D動(dòng)畫(huà)的設(shè)計(jì)技術(shù)

1、第十一章 3D動(dòng)畫(huà)的設(shè)計(jì)技術(shù)圖11-0103 點(diǎn)的過(guò)程動(dòng)畫(huà)with(plots):with(plottools):N:=24:F:=i->point(cos(i*2*Pi/12),sin(i*2*Pi/12),3,color=blue,symbol=DIAMOND,symbolsize=55):display(seq(F(i),i=0.N),insequence=true,axes=FRAME,orientation=-12,35);d1:=%:PLOT3D(ANIMATE(seq(F(i),i=0.N),AXESSTYLE(FRAME);d2:=%:;spacecurve(cos(i*

2、2*Pi/12),sin(i*2*Pi/12),3,i=0.N);d3:=%:display(d1,d3);display(d2,d3);圖 1 使用對(duì)象函數(shù)制作的孤點(diǎn)過(guò)程動(dòng)畫(huà)（連環(huán)畫(huà)）with(plots):N:=24:h:=4:F:=i->pointplot3d(cos(4*Pi*i/N),sin(4*Pi*i/N),h/N*i,grid=5,3,symbol=circle,symbolsize=23,style=POINT,color=blue):display(seq(F(i),i=0.N),insequence=true,axes=box);d1:=%:;PLOT3D(ANIM

3、ATE(seq(op(F(i),i=0.N);d2:=%:;spacecurve(cos(i*4*Pi/24),sin(i*4*Pi/24),4*i/24,i=0.24,color=red,style=LINE);d3:=%:display(d2,d3,axes=frame);圖 2 使用繪圖函數(shù)制作的孤點(diǎn)過(guò)程動(dòng)畫(huà)（連環(huán)畫(huà)）使用變換函數(shù)和對(duì)象函數(shù)制作孤點(diǎn)過(guò)程動(dòng)畫(huà)with(plots):with(plottools):a:=3:b:=2:k:=6:n:=2:m:=0:N:=72:t:=2*Pi*i/N:L:=point(-n,m,m,color=blue,symbol=circle,symbol

4、size=23):L1:=i->translate(L,a*cos(k*Pi*i/N),b*sin(k*Pi*i/N),0):display(seq(L1(i),i=0.N),axes=normal,labels=x,y,z,insequence=true,orientation=-80,65);PLOT3D(ANIMATE(seq(L1(i),i=0.N),ORIENTATION(-80,65),AXES(FRAME);內(nèi)層動(dòng)畫(huà)with(plots):R:=24:a:=0:b:=4*Pi:f:=n->cos(a+(b-a)*n/R):g:=n->sin(a+(b-a)*n/

5、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=0.R),insequence=true,axes=box,view=-1.1.1.1,-1.1.1.1,0.7,orientation=9,71);圖 3 用內(nèi)層方法設(shè)計(jì)的點(diǎn)過(guò)程動(dòng)畫(huà)

6、圖11-0411 點(diǎn)的蹤跡動(dòng)畫(huà)使用對(duì)象函數(shù)制作點(diǎn)蹤跡動(dòng)畫(huà)(勻步長(zhǎng))A, 使用對(duì)象函數(shù)plottoolspointwith(plots):with(plottools):N:=54:h:=4:r:=1-k/N:F1:=i->seq(point(r*cos(k*6*Pi/N),r*sin(k*6*Pi/N),h/N*k,symbolsize=54,symbol=CIRCLE,color=black),k=0.i):spacecurve(r*cos(6*Pi*k/N),r*sin(6*Pi*k/N),h/N*k,k=0.N,color=green):d01:=%:display(ANIMATE

7、(seq(F1(i),i=0.N),insequence=true,axes=FRAME,orientation=65,65,view=-1.1,-1.1,0.4):;d11:=%:;display(d01,d11);B,使用對(duì)象函數(shù)plottoolscurveF2:=i->curve(seq(r*cos(k*6*Pi/N),r*sin(k*6*Pi/N),h/N*k,k=0.i),thickness=3,color=red,style=POINT,symbolsize=36,symbol=DIAMOND):spacecurve(r*cos(6*Pi*k/N),r*sin(6*Pi*k/

8、N),h/N*k,k=0.N,color=magenta):d02:=%:display(ANIMATE(seq(F2(i),i=0.N),insequence=true,axes=box,orientation=65,65,view=-1.1,-1.1,0.5):;d12:=%:;display(d02,d12);C,使用對(duì)象函數(shù)plottoolspolygonF3:=i->polygon(seq(r*cos(k*6*Pi/N),r*sin(k*6*Pi/N),h/N*k,k=0.i),thickness=3,color=blue,style=POINT,symbolsize=36,s

9、ymbol=DIAMOND):spacecurve(r*cos(6*Pi*k/N),r*sin(6*Pi*k/N),h/N*k,k=0.N,color=cyan):d03:=%:display(ANIMATE(seq(F3(i),i=0.N),insequence=true,axes=box,orientation=65,65,view=-1.1,-1.1,0.5):;d13:=%:;display(d03,d13);使用三個(gè)不同對(duì)象函數(shù)的方案，自左至右：A,B,C圖 4 效果相同的連環(huán)畫(huà)使用繪圖函數(shù)制作點(diǎn)蹤跡動(dòng)畫(huà)(勻步長(zhǎng))A,使用pointplot3d函數(shù)with(plots):with(p

10、lottools):N:=54:h:=4:r:=(1-k/N)2:F1:=i->pointplot3d(seq(r*cos(k*6*Pi/N),r*sin(k*6*Pi/N),h*r/N*k,k=0.i),symbol=DIAMOND,color=blue,symbolsize=12):spacecurve(r*cos(6*Pi*k/N),r*sin(6*Pi*k/N),h*r/N*k,k=0.N):d0:=%:display(seq(F1(i),i=0.N),insequence=true,axes=box,view=-1.1,-1.1,0.0.8,orientation=67,73)

11、:;d11:=%:;display(d0,d11);B,使用polygonplot3d函數(shù)with(plots):with(plottools):N:=54:h:=4:r:=(1-k/N)2:F2:=i->polygonplot3d(seq(r*cos(k*6*Pi/N),r*sin(k*6*Pi/N),h*r/N*k,k=0.i),symbol=DIAMOND,color=blue,style=POINT,symbolsize=12):spacecurve(r*cos(6*Pi*k/N),r*sin(6*Pi*k/N),h*r/N*k,k=0.N):d0:=%:display(seq(

12、F2(i),i=0.N),insequence=true,axes=box,view=-1.1,-1.1,0.0.8,orientation=67,73):d12:=%:display(d0,d12);C,使用spacecurve函數(shù)with(plots):with(plottools):N:=54:h:=4:r:=(1-k/N)2:F3:=i->spacecurve(seq(r*cos(k*6*Pi/N),r*sin(k*6*Pi/N),h*r/N*k,k=0.i),style=POINT,symbolsize=12,symbol=DIAMOND,color=blue):spacecu

13、rve(r*cos(6*Pi*k/N),r*sin(6*Pi*k/N),h*r/N*k,k=0.N):d0:=%:display(seq(F3(i),i=0.N),insequence=true,axes=box,view=-1.1,-1.1,0.0.8,orientation=67,73):d13:=%:display(d0,d13);使用三個(gè)不同繪圖函數(shù)的方案，自左至右：A,B,C圖 5 效果相同的連環(huán)畫(huà)使用變換函數(shù)制作點(diǎn)蹤跡動(dòng)畫(huà)(勻步長(zhǎng))with(plots):with(plottools):N:=54:h:=4:r:=k/N:a:=1:b:=2:c:=0:point(a,b,c,sym

14、bolsize=12,symbol=CIRCLE,color=black):G:=%:F:=i->seq(translate(G,r*cos(k*6*Pi/N),r*sin(k*6*Pi/N),h/N*k),k=0.i):spacecurve(a+r*cos(6*Pi*k/N),b+r*sin(6*Pi*k/N),c+h/N*k,k=0.N,color=green):d0:=%:display(ANIMATE(seq(F(i),i=0.N),insequence=true,axes=FRAME,orientation=65,65,view=a-1.a+1,b-1.b+1,c.c+4):d

15、1:=%:display(d0,d1);Q:=%:圖 6 用變換函數(shù)制作的點(diǎn)蹤跡動(dòng)畫(huà)(勻步長(zhǎng))點(diǎn)的步進(jìn)式蹤跡動(dòng)畫(huà)（勻步長(zhǎng)）with(plots):R:=8:a:=0:b:=2*Pi:w:=3:f:=i->cos(a+(b-a)*i/R/w):g:=i->sin(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),SYMBOL(CIRCLE,18),COLOR(RGB,1,0,0):display(seq(F(n),n=0.R),insequence=t

16、rue,axes=box,orientation=70,50,view=-1.1,-1.1,0.3.3);Q:=%:PLOT3D(ANIMATE(seq(F(n),n=0.R),AXES(FRAME):;圖 7點(diǎn)元步進(jìn)式蹤跡（勻步長(zhǎng)）動(dòng)畫(huà)點(diǎn)的步進(jìn)式蹤跡動(dòng)畫(huà)（變步長(zhǎng)）with(plots):R:=8: K:=21:a:=0:b:=2*Pi:f:=i->cos(a+(b-a)*i/K):g:=i->sin(a+(b-a)*i/K):h:=i->(a+(b-a)*i/K)/2:F:=n->POINTS(seq(evalf(f(i),g(i),h(i),i=0.K/R*n),S

17、YMBOL(CIRCLE,18),COLOR(RGB,0,0,1):display(seq(F(n),n=0.R),insequence=true,axes=frame,orientation=30,65);Q:=%:PLOT3D(ANIMATE(seq(F(n),n=0.R),AXES(FRAME):;圖 8 點(diǎn)元步進(jìn)式蹤跡（變步長(zhǎng)）動(dòng)畫(huà)點(diǎn)的鏈伸式蹤跡動(dòng)畫(huà)（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)->sin(a+(b-a)*i/K*n/R):h:=(i,n)-&g

18、t;(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),SYMBOL(CIRCLE,18),COLOR(RGB,1,0,0):display(seq(F(n),n=0.R),insequence=true,axes=box);PLOT3D(ANIMATE(seq(F(n),n=0.R),AXES(FRAME);圖 9 全元族鏈伸蹤跡動(dòng)畫(huà)點(diǎn)的鏈伸式蹤跡動(dòng)畫(huà)（變?cè)澹瑒虿介L(zhǎng)）with(plots):K:=15:R:=8:w:=2:u:=w*R/K:a:=0:b:=2*Pi:f:=(i,n)->co

19、s(a+(b-a)*i/K*n/R/u):g:=(i,n)->sin(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=0.w*n),SYMBOL(CIRCLE,18),COLOR(RGB,1,0,0):display(seq(F(n),n=0.R),insequence=true,axes=box,orientation=73,58):;PLOT3D(ANIMATE(seq(F(n),n=0.R),AXES(FRAME);圖 10

20、點(diǎn)元鏈伸式蹤跡（變?cè)澹炔介L(zhǎng)）動(dòng)畫(huà)點(diǎn)的鏈伸式蹤跡動(dòng)畫(huà)（變?cè)?，變步長(zhǎng)）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)->sin(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),insequen

21、ce=true,axes=box);PLOT3D(ANIMATE(seq(F(n),n=0.R),AXES(FRAME),ORIENTATION(5,55);圖 11 點(diǎn)元鏈伸式蹤跡（變?cè)?，變步長(zhǎng)）動(dòng)畫(huà)圖11-1215 線的過(guò)程動(dòng)畫(huà)使用對(duì)象函數(shù)制作線元的過(guò)程動(dòng)畫(huà)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*sin(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

22、,-1/2,2*cos(i*2*Pi/N)+7,0,0,2*cos(i*2*Pi/N)+8,0,color=black,thickness=4):display(seq(F(i),i=0.N),insequence=true,axes=frame):;PLOT3D(ANIMATE(seq(F(i),i=0.N),AXESSTYLE(FRAME):;圖 12用對(duì)象函數(shù)制作的線元過(guò)程動(dòng)畫(huà)（曲柄連桿機(jī)構(gòu)的運(yùn)動(dòng)）使用繪圖函數(shù)制作線元的過(guò)程動(dòng)畫(huà)with(plots):N:=27:r:=25:F:=i->spacecurve(r*cos(i*2*Pi/N)+t*cos(t),r*sin(i*2*Pi

23、/N)+t*sin(t),t,t=0.6*Pi,color=black,thickness=3):display(seq(F(i),i=0.N),insequence=true,axes=normal):PLOT3D(ANIMATE(seq(F(i),i=0.N),AXESSTYLE(FRAME):圖 13 用繪圖函數(shù)制作的線元過(guò)程動(dòng)畫(huà)使用變換函數(shù)制作線元的過(guò)程動(dòng)畫(huà)with(plots):with(plottools):N:=8:r:=15:spacecurve(t*cos(t),t*sin(t),-t/7,t=0.6*Pi,color=red,thickness=3):L:=%:F:=i-&

24、gt;translate(L,r*cos(i*2*Pi/N),r*sin(i*2*Pi/N),0):display(seq(F(i),i=0.N),insequence=true,axes=box):d1:=%:spacecurve(r*cos(t),r*sin(t),0,t=0.2*Pi,color=blue):d0:=%:display(d0,d1,orientation=50,73);Q:=%:圖 14用變換函數(shù)制作的線元過(guò)程動(dòng)畫(huà)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)+

25、sin(c+(d-c)*n/R):g:=(i,n)->(a+(b-a)*i/M)/6+(c+(d-c)*n/R):h:=(i,n)->sin(a+(b-a)*i/M):F:=n->CURVES(seq(evalf(f(i,n),g(i,n),h(i,n),i=0.M),THICKNESS(3),COLOR(RGB,1,0,0):display(seq(F(n),n=0.R),insequence=true,axes=NORMAL,labels=x,y,z,orientation=63,73);圖 15 一個(gè)內(nèi)層線元過(guò)程動(dòng)畫(huà)的連環(huán)畫(huà)圖11-1623 線的的蹤跡動(dòng)畫(huà)使用對(duì)象函數(shù)制

26、作線元的蹤跡動(dòng)畫(huà)(勻步長(zhǎng))with(plots):with(plottools):R:=16:G:=n->seq(curve(0,0,0,cos(i*2*Pi/R),sin(i*2*Pi/R),5,1.5*cos(i*2*Pi/R),1.5*sin(i*2*Pi/R),5,cos(i*2*Pi/R),sin(i*2*Pi/R),2,cos(i*2*Pi/R),sin(i*2*Pi/R),3,linestyle=1,thickness=3,color=red),i=0.n):display(ANIMATE(seq(G(n),n=0.R),insequence=true,axes=frame

27、):圖 16 用對(duì)象函數(shù)制作線元的蹤跡動(dòng)畫(huà)使用繪圖函數(shù)制作線元的蹤跡動(dòng)畫(huà)(勻步長(zhǎng))with(plots):R:=24:r:=8:G:=n->seq(spacecurve(0+2*Pi*i/R,t*cos(t)-30+r*sin(2*Pi*i/R),t*sin(t),t=0.6*Pi,color=black,thickness=1),i=0.n):display(seq(display(G(n),n=0.R),insequence=true,axes=frame);圖 17用繪圖函數(shù)制作線元的蹤跡動(dòng)畫(huà)使用變換函數(shù)制作線元的蹤跡動(dòng)畫(huà)(勻步長(zhǎng))restart:with(plottools):w

28、ith(plots):R:=24:r:=2:t:=4*Pi*i/R:L:=curve(0,0,0,1/3,-1/7,1.2,1,0,1,1/3,1/7,1.2,0,0,0,thickness=3,color=COLOR(RGB,0.2,0.8,0.1):f:=i->translate(rotate(L,0,0,-t),r*cos(t),r*sin(t),t/1):;spacecurve(r*cos(t1),r*sin(t1),t1/1,t1=0.4*Pi,color=brown,thickness=2):d0:=%:G:=n->seq(f(i),i=0.n):display(ANI

29、MATE(seq(G(n),n=0.R),insequence=true,orientation=54,61,axes=frame):;dh:=%:display(dh,d0);圖 18用變換函數(shù)制作線元的蹤跡動(dòng)畫(huà)線的步進(jìn)式蹤跡動(dòng)畫(huà)（勻步長(zhǎng)）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(ev

30、alf(f(i,k),g(i,k),h(i,k),i=0.M),k=0.w*n),THICKNESS(2),COLOR(RGB,0,0,1):PLOT3D(ANIMATE(seq(F(n),n=0.R),AXES(FRAME);Q:=%:圖 19 線元?jiǎng)虿介L(zhǎng)步進(jìn)式蹤跡動(dòng)畫(huà)的內(nèi)層設(shè)計(jì)線的步進(jìn)式蹤跡動(dòng)畫(huà)（變步長(zhǎng)）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)2+3*sin(c+(d-c)*k/R/

31、u):F:=n->CURVES(seq(seq(evalf(f(i,k),g(i,k),h(i,k),i=0.M),k=0.M/R*n),THICKNESS(2),COLOR(RGB,1,0,0):PLOT3D(ANIMATE(seq(F(n),n=0.R),AXES(NORMAL),ORIENTATION(30,75);圖 20線元變步長(zhǎng)步進(jìn)蹤跡動(dòng)畫(huà)的內(nèi)層設(shè)計(jì)線的鏈伸式蹤跡動(dòng)畫(huà)（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*sin(c+(d-c)*k/K*n/R):g:=(i,k,

32、n)->(c+(d-c)*k/K*n/R):h:=(i,k,n)->1-(a+(b-a)*i/M)3: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),ORIENTATION(-23,74);圖 21 線元全元族鏈伸動(dòng)畫(huà)的內(nèi)層設(shè)計(jì)線的鏈伸式蹤跡動(dòng)畫(huà)（變?cè)?，勻步長(zhǎng)）M:=18:R:=8:w:=2:a:=0:b:=2*Pi:c:=0:d:=2*Pi:

33、m:=5:f:=(i,k,n)->m*cos(a+(b-a)*i/M)+3*sin(c+(d-c)*k/R*n/R/w):g:=(i,k,n)->(c+(d-c)*k/R*n/R/w):h:=(i,k,n)->m*sin(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),COLOR(HUE,k/16),THICKNESS(2),k=0.w*n):PLOT3D(ANIMATE(seq(F(n),n=0.R),AXES(NORMAL);圖 22 內(nèi)層線元變?cè)鍎虿介L(zhǎng)鏈伸動(dòng)畫(huà)的設(shè)

34、計(jì)線的鏈伸式蹤跡動(dòng)畫(huà)（變?cè)?，變步長(zhǎng)）M:=5:K:=13:R:=8: a:=-1:b:=1:c:=0:d:=2*Pi:f:=(i,k,n)->(a+(b-a)*i/M)+1/2*sin(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/M)2: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),COLOR(RGB,1,0,0):PLOT3D(ANIMAT

35、E(seq(F(n),n=0.R),AXES(NORMAL),ORIENTATION(35,60);Q:=%:圖 23 內(nèi)層線元變?cè)遄儾介L(zhǎng)鏈伸動(dòng)畫(huà)的設(shè)計(jì)圖11-2427 面體的過(guò)程動(dòng)畫(huà)使用對(duì)象函數(shù)制作面體的過(guò)程動(dòng)畫(huà)with(plots):with(plottools):N:=8:F:=i->cone(4*cos(i*2*Pi/N),4*sin(i*2*Pi/N),3,(2+sin(i)*1.1,color=green,grid=8,5):display(seq(F(i),i=0.N),insequence=true,axes=box,scaling=unconstrained,orie

36、ntation=36,65);圖 24 面體的外層過(guò)程動(dòng)畫(huà)使用繪圖函數(shù)制作面體的過(guò)程動(dòng)畫(huà)restart:with(plots):with(plottools):N:=8:F:=i->plot3d(x,sin(x),y*5*i,x=0.2*Pi*(i/(2*N)+.5),y=0.1,grid=18,4,color=cyan):display(seq(F(i),i=0.N),insequence=true,axes=box);圖 25用繪圖函數(shù)制作面體的過(guò)程動(dòng)畫(huà)使用變換函數(shù)制作面體的過(guò)程動(dòng)畫(huà)with(plots):with(plottools):l:=2:a:=3:b:=2:L:=plot3

37、d(u,v,-u2-v2,u=-1.1,v=-1.1,grid=6,6,color=magenta):N:=24:t:=2*Pi*i/N:L1:=i->translate(L,a*cos(t),b*sin(t),0):;display(seq(L1(i),i=0.N),view=-(a+1).a+1,-(b+1).b+1,-2.0,axes=normal,labels=x,y,z,insequence=true,orientation=55,55);PLOT3D(ANIMATE(seq(op(op(L1(i),i=0.N),AXES(FRAME):圖 26 用變換函數(shù)制作面體的過(guò)程動(dòng)畫(huà)r

38、estart:with(plots):M:=6:N:=4:R:=15:a:=-3:b:=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/M)2+(c+(d-c)*j/N)2)*(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):PLOT3D(ANIMATE(seq(F(n),n=0.R

39、),AXES(BOX),ORIENTATION(9,71);圖 27面元過(guò)程動(dòng)畫(huà)的內(nèi)層設(shè)計(jì)圖11-2835 面體的蹤跡動(dòng)畫(huà)使用對(duì)象函數(shù)制作面體的蹤跡動(dòng)畫(huà)(勻步長(zhǎng))with(plots):with(plottools):R:=24:G:=n->seq(polygon(0,0,0,cos(i*2*Pi/R),sin(i*2*Pi/R),5,cos(i*2*Pi/R),sin(i*2*Pi/R),2,thickness=3,color=green),i=0.n):PLOT3D(ANIMATE(seq(G(n),n=0.R),AXES(BOX),ORIENTATION(150,75);Q:=%:

40、display(ANIMATE(seq(G(n),n=0.R),insequence=true,axes=frame):圖 28 用對(duì)象函數(shù)制作的面體蹤跡動(dòng)畫(huà)使用繪圖函數(shù)制作面體的蹤跡動(dòng)畫(huà)(勻步長(zhǎng))with(plots):N:=8:a:=4:G:=i->(u-i/N,v+i/N,(u2+v2)+(a*i/N)2,u=-2.2,v=-1.1,grid=5,5,color=cyan):GG:=n->display(seq(plot3d(G(i),i=0.n):display(seq(GG(n),n=0.N),insequence=true,axes=frame,orientation=

41、-15,60);圖 29只用繪圖函數(shù)和display設(shè)計(jì)的曲面步進(jìn)蹤跡動(dòng)畫(huà)使用變換函數(shù)制作面體的蹤跡動(dòng)畫(huà)(勻步長(zhǎng))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),insequence=true,axes=frame,orientation=-13,53);圖 30用變換函數(shù)制作的

42、面體蹤跡動(dòng)畫(huà)體步進(jìn)式蹤跡動(dòng)畫(huà)（勻步長(zhǎng)）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)2+(c+(d-c)*j/N)2+5*sin(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=0.

43、M),j=0.N),COLOR(HUE,k/16),k=0.w*n):PLOT3D(ANIMATE(seq(F1(n),n=0.R),AXES(BOX),SCALING(CONSTRAINED),ORIENTATION(23,64);圖 31 面元?jiǎng)虿介L(zhǎng)步進(jìn)蹤跡動(dòng)畫(huà)的內(nèi)層設(shè)計(jì)面體步進(jìn)式蹤跡動(dòng)畫(huà)（變步長(zhǎng)）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*sin(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