【正文】 )..f(xi),z=0..f(xi)g(xi),color=yellow,style=patchnogrid): qumian1[i]:=plot3d([x,f(x),(f(x)g(x))*t],t=0..1,x=a..xi,color=green): qumian2[i]:=plot3d([x,g(x),(f(x)g(x))*t],t=0..1,x=a..xi,color=green): qumian3[i]:=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(zhengfangxing[i],i=0..K),insequence=true): zhengfangban:=display(seq(zhengfangban[i],i=0..K),insequence=true): qumian1:=display(seq(qumian1[i],i=0..K),insequence=true): qumian2:=display(seq(qumian2[i],i=0..K),insequence=true): qumian3:=display(seq(qumian3[i],i=0..K),insequence=true): display(xzou,yzou,base,quxianf,quxiang,zhengfangban,zhengfangxing,qumian1,qumian2,qumian3,scaling=constrained)。( ) sin + 2f x x?x( ) s in ( 1) 1g x x? ? ? y July 1, 2022 四川大學(xué)數(shù)學(xué)學(xué)院 徐小湛 切片法 27 with(plots): f:=xsin(x)+2: g:=xsin(x1)1: a:=Pi:b:=2*Pi: xzou:=spacecurve([x,0,0],x=a1..b+1,thickness=3,color=black): yzou:=spacecurve([0,y,0],y=2..3,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=a1..b+1,thickness=3,color=red): quxiang:=spacecurve([x,g(x),0],x=a1..b+1,thickness=3,color=red): K:=60:for i from 0 to K do xi:=a+i*(ba)/K: banyuan[i]:=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): dixian[i]:=spacecurve([xi,y,0],y=g(xi)..f(xi),thickness=3,color=blue): banyuanban[i]:=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): qumian[i]:=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(banyuan[i],i=0..K),insequence=true): dixian:=display(seq(dixian[i],i=0..K),insequence=true): banyuanban:=display(seq(banyuanban[i],i=0..K),insequence=true): qumian:=display(seq(qumian[i],i=0..K),insequence=true): display(xzou,yzou,quxianf,quxiang,banyuanban,base,banyuan,qumian,dixian,scaling=constrained)。 動畫的 Maple程序 。 動畫的 Maple程序 July 1, 2022 四川大學(xué)數(shù)學(xué)學(xué)院 徐小湛 切片法 30 xy2222 1xyxabx??例 8 立 體 以 橢 圓 為 底 ， 在 處 的垂 直 于 軸 的 截 面 是 一 個 半 圓 。2 2 2x y R?? July 1, 2022 四川大學(xué)數(shù)學(xué)學(xué)院 徐小湛 切片法 24 with(plots): R:=: f:=xsqrt(R^2x^2): g:=xsqrt(R^2x^2): a:=R:b:=R:H:=2: xzou:=spacecurve([x,0,0],x=a1..b+1,thickness=3,color=black): yzou:=spacecurve([0,y,0],y=a1..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*(ba)/K: zhengfangxing[i]:=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): zhengfangban[i]:=plot3d([xi,y,z],y=g(xi)..f(xi),z=0..f(xi)g(xi),color=yellow,style=patchnogrid): qumian1[i]:=plot3d([x,f(x),(f(x)g(x))*t],t=0..1,x=a..xi,color=green): qumian2[i]:=plot3d([x,g(x),(f(x)g(x))*t],t=0..1,x=a..xi,color=green): qumian3[i]:=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(zhengfangxing[i],i=0..K),insequence=true): zhengfangban:=display(seq(zhengfangban[i],i=0..K),insequence=true): qumian1:=display(seq(qumian1[i],i=0..K),insequence=true): qumian2:=display(seq(qumian2[i],i=0..K),insequence=true): qumian3:=display(seq(qumian3[i],i=0..K),insequence=true): display(xzou,yzou,base,quxian,zhengfangban,zhengfangxing,qumian1,qumian2,qumian3,scaling=constrained,orientation=[60,70])。 July 1, 2022 四川大學(xué)數(shù)學(xué)學(xué)院 徐小湛 切片法 17 R:=: f:=xsqrt(R^2x^2): g:=xsqrt(R^2x^2): a:=R:b:=R:H:=2: xzou:=spacecurve([x,0,0],x=a1..b+1,thickness=3,color=black): yzou:=spacecurve([0,y,0],y=a1..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 d