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平面区域的正向边界曲线（动画）

2012-04-24 22:40:29| 分类：高等数学图形动画 | 标签： |举报 |字号大中小订阅

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一个平面区域的边界曲线的正向是这样规定的：当你沿着边界的正向行走时，你附近的区域总是在你的左边。

以下动画显示了正向边界曲线的方向。

动画1的Maple程序：

with(plots):

x:=t->2*cos(t):y:=t->sin(t):

Quxian:= plot([x(t),y(t),t=0..2*Pi],thickness=5,color=gray,filled=true):

K:=40:

for i from 1 to K do

ti:=i*2*Pi/K:quxian[i]:=plot([x(t),y(t),t=0..ti],thickness=3):od:

quxian:=display(seq(quxian[i],i=1..K),insequence=true):

display(quxian,Quxian,scaling=constrained);

动画2的Maple程序：
with(plots):

x1:=t->4*cos(t):y1:=t->2*sin(t):

x2:=t->cos(t):y2:=t->sin(t):

Quxian1:= plot([x1(t),y1(t),t=0..2*Pi],color=green,filled=true):

Quxian2:= plot([x2(t),y2(t),t=0..2*Pi],color=white,filled=true):

K:=50:

for i from 1 to K do

ti:=i*2*Pi/K:

quxian1[i]:=plot([x1(t),y1(t),t=0..ti],thickness=4):

quxian2[i]:=plot([x2(-t),y2(-t),t=0..ti],thickness=4):od:

quxian1:=display(seq(quxian1[i],i=1..K),insequence=true):

quxian2:=display(seq(quxian2[i],i=1..K),insequence=true):

display(quxian2,quxian1,Quxian2,Quxian1,scaling=constrained);

动画3的Maple程序：
with(plots):

x1:=t->4*cos(t):y1:=t->2*sin(t):

x2:=t->1.4*cos(t)-1:y2:=t->1.2*sin(t):

x3:=t->cos(t)+2:y3:=t->sin(t)/2:

Quxian1:= plot([x1(t),y1(t),t=0..2*Pi],color=gray,filled=true):

Quxian2:= plot([x2(t),y2(t),t=0..2*Pi],color=white,filled=true):

Quxian3:= plot([x3(t),y3(t),t=0..2*Pi],color=white,filled=true):

K:=50:

for i from 1 to K do

ti:=i*2.5*Pi/K:

quxian1[i]:=plot([x1(t),y1(t),t=0..ti],thickness=4):

quxian2[i]:=plot([x2(-t),y2(-t),t=0..ti],thickness=4):

quxian3[i]:=plot([x3(-t),y3(-t),t=0..ti],thickness=4):od:

quxian1:=display(seq(quxian1[i],i=1..K),insequence=true):

quxian2:=display(seq(quxian2[i],i=1..K),insequence=true):

quxian3:=display(seq(quxian3[i],i=1..K),insequence=true):

display(quxian3,quxian2,quxian1,Quxian3,Quxian2,Quxian1,scaling=constrained);

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