第11章-3D动画的设计技术

1、Maple的图形动画技术一一用Maple（69）制作数学动画课件第十一章3D动画的设计技术图11-0103点的过程动画with(plots):with(plottools):N:=24:F:=i-poi nt(cos(i*2*Pi/12),s in (i*2*Pi/12),3,color=bl ue,symbol=DIAMOND,symbolsize=55): display(seq(F(i),i=O.N),i nseque nce=true,axes=FRAME,ori en tatio n=-12,35);d1:=%:PLOT3D(ANIMATE(seq(F(i),i=O.N),AXESS

2、TYLE(FRAME);d2:= %:;spacecurve(cos(i*2*Pi/12),si n( i*2*Pi/12),3,i=0.N);d3:=%:display(d1,d3);display(d2,d3);flyi .-丄：图1使用对象函数制作的孤点过程动画(连环画)with(plots):N:=24:h:=4:F:=i-poi ntplot3d(cos(4*Pi*i/N),si n(4*Pi*i/N),h/N*i,g rid=5,3,symbol=circle,symbolsize=23,style=POINT,color =blue):display(seq(F(i),i=0.N

3、),i nseque nce=true,axes=box);d1:= %:;PLOT3D(ANIMATE(seq(op(F(i),i=O.N);d2:=%:;spacecurve(cos(i*4*Pi/24),si n( i*4*Pi/24),4*i/24,i=0. 24,color=red,style=LINE);d3:=%: display(d2,d3,axes=frame);Maple的图形动画技术一一用Maple（69）制作数学动画课件3图2使用绘图函数制作的孤点过程动画(连环画)使用变换函数和对象函数制作孤点过程动画with(plots):with(plottools):a:=3:b

4、:=2:k:=6:n :=2:m:=0: N:=72:t:=2*Pi*i/N:L:=poi nt( -n ,m,m,color=blue,symbol=circle,symbolsize=23):L1:=i-tra nslate(L,a*cos(k*Pi*i/N),b*si n(k*Pi*i/N),0)display(seq(L1(i),i=0.N),axes=n ormal,labels=x,y,z,i n seque nce=true,orie ntati on=-80,65);PL0T3D(ANIMATE(seq(L1(i),i=0.N),0RIENTATI0N(-80,65),A XE

5、S(FRAME);内层动画with(plots): R:=24:a:=0:b:=4*Pi:f:二n-cos(a+(b-a)* n/R):g:=n-s in (a+(b-a)* n/R):h:=n-(a+(b-a)* n/R)/2:F:=n-POINTS(evalf(f( n),g( n),h( n),SYMBOL(CIRCLE,36) ,COLOR(RGB,1,0,0):PLOT3D(ANIMATE(seq(F( n),n=0.R),AXES(FRAME),VIEW(-1.1. .1.1,-1.1.1.1,0.7),ORIENTATION(9,71);display(seq(F( n), n=

6、0.R),i nseque nce=true,axes=box,view=-1.1. 1.1,-1.1.1.1,0.7,orie ntati on=9,71);图3用内层方法设计的点过程动画图11-0411点的踪迹动画 使用对象函数制作点踪迹动画(匀步长)A, 使用对象函数 plottoolspoint with(plots):with(plottools): N:=54:h:=4:r:=1-k/N: F1:=i-seq(poi nt( r*cos(k*6*Pi/N),r*si n( k*6*Pi/N),h/N* k,symbolsize=54,symbol=CIRCLE,color=blac

7、k),k=0.i): spacecurve( r* cos(6*Pi*k/N),r*s in (6*Pi*k/N),h/N*k,k=0. .N,color=gree n):d01:=%: display(ANIMATE(seq(F1(i),i=0.N),i nseque nce=true,axes =FRAME,orie ntatio n=65,65,view=-1.1,-1.1,0.4):;d1 1:=%:;display(d01,d11);B, 使用对象函数 plottoolscurve F2:=i-curve(seq( r* cos(k*6*Pi/N),r*si n( k*6*Pi/N)

8、,h/N *k,k=0.i),thick ness=3,color=red,style=POINT,symbolsi ze=36,symbol=DIAMOND):spacecurve( r* cos(6*Pi*k/N),r*s in (6*Pi*k/N),h/N*k,k=0. .N,color=mage nta):d02:=%: display(ANIMATE(seq(F2(i),i=0.N),i nseque nce=true,axes =box,orie ntatio n=65,65,view=-1.1,-1.1,0.5):;d12: =%:;display(d02,d12);C, 使用对

9、象函数 plottoolspolygo n F3:=i-polygo n( seq( r* cos(k*6*Pi/N),r*si n( k*6*Pi/N),h /N*k,k=0.i),thick ness=3,color=blue,style=POINT,symbo lsize=36,symbol=DIAMOND):spacecurve( r* cos(6*Pi*k/N),r*s in (6*Pi*k/N),h/N*k,k=0. .N,color=cya n):d03:=%: display(ANIMATE(seq(F3(i),i=0.N),i nseque nce=true,axes =bo

10、x,orie ntatio n=65,65,view=-1.1,-1.1,0.5):;d13: =%:;使用三个不同对象函数的方案，自左至右:A,B,Cdisplay(d03,d13);图4 效果相同的连环画使用绘图函数制作点踪迹动画(匀步长)A, 使用 pointplot3d函数with(plots):with(plottools): N:=54:h:=4:r:=(1-k/N)A2: F1:=i-poi ntplot3d(seq( r*cos(k*6*Pi/N),r*si n(k*6*Pi/N ),h*r/N*k,k=0.i),symbol=DIAMOND,color=blue,symbol

11、siz e=12):spacecurve( r* cos(6*Pi*k/N),r*s in (6*Pi*k/N),h*r/N*k,k= 0.N): d0:=%:display(seq(F1(i),i=0.N),i nseque nce=true,axes=box,view =-1.1,-1.1,0.0.8,orie ntatio n=67,73):;d11:=%:display(d0,d11);B, 使用 polygonplot3d函数with(plots):with(plottools):N:=54:h:=4:r:=(1-k/N)A2: F2:=i-polyg on plot3d(seq(

12、r* cos(k*6*Pi/N),r*si n( k*6*Pi /N),h*r/N*k,k=0.i),symbol=DIAMOND,color=blue,style=P OINT,symbolsize=12):spacecurve( r* cos(6*Pi*k/N),r*s in (6*Pi*k/N),h*r/N*k,k= 0.N): d0:=%: display(seq(F2(i),i=0.N),i nseque nce=true,axes=box,view =-1.1,-1.1,0.0.8,orie ntatio n=67,73):d12:=%: display(d0,d12);C, 使用

13、spacecurve 函数 with(plots):with(plottools):N:=54:h:=4:r:=(1-k/N)A2: F3:=i-spacecurve(seq( r*cos(k*6*Pi/N),r*si n( k*6*Pi/N) ,h*r/N*k,k=0.i),style=POINT,symbolsize=12,symbol=DIA MOND,color=blue):第2编第1章 Maple的3D图形基本功能spacecurve(r* cos(6*Pi*k/N),r*s in (6*Pi*k/N),h*r/N*k,k=0.N): d0:=%:display(seq(F3(i),

14、i=0.N),in seque nce=true,axes=box,view =-1.1,-1.1,0.0.8,orie ntatio n=67,73):d13:=%: display(d0,d13);.u D n Q o o o Q图5 效果相同的连环画#使用变换函数制作点踪迹动画（匀步长）with(plots):with(plottools):N:=54:h:=4:r:=k/N:a:=1:b:=2:c:=0:poi nt(a,b,c,symbolsize=12,symbol=CIRCLE,color=black):G:=%:F:=i-seq(tra nslate(G,r*cos(k*6*P

15、i/N),r*si n( k*6*Pi/N), h/N*k),k=0.i):spacecurve(a+r*cos(6*Pi*k/N),b+r*si n( 6*Pi*k/N),c+h/N*k ,k=0.N,color=gree n):d0:=%:display(ANIMATE(seq(F(i),i=0.N),i nseque nce=true,axes= FRAME,orie ntatio n=65,65,view=a-1.a+1,b-1.b+1,c.c+ 4):d1:=%:display(d0,d1);Q:=%:图6用变换函数制作的点踪迹动画(匀步长) 点的步进式踪迹动画(匀步长) with(

16、plots):R:=8:a:=0:b:=2*Pi:w:=3: f:=i-cos(a+(b-a)*i/R/w):g:=i-si n(a+(b-a)*i/R/w):h:=i-(a+(b-a)*i/R/w)/2:F:=n-POINTS(seq(evalf(f(i),g(i),h(i),i=0.w* n),SYMB0L(CIRCLE,18),C0L0R(RGB,1,0,0):display(seq(F( n), n=0.R),i nseque nce=true,axes=box,orie n tatio n=70,50,view=-1.1,-1.1,0.3.3);Q:=%: PLOT3D(ANIMAT

17、E(seq( F(n), n=0.R),AXES(FRAME):;图7点元步进式踪迹（匀步长）动画点的步进式踪迹动画（变步长）with(plots):R:=8: f:=i-cos(a+(b-a)*i/ g:=i-s in (a+(b-a)*i/ h:=i-(a+(b-a)*i/K :=21:a:=0:b:=2*Pi:K):K):K)/2:K/R* n),SF:=n-POINTS(seq(evalf(f(i),g(i),h(i),i=0.YMBOL(CIRCLE,18),COLOR(RGB,0,0,1): Maple的图形动画技术一一用Maple（69）制作数学动画课件display(seq(F

18、( n), n=O.R),i nseque nce=true,axes=frame,ori en tatio n=30,65);Q:=%:PL0T3D(ANIMATE(seq( F(n), n=0.R),AXES(FRAME):; - 一/”j亠“亠 *#匚：、图8 点元步进式踪迹（变步长）动画点的链伸式踪迹动画(全元族)with(plots):K:=18:R:=8:a:=0:b:=2*Pi:f:=(i, n)-cos(a+(b-a)*i/K* n/R): g:=(i, n)-si n(a+(b-a)*i/K* n/R): h:=(i, n)-(a+(b-a)*i/K* n/R)/2:F:=n

19、-POINTS(seq(evalf(f(i, n),g(i, n),h(i, n),i=0.K) ,SYMBOL(CIRCLE,18),COLOR(RGB,1,0,0): display(seq(F( n), n=0.R),i nseque nce=true,axes=box); PLOT3D(ANIMATE(seq(F( n),n=0.R),AXES(FRAME);图9点的链伸式踪迹动画（变元族，匀步长）with（plots）:K:=15:R:=8:w:=2:u:=w*R/K:a:=0:b:=2*Pi:f:=(i, n)-cos(a+(b-a)*i/K* n/R/u):g:=(i, n)-s

20、i n(a+(b-a)*i/K* n/R/u):h:=(i, n)-(a+(b-a)*i/K* n/R/u)/2:F:=n-POINTS(seq(evalf(f(i, n),g(i, n),h(i, n),i=O.w* n),SYMBOL(CIRCLE,18),COLOR(RGB,1,0,0): display(seq(F( n), n=0.R),i nseque nce=true,axes=box,orie n tatio n=73,58):;PLOT3D(ANIMATE(seq( F(n), n=0.R),AXES(FRAME);图10 点元链伸式踪迹（变元族，等步长）动画点的链伸式踪迹动

21、画(变元族，变步长)with(plots):K:=19:R:=8:a:=0:b:=2*Pi:f:=(i, n)-cos(a+(b-a)*i/K* n/R):g:=(i, n)-si n(a+(b-a)*i/K* n/R):h:=(i, n)-(a+(b-a)*i/K* n/R)/2:F:=n-POINTS(seq(evalf(f(i, n),g(i, n),h(i, n),i=0.K/R* n),SYMBOL(DIAMOND,18),COLOR(RGB,0,0,1): display(seq(F( n), n=0.R),i nseque nce=true,axes=box);PLOT3D(AN

22、IMATE(seq(F( n),n=0.R),AXES(FRAME),ORIENTATION(5,55);II IIj 一-F1+ a 4L j8图11点元链伸式踪迹(变元族，变步长)动画图11-1215线的过程动画使用对象函数制作线元的过程动画with(plots):with(plottools):N:=8:F:=i-curve(-1,0,0,1,0,0,0,0,0,0,2*cos(i*2*Pi/N),2*si n( i*2*Pi/N),0,2*cos(i*2*Pi/N)+5,0,0,2*cos(i*2*Pi/N)+8,0,1/2,2*cos(i*2*Pi/N)+7,0,-1/2,2*cos

23、(i*2*Pi/N)+7,0,0,2*cos(i*2*Pi/N)+8,0,color=black,thick ne ss=4):display(seq(F(i),i=0.N),i nseque nce=true,axes=frame):;PLOT3D(ANIMATE(seq(F(i),i=0.N),AXESSTYLE(FRAME):;0图12用对象函数制作的线元过程动画(曲柄连杆机构的运动) 使用绘图函数制作线元的过程动画with(plots):N:=27:r:=25:F:=i-spacecurve( r* cos(i*2*Pi/N)+t*cos(t),r*si n( i*2*Pi/N)+t*

24、si n(t),t,t=0.6*Pi,color=black,thick ness=3):display(seq(F(i),i=0.N),i nseque nce=true,axes=n ormal):PLOT3D(ANIMATE(seq(F(i),i=0.N),AXESSTYLE(FRAME):AT*弋IQ9X 11 -zlz-C tra nslate(L,r*cos(i*2*Pi/N),r*si n(i*2*Pi/N),0): display(seq(F(i),i=0.N),i nseque nce=true,axes=box):d1:= %:spacecurve(r*cos(t),r*s

25、i n( t),0,t=0.2*Pi,color=blue): d0:=%:display(d0,d1,orie ntatio n=50,73);Q:=%:第2编第1章 Maple的3D图形基本功能图14用变换函数制作的线元过程动画with(plots):M:=36:R:=24:a:=0:b:=4*Pi: c:=0:d:=2*Pi:f:=(i, n)-cos(a+(b-a)*i/M)+si n( c+(d-c)* n/R): g:=(i, n)-(a+(b-a)*i/M)/6+(c+(d-c)* n/R): h:=(i, n)-si n(a+(b-a)*i/M):F:=n-CURVES(seq

26、(evalf(f(i, n),g(i, n),h(i, n),i=0.M ),THICKNESS(3),C0L0R(RGB,1,0,0): display(seq(F( n), n=0.R),i nseque nce=true,axes=NORMAL,la bels=x,y,z,orie ntatio n=63,73);图15 一个内层线元过程动画的连环画图11-1623线的的踪迹动画使用对象函数制作线元的踪迹动画(匀步长)with(plots):with(plottools):R:=16:G:=n-seq(curve(0,0,0,cos(i*2*Pi/R),s in (i*2*Pi/R),5

27、,1.5*cos(i*2*Pi/R),1.5*si n( i*2*Pi/R),5,cos(i*2*Pi/R),si n( i*2*Pi/R),2,cos(i*2*Pi/R),si n( i*2*Pi/R),3,lin estyle=1,thick ness=3,color=red),i=0. n):display(ANIMATE(seq(G( n), n=0.R),i nseque nce=true,axes= frame):图16 用对象函数制作线元的踪迹动画使用绘图函数制作线元的踪迹动画(匀步长)with(plots):R:=24:r:=8:G:=n-seq(spacecurve(0+2*

28、Pi*i/R,t*cos(t)-30+r*si n(2*Pi *i/R),t*si n(t),t=0.6*Pi,color=black,thick ness=1),i=0.n):display(seq(display(G( n), n=0.R),i nseque nce=true,axes= frame);图17 用绘图函数制作线元的踪迹动画使用变换函数制作线元的踪迹动画(匀步长)restart:with(plottools):with(plots):R:=24:r:=2:t:=4*Pi*i/R:L:=curve(0,0,0,1/3,-1/7,1.2,1,0,1,1/3,1/7,1.2, 0,

29、0,0,thick ness=3,color=COLOR(RGB,0.2,0.8,0.1): f:=i-tra nslate(rotate(L,0,0,-t),r*cos(t),r*si n( t),t/1)Jspacecurve( r* cos(t1),r*si n( t1),t1/1,t 1= 0.4*Pi,color= brow n,thick ness=2):d0:=%:G:=n-seq(f(i),i=0. n):#Maple的图形动画技术一一用Maple（69）制作数学动画课件display(ANIMATE(seq(G( n), n=O.R),i nseque nce=true,or

30、ien tatio n=54,61,axes=frame):;dh:=%: display(dh,dO);图18用变换函数制作线元的踪迹动画线的步进式踪迹动画（匀步长）M:=24:R:=8:w:=2:a:=-2*Pi:b:=2*Pi:c:=0:d:=2*Pi:f：=(i,k)-(a+(b-a)*i/M)+3*sin(c+(d-c)*k/R/w):g:=(i, k)-(c+(d-c)*k/R/w):h:=(i, k)-cos(a+(b-a)*i/M):F:=n-CURVES(seq(seq(evalf(f(i,k),g(i,k),h(i,k),i=0.M),k=0.w*n),THICKNESS(

31、2),COLOR(RGB,0,0,1):PLOT3D(ANIMATE(seq(F(n),n=O.R),AXES(FRAME);Q:=%:JU邈_徳、-图19线元匀步长步进式踪迹动画的内层设计线的步进式踪迹动画（变步长）M:=21:R:=8:u:=M/R:a:=-4:b:=4:c:=0:d:=2*Pi: f:=(i,k)-(a+(b-a)*i/M):g:=(i,k)-(c+(d-c)*k/R/u): h:=(i,k)-(a+(b-a)*i/M)A2+3*si n( c+(d-c)*k/R/u): F:=n-CURVES(seq(seq(evalf(f(i,k),g(i,k),h(i,k),i=

32、0.M),k=0.M/R* n),THICKNESS(2),COLOR(RGB,1,0,0): PL0T3D(ANIMATE(seq(F( n), n=0.R),AXES(NORMAL),ORIENTATI ON(30,75);17图20线元变步长步进踪迹动画的内层设计 线的链伸式踪迹动画（全元族）M:=15:K:=12:R:=8:a:=-1:b:=1:c:=0:d:=2*Pi:f:=(i,k ,n )-(a+(b-a)*i/M)-2*si n( c+(d-c)*k/K* n/R):g:=(i,k, n)-(c+(d-c)*k/K* n/R):h:=(i,k, n)-1-(a+(b-a)*i/

33、M)A3:F:=n-CURVES(seq(seq(evalf(f(i,k ,n ),g(i,k, n) ,h(i,k ,n ),i=0.M),k=0.K),THICKNESS(2),COLOR(RGB,1,0,0):PLOT3D(ANIMATE(seq(F( n),n=0.R),AXES(FRAME),ORIENTATIO N(-23,74);图21线元全元族链伸动画的内层设计线的链伸式踪迹动画(变元族，匀步长)M:=18:R:=8:w:=2:a:=0:b:=2*Pi:c:=0:d:=2*Pi:m:=5:f:=(i,k, n)-m*cos(a+(b-a)*i/M)+3*s in (c+(d-c

34、)*k/R* n/R/w):g:=(i,k, n)-(c+(d-c)*k/R* n/R/w):h:=(i,k, n)-m*si n( (a+(b-a)*i/M):F:=n-seq(CURVES(seq(evalf(f(i,k, n) ,g(i,k ,n ),h(i,k ,n ),i=0.M),C0L0R(HUE,k/16),THICKNESS(2),k=0.w* n): PL0T3D(ANIMATE(seq( F(n), n=0.R),AXES(NORMAL);图22内层线元变元族匀步长链伸动画的设计 线的链伸式踪迹动画(变元族，变步长)M:=5:K:=13:R:=8:a:=-1:b:=1:c

35、:=0:d:=2*Pi:f:=(i,k, n)-(a+(b-a)*i/M)+1/2*si n( c+(d-c)*k/K* n/R):g:=(i,k, n)-(c+(d-c)*k/K* n/R):h:=(i,k, n)-1/5*(a+(b-a)*i/MF2:F:=n-CURVES(seq(seq(evalf(f(i,k ,n ),g(i,k, n) ,h(i,k ,n),i=0.M),k=0.K/R* n),THICKNESS(2),C0L0R(RGB,1,0,0):PL0T3D(ANIMATE(seq(F( n), n=0.R),AXES(N0RMAL),0RIENTATI0N(35,60);

36、Q:=%:图23内层线元变元族变步长链伸动画的设计图11-2427 面体的过程动画使用对象函数制作面体的过程动画with(plots):with(plottools):N:=8:F:=i-co ne(4*cos(i*2*Pi/N),4*si n( i*2*Pi/N),3,(2+si n( i)*1.1,color=gree n, grid=8,5): display(seq(F(i),i=O.N),i nseque nce=true,axes=box,scali ng=uncon strai ned,orie ntatio n=36,65);使用绘图函数制作面体的过程动画restart:wit

37、h(plots):with(plottools):N:=8:F:=i-plot3d(x,si n(x),y*5*i,x=0.2*Pi*(i/(2*N)+.5),y=O.1,grid=18,4,color=cya n): display(seq(F(i),i=0.N),i nseque nce=true,axes=box);图25 用绘图函数制作面体的过程动画使用变换函数制作面体的过程动画with(plots):with(plottools):l:=2:a:=3:b:=2:L:=plot3d(u,v,-uA2-vA2,u=-1.1,v=-1.1,grid=6,6,col or=mage nta)

38、:N:=24:t:=2*Pi*i/N:L1:=i-tra nslate(L,a*cos(t),b*si n(t),O):; display(seq(L1(i),i=0.N),view=-(a+1).a+1,-(b+1).b+1 ,-2.0,axes=no rmal,labels=x,y,z,i nseque nce=true,orie ntatio n=55,55);PLOT3D(ANIMATE(seq(op(op(L1(i),i=0.N),AXES(FRAME) ):图26 用变换函数制作面体的过程动画restart:with(plots):M:=6:N:=4:R:=l5:a:=-3:b:=

39、3:c:=-4:d:=4:u:=0:v:=30:f:=(i,j, n)-(a+(b-a)*i/M):g:=(i,j, n)-(c+(d-c)*j/N):h:=(i,j, n)-(a+(b-a)*i/MF2+(c+(d-c)*j/NF2)*(u+(v-u)*n/R):F:=n-MESH(evalf(seq(seq(f(i,j, n),g(i,j, n),h(i,j, n),i=0.M),j=0.N),COLOR(HUE, n/16):PL0T3D(ANIMATE(seq(F( n),n=0.R),AXES(BOX),ORIENTATION(9,71);面元过程动画的内层设计图11-2835 面体

40、的踪迹动画使用对象函数制作面体的踪迹动画(匀步长) with(plots):with(plottools):R:=24:G:=n-seq(polygo n(0,0,0,cos(i*2*Pi/R),s in (i*2*Pi/R ),5,cos(i*2*Pi/R),si n( i*2*Pi/R),2,thick ness=3,color =gree n),i=0. n):PLOT3D(ANIMATE(seq(G( n),n=0.R),AXES(BOX),ORIENTATION( 150,75);Q:=%:display(ANIMATE(seq(G( n),n=0.R),i nseque nce=t

41、rue,axes= frame):Maple的图形动画技术一一用Maple（69）制作数学动画课件图28用对象函数制作的面体踪迹动画使用绘图函数制作面体的踪迹动画(匀步长)with(plots):N:=8:a:=4: G:=i-(u-i/N,v+i/N,(uA2+vA2)+(a*i/N)A2,u=-2.2,v=-1.1,grid=5,5,color=cya n):GG:=n-display(seq(plot3d(G(i),i=0. n):display(seq(GG( n), n=0.N),i nseque nce=true,axes=frame,or ien tatio n=-15,60);

42、图29 只用绘图函数和display设计的曲面步进踪迹动画 使用变换函数制作面体的踪迹动画(匀步长) with(plots):with(plottools):R:=9:L:=cuboid(2,2,2,1,1,1,style=patch): f:=i-rotate(L,0,0,2*Pi*i/R):;display(seq(f(i),i=0.R);GG:=n-display(seq(f(i),i=0. n):display(seq(GG( n), n=0.R),i nseque nce=true,axes=frame,or ien tatio n=-13,53);19I图30 用变换函数制作的面体

43、踪迹动画体步进式踪迹动画(匀步长)restart:with(plots):M:=4:N:=6:R:=12:w:=1: a:=-2:b:=2:c:=-2:d:=2:u:=0:v:=2*Pi:f:=(i,j,k)-(a+(b-a)*i/M): g:=(i,j,k)-(c+(d-c)*j/N)+5*cos(u+(v-u)*k/R): h:=(i,j,k)-(a+(b-a)*i/M)A2+(c+(d-c)*j/N)A2+5*si n( u+(v- u)*k/R):F1:=n-seq(MESH(seq(seq(evalf(f(i,j,k),g(i,j,k),h(i ,j,k),i=O.M),j=O.N)

44、,COLOR(HUE,k/16),k=0.w* n): PL0T3D(ANIMATE(seq(F1( n), n=0. .R ),AXES(BOX),SCALING(CON STRAINED),ORIENTATION(23,64);图31面元匀步长步进踪迹动画的内层设计 面体步进式踪迹动画（变步长）restart:M:=3:N:=7:R:=8:K:=21:r:=15:u:=K/R:a1:=-3:b1:=1:a2:=-4:b2:=1:c:=0:d:=2*Pi: f:=(i,j,k)-(a1+(b1-a1)*i/M)+r*cos(c+(d-c)*k/R/u): g:=(i,j,k)-(a2+(b2-a2)*j/N)+r*si n(c+(d-c)*k/R/u):h:=(i,j,k)-12*(a1+(b1-a1)*i/M)*(a2+(b2-a2)*j/N):F1:=n-seq(MESH(seq(seq(evalf(f(i,j,k),g(i,