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圆环面螺线

2009-08-06 23:46:21| 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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高等数学图形与动画

圆环面螺线（Toroidal spiral）

圆环面螺线就是在圆环面上一种螺旋线，其参数方程为：

with(plots):

x:=t->(4+sin(20*t))*cos(t): y:=(4+sin(20*t))*sin(t):z:=t->cos(20*t):

spacecurve([x(t), y(t), z(t)], t=0..2*Pi, thickness=4, color=red, axes=normal, numpoints=1000, scaling=constrained);

with(plots):a:=4:b:=1:b1:=0.95*b:c:=20:

quxian:=spacecurve([(a+b*cos(c*t))*cos(t),(a+b*cos(c*t))*sin(t),b*sin(c*t)],t=0..2*Pi,numpoints=250,

color=red,thickness=4):

qumian:=plot3d([(a+b1*cos(v))*cos(u),(a+b1*cos(v))*sin(u),b1*sin(v)],u=0..2*Pi,v=0..2*Pi,

color=green,style=patch):

display(quxian,qumian,scaling=constrained);

with(plots):

a:=4:b:=1:c:=20:

qumian:=plot3d([(a+b*cos(v))*cos(u),(a+b*cos(v))*sin(u),b*sin(v)],u=0..2*Pi,v=0..2*Pi,style=wireframe):

K:=200:for i from 1 to K do ti:=i*2*Pi/K:

quxian[i]:=spacecurve([(a+b*cos(c*t))*cos(t),(a+b*cos(c*t))*sin(t),b*sin(c*t)],t=0..ti, numpoints=250,color=red,thickness=4):od:

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

display(qumian,quxian,scaling=constrained,orientation=[0,60]);

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