已知平行截面面积求立体的体积：图形、动画、计算.ppt

切片法,*,July 1,2012,四川大学数学学院,徐小湛,已知平行截面的面积求体积,（,切片法,）,蜀南竹海,1,用数学软件,Maple,作了有关动画,这些动画生动地显示了立体的形成过程,计算了一些立体的体积,2,3,with(plots,):,f:=x-x2/10+1:,g:=x-x4/150-1:,a:=-3:b:=3:H:=3:,xzou,:=spacecurve(x,0,0,x=a-1.b+1,thickness=3,color=black):,yzou,:=spacecurve(0,y,0,y=a-1.b+1,thickness=3,color=black):,base:=plot3d(x,y,0,x=,a.b,y,=,g(x).f(x),color,=,grey,style,=,patchnogrid,):,quxianf,:=spacecurve(x,f(x),0,x=a-1.b+1,thickness=3,color=red):,quxiang,:=spacecurve(x,g(x),0,x=a-1.b+1,thickness=3,color=red):,K:=50:for i from 0 to K do xi:=,a+i,*(b-a)/K:,sanjiaoxingi,:=spacecurve(xi,g(xi),0,xi,f(xi),0,xi,(f(xi)+gxi)/2,H,xi,g(xi),0,thickness=3,color=blue):,sanjiaobani,:=plot3d(xi,y,z,y=(f(xi)+g(xi)/2-(f(xi)-g(xi)/2*(1-z/H).(f(xi)+g(xi)/2+(f(xi)-g(xi)/2*(1-z/H),z=0.H,color=,yellow,style,=,patchnogrid,):,qumian1i:=plot3d(x,f(x)+(-f(x)+g(x)/2*,t,H,*,t,t,=0.1,x=,a.xi,color,=green):,qumian2i:=plot3d(x,g(x)+(f(x)g(x)/2*,t,H,*,t,t,=0.1,x=,a.xi,color,=,green)od,:,sanjiaoxing,:=,display(seq(sanjiaoxingi,i,=0.K),insequence=true):,sanjiaoban,:=,display(seq(sanjiaobani,i,=0.K),insequence=true):,qumian1:=display(seq(qumian1i,i=0.K),insequence=true):,qumian2:=display(seq(qumian2i,i=0.K),insequence=true):,display(xzou,yzou,base,quxianf,quxiang,sanjiaoban,sanjiaoxing,qumian1,qumian2,scaling=constrained);,动画的,Maple,程序,4,f:=x-(3/2)*(x2/10+x4/150+2):,a:=-3:b:=3:,Integrate(f(x),x,=,a.b,)=,integrate(f(x),x,=,a.b,);,现在来求这个立体的体积,5,这个立体叫做,正劈锥体,6,with(plots,):,R:=1:,f:=x-sqrt(R2-x2):,g:=x-sqrt(R2-x2):,a:=-,R:b,:=R:H:=2xzou,:=spacecurve(x,0,0,x=a-1.b+1,thickness=3,color=black):,yzou,:=spacecurve(0,y,0,y=a-1.b+1,thickness=3,color=black):,base:=plot3d(x,y,0,x=,a.b,y,=,g(x).f(x),color,=,grey,style,=,patchnogrid,):,quxian,:=,spacecurve(R,*,cos(t),R,*sin(t),0,t=0.2*,Pi,thickness,=3,color=red):,K:=60:for i from 0 to K do xi:=,a+i,*(b-a)/K:,sanjiaoxingi,:=spacecurve(xi,g(xi),0,xi,f(xi),0,xi,(f(xi)+g(xi)/2,H,xi,g(xi),0,thickness=3,color=blue):,sanjiaobani,:=plot3d(xi,y,z,y=(f(xi)+g(xi)/2-(f(xi)-g(xi)/2*(1-z/H).(f(xi)+g(xi)/2+(f(xi)-g(xi)/2*(1-z/H),z=0.H,color=,yellow,style,=,patchnogrid,):,qumian1i:=plot3d(x,f(x)+f(x)+g(x)/2*,t,H,*,t,t,=0.1,x=,a.xi,color,=green):,qumian2i:=plot3d(x,g(x)+(f(x)-g(x)/2*,t,H,*,t,t,=0.1,x=,a.xi,color,=,green)od,:,sanjiaoxing,:=,display(seq(sanjiaoxingi,i,=0.K),insequence=true):,sanjiaoban,:=,display(seq(sanjiaobani,i,=0.K),insequence=true):,qumian1:=display(seq(qumian1i,i=0.K),insequence=true):,qumian2:=display(seq(qumian2i,i=0.K),insequence=true):,display(xzou,yzou,base,quxian,sanjiaoban,sanjiaoxing,qumian1,qumian2,scaling=,constrained,orientation,=-50,70);,动画的,Maple,程序,7,with(plots,):,R:=1:,f:=x-sqrt(R2-x2):,g:=x-sqrt(R2-x2):,a:=-,R:b,:=R:H:=2:,xzou,:=spacecurve(x,0,0,xa-1.b+1,thickness=3,color=black):,yzou,:=spacecurve(0,y,0,y=a-1.b+1,thickness=3,color=black):,base:=plot3d(x,y,0,x=,a.b,y,=,g(x).f(x),color,=,grey,style,=,patchnogrid,):,quxian,:=,spacecurve(R,*,cos(t),R,*sin(t),0,t=0.2*,Pi,thickness,=3,color=red):,xi:=0.5*R:,sanjiaoxing,:=spacecurve(xi,g(xi),0,xi,f(xi),0,xi,(f(xi)+g(xi)/2,H,xi,g(xi),0,thickness=3,color=blue):,sanjiaoban,:=plot3d(xi,y,z,y=(f(xi)+g(xi)/2-(f(xi)-g(xi)/2*(1-z/H).(f(xi)+g(xi)/2+(f(xi)-g(xi)/2*(1-z/H),z=0.H,color=,yellow,style,=,patchnogrid,):,qumian1:=plot3d(x,f(x)+(-f(x)+g(x)/2*,t,H,*,t,t,=0.1,x=,a.xi,color,=green):,qumian2:=plot3d(x,g(x)+(f(x)-g(x)/2*,t,H,*,t,t,=0.1,x=,a.xi,color,=green):,display(xzou,yzou,base,quxian,sanjiaoban,sanjiaoxing,qumian1,qumian2,scaling=,constrained,orientation,=-50,70);,8,with(plots,):,R:=1.7:,f:=x-sqrt(R2-x2):,g:=x-sqrt(R2-x2):,a:=-,R:b,:=R:H:=3:,xzou,:=spacecurve(x,0,0,x=a-1.b+1,thickness=3,color=black):,yzou,:=spacecurve(0,y,0,y=a-1.b+1,thickness=3,color=black):,base:=plot3d(x,y,0,x=,a.b,y,=,g(x).f(x),color,=,grey,style,=,patchnogrid,):,quxian,:=,spacecurve(R,*,cos(t),R,*sin(t),0,t=0.2*,Pi,thickness,=3,color=red):,K:=8:for i from 0 to K do xi:=,a+i,*(b-a)/K:,sanjiaoxingi,:=spacecurve(xi,g(xi),0,xi,f(xi),0,xi,(f(xi)+g(xi)/2,H,xi,g(xi),0,thickness=3,color=blue):,sanjiaobani,:=plot3d(xi,y,z,y=(f(xi)+g(xi)/2-(f(xi)-g(xi)/2*(1-z/H).(f(xi)+g(xi)/2+(f(xi)-g(xi)/2*(1-z/H),z=0.H,color=,yellow,style,=,patchnogrid,):,od,:,sanjiaoxing,:=,display(seq(sanjiaoxingi,i,=0.K),insequence=false):,sanjiaoban,:=,display(seq(sanjiaobani,i,=0.K),insequence=false):,qumian1:=plot3d(x,f(x)+(-f(x)+g(x)/2*,t,H,*,t,t,=0.1,x=,a.b,color,=,green,style,=,wireframe,grid,=50,30):,qumian2:=plot3d(x,g(x)+(f(x)-g(x)/2*,t,H,*,t,t,=0.1,x=,a.b,color,=,green,style,=,wireframe,grid,=50,30):,display(xzou,yzou,base,quxian,sanjiaoban,sanjiaoxing,qumian1,qumian2,scaling=,constrained,orientation,=-50,70);,9,见同济,高等数学,6,版，,281,页，例,10,现在来求这个立体的体积,10,11,with(plots,):,f:=x-sin(x/2)+2:,g:=x-cos(x/3)-2:,a:=-,Pi:b,:=Pi:,xzou,:=spacecurve(x,0,0,x=a-1.b+1,thickness=3,color=black):,yzou,:=spacecurve(0,y,0,y=a-1.b+1,thickness=3,color=black):,base:=plot3d(x,y,0,x=,a.b,y,=,g(x).f(x),color,=,grey,style,=,patchnogrid,):,quxianf,:=spacecurve(x,f(x),0,x=a-1.b+1,thickness=3,color=red):,quxiang,:=spacecurve(x,g(x),0,x=a-1.b+1,thickness=3,color=red):,K:=60:for i from 0 to K do xi:=,a+i,*(b-a)/K:,sanjiaoxingi,:=spacecurve(xi,g(xi)0,xi,f(xi),0,xi,(f(xi)+g(xi)/2,sqrt(3)/2*(f(xi)-g(xi),xi,g(xi),0,thickness=3,color=blue):,sanjiaobani,:=plot3d(xi,y,z,y=(f(xi)+g(xi)/2-(f(xi)-g(xi)/2+z/sqrt(3).(f(xi)+g(xi)/2+(f(xi)-g(xi)/2-z/sqrt(3),z=0.sqrt(3)/2*(,f(xi)-g(xi),color,=,yellow,style,=,patchnogrid,):,qumian1i:=plot3d(x,f(x)+(-f(x)+g(x)/2*t,(sqrt(3)/2)*(,f(x)-g(x,)*,t,t,=0.1,x=,a.xi,color,=green):,qumian2i:=plot3d(x,g(x)+(f(x)-g(x)/2*t,(sqrt(3)/2)*(,f(x)-g(x,)*,t,t,=0.1,x=,a.xi,color,=,green)od,:,sanjiaoxing,:=,display(seq(sanjiaoxingi,i,=0.K),insequence=true):,sanjiaoban,:=,display(seq(sanjiaobani,i,=0.K),insequence=true):,qumian1:=display(seq(qumian1i,i=0.K),insequence=true):,qumian2:=display(seq(qumian2i,i=0.K),insequence=true):,display(xzou,yzou,base,quxianf,quxiang,sanjiaoban,sanjiaoxing,qumian1,qumian2,scaling=constrained);,动画的,Maple,程序,12,f:=x-(sqrt(3)/4)*(sin(x/2)-cos(x/3)+4)2:,a:=-,Pi:b,:=Pi:,Integrate(f(x),x,=,a.b,)=,integrate(f(x),x,=,a.b,);,evalf,(%);,现在来求这个立体的体积,13,14,R:=1.6:,f:=x-sqrt(R2-x2):,g:=x-sqrt(R2-x2):,a:=-,R:b,:=R:H:=2:,xzou,:=spacecurve(x,0,0,x=a-1.b+1,thickness=3,color=black):,yzou,:=spacecurve(0,y,0,y=a-1.b+1,thickness=3,color=black):,base:=plot3d(x,y,0,x=,a.b,y,=,g(x).f(x),color,=,grey,style,=,patchnogrid,):,quxian,:=,spacecurve(R,*,cos(t),R,*sin(t),0,t=0.2*,Pi,thickness,=3,color=red):,K:=60:for i from 0 to K do xi:=,a+i,*(b-a)/K:,sanjiaoxingi,:=spacecurve(xi,g(xi),0,xi,f(xi),0,xi,(f(xi)+g(xi)/2,sqrt(3)/2*(f(xi)-g(xi),xi,g(xi),0,thickness=3,color=blue):,sanjiaobani,:=plot3d(xi,y,z,y=(f(xi)+g(xi)/2-(f(xi)-g(xi)/2+z/sqrt(3).(f(xi)+g(xi)/2+(f(xi)-g(xi)/2-z/sqrt(3),z=0.sqrt(3)/2*(,f(xi)-g(xi),color,=,yellow,style,=,patchnogrid,):,qumian1i:=plot3d(x,f(x)+(-f(x)+g(x)/2*t,(sqrt(3)/2)*(,f(x)-g(x,)*,t,t,=0.1,x=,a.xi,color,=green):,qumian2i:=plot3d(x,g(x)+(f(x)-g(x)/2*t,(sqrt(3)/2)*(,f(x)g(x,)*,t,t,=0.1,x=,a.xi,color,=,green)od,:,sanjiaoxing,:=,display(seq(sanjiaoxingi,i,=0.K),insequence=true):,sanjiaoban,:=,display(seq(sanjiaobani,i,=0.K),insequence=true):,qumian1:=display(seq(qumian1i,i=0.K),insequence=true):,qumian2:=display(seq(qumian2i,i=0.K),insequence=true):,display(xzou,yzou,base,quxian,sanjiaoban,sanjiaoxing,qumian1,qumian2,scaling=,constrained,orientation,=-50,70);,动画的,Maple,程序,15,R:=1.6:,f:=x-sqrt(R2-x2):,g:=x-sqrt(R2-x2):,a:=-,R:b,:=R:H:=2:,xzou,:=spacecurve(x,0,0,x=a-1.b+1,thickness=3,color=black):,yzou,:=spacecurve(0,y,0,y=a-1.b+1,thickness=3,color=black):,base:plot3d(x,y,0,x=,a.b,y,=,g(x).f(x),color,=,grey,style,=,patchnogrid,):,quxian,:=,spacecurve(R,*,cos(t),R,*sin(t),0,t=0.2*,Pi,thickness,=3,color=red):,xi:=0.2*R:,sanjiaoxing,:=spacecurve(xi,g(xi),0,xi,f(xi),0,xi,(f(xi)+g(xi)/2,sqrt(3)/2*(f(xi)-g(xi),xi,g(xi),0,thickness=3,color=blue):,sanjiaoban,:=plot3d(xi,y,z,y=(f(xi)+g(xi)/2-(f(xi)-g(xi)/2+z/sqrt(3).(f(xi)+g(xi)/2+(f(xi)-g(xi)/2-z/sqrt(3),z=0.sqrt(3)/2*(,f(xi)-g(xi),color,=,yellow,style,=,patchnogrid,):,qumian1:=plot3d(x,f(x)+(-f(x)+g(x)/2*t,(sqrt(3)/2)*(,f(x)-g(x,)*,t,t,=0.1,x=,a.xi,color,=green):,qumian2:=plot3d(x,g(x)+(f(x)-g(x)/2*t,(sqrt3)/2)*(,f(x)-g(x,)*,t,t,=0.1,x=,a.xi,color,=green):,display(xzou,yzou,base,quxian,sanjiaoban,sanjiaoxing,qumian1,qumian2,scaling=,constrained,orientation,=-50,70);,16,R:=1.6:,f:=x-sqrt(R2-x2):,g:=x-sqrt(R2-x2):,a:=-,R:b,:=R:H:=2:,xzou,:=spacecurve(x,0,0,x=a-1.b+1,thickness=3,color=black):,yzou,:=spacecurve(0,y,0,y=a-1.b+1,thickness=3,color=black):,base:=plot3d(x,y,0,x=,a.b,y,=,g(x).f(x),color,=,grey,style,=,patchnogrid,):,quxian,:=,spacecurve(R,*,cos(t),R,*sin(t),0,t=0.2*,Pi,thickness,=3,color=red):,K:=8:for i from 0 to K do xi:=,a+i,*(b-a)/K:,sanjiaoxingi,:=spacecurve(xi,g(xi),0,xi,f(xi),0,xi,(f(xi)+g(xi)/2,sqrt(3)/2*(f(xi)-g(xi),xi,g(xi),0,thickness=3,color=blue):,sanjiaobani,:=plot3d(xi,y,z,y=(f(xi)+g(xi)/2-(f(xi)-g(xi)/2+z/sqrt(3).(f(xi)+g(xi)/2+(f(xi)-g(xi)/2-z/sqrt(3),z=0.sqrt(3)/2*(,f(xi)-g(xi),color,=,yellow,style,=,patchnogrid,),od,:,sanjiaoxing,:=,display(seq(sanjiaoxingi,i,=0K),insequence=false):,sanjiaoban,:=,display(seq(sanjiaobani,i,=0.K),insequence=false):,qumian1:=plot3d(x,f(x)+(-f(x)+g(x)/2*t,(sqrt(3)/2)*(,f(x)-g(x,)*,t,t,=0.1,x=,a.b,style,=,wireframe,):,qumian2:=plot3d(x,g(x)+(f(x)-g(x)/2*t,(sqrt(3)/2)*(,f(x)-g(x,)*,t,t,=0.1,x=,a.b,style,=,wireframe,):,display(xzou,yzou,base,quxian,sanjiaoban,sanjiaoxing,qumian1,qumian2,scaling=,constrained,orientation,=-50,70);,17,见同济,高等数学,6,版，,286,页，,18,题,现在来求这个立体的体积,18,19,with(plots,):,f:=x-sin(x)+1:,g:=x-sin(x-1)-1:,a:=-,Pi:b,:=2*Pi:,xzou,:=spacecurve(x,0,0,x=a-1.b+1,thickness=3,color=black):,yzou,:=spacecurve(0,y,0,y=a-1.b+1,thickness=3,color=black):,base:=plot3d(x,y,0,x=,a.b,y,=,g(x).f(x),color,=,grey,style,=,patchnogrid,):,quxianf,:=spacecurve(x,f(x),0,x=a-1.b+1,thickness=3,color=red):,quxiang,:=spacecurve(x,g(x),0,x=a-1.b+1,thickness=3,color=red):,K:=60:for i from 0 to K do xi:=,a+i,*(b-a)/K:,zhengfangxingi,:spacecurve(xi,g(xi),0,xi,f(xi),0,xi,f(xi),f(xi)-g(xi),xi,g(xi),f(xi)-g(xi),xi,g(xi),0,thickness=3,color=blue):,zhengfangbani,:=plot3d(xi,y,z,y=,g(xi).f(xi),z,=0.f(xi)-g(xi),color=,yellow,style,=,patchnogrid,):,qumian1i:=plot3d(x,f(x),(f(x)-g(x)*,t,t,=0.1,x=,a.xi,color,=green):,qumian2i:=plot3d(x,g(x),(f(x)-g(x)*,t,t,=0.1,x=,a.xi,color,=green):,qumian3i:=plot3d(x,g(x)+(f(x)-g(x)*,t,f(x)-g(x),t,=0.1,x=,a.xi,color,=,green)od,:,zhengfangxing,:=,display(seq(zhengfangxingi,i,=0.K),insequence=true):,zhengfangban,:=,display(seq(zhengfangbani,i,=0.K),insequence=true):,qumian1:=display(seq(qumian1i,i=0K),insequence=true):,qumian2:=display(seq(qumian2i,i=0.K),insequence=true):,qumian3:=display(seq(qumian3i,i=0.K),insequence=true):,display(xzou,yzou,base,quxianf,quxiang,zhengfangban,zhengfangxing,qumian1,qumian2,qumian3,scaling=constrained);,动画的,Maple,程序,20,21,22,23,with(plots,):,R:=1.6:,f:=x-sqrtR2-x2):,g:=x-sqrt(R2-x2):,a:=-,R:b,:=R:H:=2:,xzou,:=spacecurve(x,0,0,x=a-1.b+1,thickness=3,color=black):,yzou,:=spacecurve(0,y,0,y=a-1.b+1,thickness=3,color=black):,base:=plot3d(x,y,0,x=,a.b,y,=,g(x).f(x),color,=,grey,style,=,patchnogrid,):,quxian,:=,spacecurve(R,*,cos(t),R,*sin(t),0,t=0.2*,Pi,thickness,=3,color=red):,K:=60:for i from 0 to K do xi:=,a+i,*(b-a)/K:,zhengfangxingi,:=spacecurve(xi,g(xi),0,xi,f(xi),0,xi,f(xi),f(xi)-g(xi),xi,g(xi),f(xi)-g(xi),xi,g(xi),0,thickness=3,color=blue):,zhengfangbani,:=plot3d(xi,y,z,y=,g(xi).f(xi),z,=0.f(xi)-g(xi),color=,yellow,style,=,patchnogrid,):,qumian1i:=plot3d(x,f(x),(f(x)-g(x)*,t,t,=0.1,x=,a.xi,color,=green):,qumian2i:=plot3d(x,g(x),(f(x)-g(x)*,t,t,=0.1,x=,a.xi,color,=green):,qumian3i:=plot3d(x,g(x)+(f(x)-g(x)*,t,f(x)-g(x),t,=0.1,x=,a.xi,color,=,grey)od,:,zhengfangxing,:=,display(seq(zhengfangxingi,i,=0.K),insequence=true):,zhengfangban,:=,display(seq(zhengfangbani,i,=0.K),insequence=true):,qumian1:=display(seq(qumian1i,i=0.K),insequence=true):,qumian2:=display(seq(qumian2i,i=0.K),insequence=true):,qumian3:=display(seq(qumian3i,i=0.K),insequence=true):,display(xzou,yzou,base,quxian,zhengfangban,zhengfangxing,qumian1,qumian2,qumian3,scaling=,constrained,orientation,=-60,70);,动画的,Maple,程序,24,这个体积刚好等于,牟合方盖,的体积见同济,高等数学,6,版，下册,143,页，例,4,现在来求这个立体的体积,25,26,with(plots,):,f:=x-sin(x)+2:,g:=x-sin(x-1)-1:,a:=-,Pi:b,:=2*Pi:,xzou,:=spacecurve(x,0,0,x=a-1.b+1,thickness=3,color=black):,yzou,:=spacecurve(0,y,0,y=-2.3,thickness=3,color=black):,baseplot3d(x,y,0,x=,a.b,y,=,g(x).f(x),color,=,grey,style,=,patchnogrid,):,quxianf,:=spacecurve(x,f(x),0,x=a-1.b+1,thickness=3,color=red):,quxiang,:=spacecurve(x,g(x),0,x=a-1.b+1,thickness=3,color=red):,K:=60:for i from 0 to K do xi:=,a+i,*(b-a)/K:,banyuani,:=spacecurve(xi,(f(xi)+g(xi)/2+(f(xi)-g(xi)/2cos(t),(f(xi)-g(xi)/2*,sin(t),t,=0.Pi,thickness=3,color=blue):,dixiani,:=spacecurve(xi,y,0,y=,g(xi).f(xi),thickness,=3,color=blue):,banyuanbani,:=plot3d(xi,(f(xi)+g(xi)/2+r*,cos(t),r,*,sin(t),r,=0.(f(xi)-g(xi)/2,t=0.Pi,color=,yellow,style,=,patchnogrid,):,qumiani,:=plot3d(x,(f(x)+g(x)/2+(f(x)-g(x)/2*cos(t),(f(x)-g(x)/2*,sin(t),t,=0.Pi,x=,a.xi,color,=,green)od,:,banyuan,:=,display(seq(banyuani,i,=0.K),insequence=true):,dixian,:=,display(seq(dixiani,i,=0.K),insequence=true):,banyuanban,:=,display(seq(banyuanbani,i,=0.K),insequence=true):,qumian,:=,display(seq(qumiani,i,=0.K),insequence=true):,display(xzou,yzou,quxianf,quxiang,banyuanban,base,banyuan,qumian,dixian,scaling,=constrained);,动画的,Maple,程序,27,28,with(plots,):,f:=x-sin(x)+2:,g:=x-sin(x-1)-1:,a:=-,Pi:b,:=2*Pi:,xzou,:=spacecurve(x,0,0,x=a-1.b+1,thickness=3,color=black):,yzou,:=spacecurve(0,y,0,y=-2.3,thickness=3,color=black):,quxianf,:=spacecurve(x,f(x),0,x=a-1.b+1,thickness=3,color=red):,quxiang,:=spacecurve(x,g(x),0,x=a-1.b+1,thickness=3,color=red):,K:=60:for i from 0 to K do xi:=,a+i,*(b-a)/K:,banyuani,:=spacecurve(xi,(f(xi)+g(xi)/2+(f(xi)-g(xi)/2*cos(t),(f(xi)-g(xi)/2*,sin(t),t,=0.Pi,thickness=3,color=blue):,dixiani,:=spacecurve(xi,y,0,y=,g(xi).f(xi),thickness,=3,color=blue):,banyuanbani,:=plot3d(xi,(f(xi)+g(xi)/2+r*,cos(t),r,*,sin(t),r,=0.(f(xi)-g(xi)/2,t=0.Pi,color=,yellow,style,=,patchnogrid,):,basei,:=plot3d(x,y,0,x=,a.xi,y,=,f(x).g(x),color,=,gray,style,=,patchnogrid,):,qumiani,:=plot3d(x,(f(x)+g(x)/2+(f(x)-g(x)/2*cos(t),(f(x)-g(x)/2*,sin(t),t,=0.Pi,x=,a.xi,color,=,green)od,:,banyuan,:=,display(seq(banyuani,i,=0.K),insequence=true):,dixian,:=,display(seq(dixiani,i,=0.K),insequence=true):,base:=,display(seq(basei,i,=0.K),insequence=true):,banyuanban,:=,display(seq(banyuanbani,i,=0.K),insequence=true):,qumian,:=,display(seq(qumiani,i,=0.K),insequence=true):,display(xzou,yzou,quxianf,quxiang,banyuanban,base,banyuan,qumian,dixian,scaling,=constrained);,动画的,Maple,程序,29,30,with(plots,):,A:=2:B:=1:,a:=-,A:b,:=A:,f:=x-(B/A)*sqrt(A2-x2):,g:=x-(B/A)*sqrt(A2-x2):,xzou,:=spacecurve(x,0,0,x=-A-.5.A+.5,thickness=3color=black):,yzou,:=spacecurve(0,y,0,y=-B-.5.B+.5,thickness=3,color=black):,base:=plot3d(x,y,0,x=,a.b,y,=,g(x).f(x),color,=,grey,style,=,patchnogrid,):,quxian,:=,spacecurve(A,*,cos(t),B,*sin(t),0,t=0.2*,Pi,thickness,=3,color=red):,K:=60:for i from 0 to K do xi:=,a+i,*(b-a)/K:,banyuani,:=spacecurve