=0..2*Pi,frames=50);

p1:=plot([cos(t)^3,sin(t)^3,t=0..2*Pi],color=blue):

p2:=animate([cos(s)^2*cos(t),sin(s)^2*sin(t),t=0..2*Pi],s=0..2*Pi,frames=100):

display(p1,p2,axes=none);

　
with(plots):
x:=5*cos(t);y:=3*sin(t);
x1:=diff(x,t);y1:=diff(y,t);
x2:=diff(x1,t);y2:=diff(y1,t);
 w:=x1*y2-x2*y1;
r:=(x1^2+y1^2)^(3/2)/abs(w);
xc:=x-(x1^2+y1^2)/w*y1;yc:=y+(x1^2+y1^2)/w*x1;
p1:=plot([x,y,t=0..2*Pi],scaling=constrained):
p2:=animate([xc+r*cos(s),yc+r*sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,color=blue,frames=100):
p3:=animate([(1-s)*xc+s*x,(1-s)*yc+s*y,s=0..1],t=0..2*Pi,color=green,frames=100,scaling=constrained):
p4:=plot([xc,yc,t=0..2*Pi],scaling=constrained,color=yellow):
 display(p1,p2,p3,p4,axes=none,thickness=3);

with(plots):
n:=3;
x:=cos(n*t)-n*cos(t);y:=sin(n*t)-n*sin(t);
x1:=diff(x,t);y1:=diff(y,t);
x2:=diff(x1,t);y2:=diff(y1,t);
w:=x1*y2-x2*y1;
r:=(x1^2+y1^2)^(3/2)/abs(w);
xc:=x-(x1^2+y1^2)/w*y1;yc:=y+(x1^2+y1^2)/w*x1;
p1:=plot([x,y,t=0..2*Pi],scaling=constrained):
p2:=animate([xc+r*cos(s),yc+r*sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,color=blue,frames=100):
p3:=animate([(1-s)*xc+s*x,(1-s)*yc+s*y,s=0..1],t=0..2*Pi,color=green,frames=100,scaling=constrained):
p4:=plot([xc,yc,t=0..2*Pi],scaling=constrained,color=yellow):
 display(p1,p2,p3,p4,axes=none,thickness=3,view=[-5..5,-5..5]);

with(plots);
n:=-3;
x:=cos(n*t)-n*cos(t);y:=sin(n*t)-n*sin(t);
x1:=diff(x,t);y1:=diff(y,t);
x2:=diff(x1,t);y2:=diff(y1,t);
w:=x1*y2-x2*y1;
r:=(x1^2+y1^2)^(3/2)/abs(w);
xc:=x-(x1^2+y1^2)/w*y1;yc:=y+(x1^2+y1^2)/w*x1;
p1:=plot([x,y,t=0..2*Pi],scaling=constrained):
p2:=animate([xc+r*cos(s),yc+r*sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,color=blue,frames=100):
p3:=animate([(1-s)*xc+s*x,(1-s)*yc+s*y,s=0..1],t=0..2*Pi,color=green,frames=100,scaling=constrained):
p4:=plot([xc,yc,t=0..2*Pi],scaling=constrained,color=yellow):
display(p1,p2,p3,p4,axes=none,thickness=3,view=[-8..8,-8..8]);

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