【正文】 =c..d,)。例1 作出以圓 x=2+2cost，y=4+2sint, z=2 (0≤t≤2π)為準(zhǔn)線，頂點(diǎn)為M(1, 1, 0)的錐面的圖形。解 柱面的參數(shù)方程為：。輸入以下命令。x:=t2*cos(t): y:=t4+2*sin(t): z:=t2:x0:=1: y0:=1: z0:=0: a:=0: b:=2*Pi: S:=1:plot3d([x0+s*(x(t)x0),y0+s*(y(t)y0),z0+s*(z(t)z0)],t=a..b,s=0..S, color=yellow, axes=normal,color=yellow, lightmodel=light3, scaling=constrained)。輸出圖形： 例2 作出以曲線 x=t，y=2sint, z=4 (1≤t≤6)為準(zhǔn)線，頂點(diǎn)為M(0, 0, 0)的錐面的圖形。解 柱面的參數(shù)方程為：。輸入以下命令。x:=tt: y:=t2*sin(t): z:=t4:x0:=0: y0:=0: z0:=0: a:=1: b:=6: S:=2:plot3d([x0+s*(x(t)x0),y0+s*(y(t)y0),z0+s*(z(t)z0)],t=a..b,s=0..S, color=yellow, axes=frame, color=yellow,lightmodel=light3, scaling=constrained)。輸出圖形： 返回目錄空間曲線作空間參數(shù)曲線 的圖形?？臻g曲線作圖的基本命令是：with(plots): x:=tx(t): y:=ty(t): z:=tz(t):spacecurve([x(t), y(t), z(t)], t=a..b)。例1 作出曲線的圖形。 解 輸入以下命令。with(plots):x:=tcos(t): y:=tsin(t): z:=tt:a:=0: b:=4*Pi:spacecurve([x(t),y(t),z(t)], t=a..b, thickness=4,color=red, axes=normal)。輸出圖形（圓柱螺旋線）：例2 作出曲線的圖形。 解 輸入以下命令。with(plots):x:=tt*cos(t): y:=tt*sin(t): z:=tt:a:=0: b:=8*Pi:spacecurve([x(t), y(t), z(t)], t=a..b, thickness=4, color=red, axes=normal, numpoints=1000)。輸出圖形（圓錐螺旋線）：例3 作出曲線的圖形。 解 輸入以下命令。 with(plots):x:=tt: y:=tt^2: z:=tt^3:a:=2:b:=2:spacecurve([x(t), y(t), z(t)], t=a..b, thickness=4, color=red,axes=normal)。輸出圖形（twisted cubic）：例4 作出曲線的圖形。 解 輸入以下命令。with(plots):x:=t(4+sin(20*t))*cos(t): y:=(4+sin(20*t))*sin(t):z:=tcos(20*t):a:=0: b:=2*Pi:spacecurve([x(t), y(t), z(t)], t=a..b, thickness=4, color=red,axes=normal, numpoints=1000, scaling=constrained)。輸出圖形（圓環(huán)螺線）：例 作出曲線的圖形（圓柱螺線）。（同濟(jì)六版33頁，例3） with(plots):x:=tcos(t): y:=tsin(t): z:=tt: a:=0: b:=15:spacecurve([x(t),y(t),z(t)], t=a..b, thickness=4,color=red, axes=normal)。 兩曲面的交線空間曲線的一般方程 。空間曲線是兩個曲面的交線。對于這種情況，只有將交線的參數(shù)方程找到，再用前面的方法作出曲線的圖形。例1 作出曲線的圖形。 解首先寫出兩曲面的參數(shù)方程：和 。輸入以下命令：with(plots):a:=:b:=1:qumian1:=plot3d([a*cos(t), b*sin(t),z], z=0..2, t=0..2*Pi, color=yellow):qumian2:=plot3d([u*cos(t), u*sin(t), 2u^2], u=2..2, t=0..2*Pi, color=green):display(qumian1, qumian2, scaling=constrained,orientation=[40,60], axes=frame)。輸出圖形：交線的參數(shù)方程為：。 輸入以下命令：a:=:b:=1:qumian1:=plot3d([a*cos(t), b*sin(t),z], z=0..2, t=0..2*Pi, color=yellow):qumian2:=plot3d([u*cos(t), u*sin(t), 2u^2], u=2..2, t=0..2*Pi, color=green):x:=ta*cos(t): y:=tb*sin(t): z:=(x,y)2x^2y^2:quxian:=spacecurve([x(t), y(t), z(x(t), y(t))], t=0..2*Pi,thickness=4, color=red):display(qumian1, qumian2, quxian, scaling=constrained,orientation=[40,60], axes=frame)。輸出圖形：例2 作出兩張拋物面和的交線的圖形。 with(plots):R:=1:qumian1:=plot3d([u*cos(t)/sqrt(2),u*sin(t)/sqrt(3),u^2],u=0..2,t=0..2*Pi,color=yellow):qumian2:=plot3d([u*cos(t)/sqrt(2),u*sin(t),4u^2],u=0..2,t=0..2*Pi,color=green):quxian:=spacecurve([cos(t),sin(t),2+sin(t)*sin(t)],t=0..2*Pi,color=red,thickness=8):x_axis:=plot3d([u,0,0],u=1..1,v=0..,thickness=3):y_axis:=plot3d([0,u,0],u=1..1,v=0..,thickness=3):z_axis:=plot3d([0,0,u],u=..,v=0..,thickness=3):xyz:=display(x_axis,y_axis,z_axis,thickness=3):display(qumian1,qumian2,quxian,xyz,scaling=constrained,orientation=[40,60])。 with(plots):a:=1: u:=(x,y)2*x^2+3*y^2: v:=(x,y)42*x^2y^2:qumian1:=plot3d(u(x,y),x=a..a,y=sqrt(a^2x^2)..sqrt(a^2x^2),color=yellow):qumian2:=plot3d(v(x,y),x=a..a,y=sqrt(a^2x^2)..sqrt(a^2x^2),color=green):quxian:=spacecurve([cos(t),sin(t),u(cos(t),sin(t))],t=0..2*Pi,color=red,thickness=8): x_axis:=plot3d([u,0,0],u=1..1,v=0..,thickness=3):y_axis:=plot3d([0,u,0],u=1..1,v=0..,thickness=3):z_axis:=plot3d([0,0,u],u=..,v=0..,thickness=3):xyz:=display(x_axis,y_axis,z_axis,thickness=3):display(qumian1,qumian2,quxian,xyz,scaling=constrained,orientation=[40,60])。例3 作出球面和的交線的圖形（維維安尼曲線）。（同濟(jì)六版32頁，例1） with(plots): R:=1:zhumian1:=plot3d([R*sin(u)*cos(v), R*sin(u)*sin(v), R*cos(u)], u=0..Pi, v=0..2*Pi, color=yellow):zhumian2:=plot3d([(R/2)*(1+cos(t)), (R/2)*sin(t), z], z=.., t=0..2*Pi, color=green):z:=(x,y)sqrt(R^2x^2y^2): x:=t(R/2)*(1+cos(t)): y:=t(R/2)*sin(t):quxian1:=spacecurve([(R/2)*(1+cos(t)), (R/2)*sin(t), z(x(t),y(t))], t=0..2*Pi, thickness=5,color=red):quxian2:=spacecurve([(R/2)*(1+cos(t)), (R/2)*sin(t), z(x(t),y(t))], t=0..2*Pi,thickness=5,color=red):display(zhumian1,zhumian2,quxian1,quxian2, scaling=constrained,orientation=[40,65],axes=frame)。with(plots):R:=1:qiumian:=plot3d([R*sin(s)*cos(t),R*sin(s)*sin(t),R*cos(s)],s=0..Pi/2,t=0..2*Pi,color=yellow):zhumian:=plot3d([R*(cos(t/2))^2,(R/2)*sin(t),z],t=0..2*Pi,z=0..*R,color=green):quxian:=spacecurve([R*(cos(t/2))^2,(R/2)*sin(t),R*sin(t/2)],t=0..2*Pi,color=red,thickness=4): x_axis:=plot3d([u,0,0],u=1..,v=0..,thickness=3):y_axis:=plot3d([0,u,0],u=1..,v=0..,thickness=3):z_axis:=plot3d([0,0,u],u=..,v=0..,thickness=3):xyz:=display(x_axis,y_axis,z_axis,thickness=3):display(qiumian,zhumian,quxian,xyz,scaling=constrained,orientation=[46,57])。with(plots):with(plottools):R:=1:qiumian:=sphere([0,0,0],R,color=yellow):zhumian:=cylinder([R/2,0,R],R/2,2*R,color=green,capped=false):quxian:=spacecurve([R*(cos(t/2))^2,(R/2)*sin(t),R*sin(t/2)],t=2*Pi..2*Pi,color=red,thickness=4): x_axis:=plot3d([u,0,0],u=1..,v=0..,thickness=3):y_axis:=plot3d([0,u,0],u=1..,v=0..,thickness=3):z_axis:=plot3d([0,0,u],u=..,v=0..,thickness=3):xyz:=display(x_axis,y_axis,z_axis,thickness=3):display(quxian,xyz,scaling=constrained,orientation=[40,75])。例4 作出兩個直交圓柱面的交線:。解 先寫出曲面的參數(shù)方程：和。 輸入以下命令：with(plots): R:=1:zhumian1:=plot3d([R*cos(t), R*sin(t), z], z=R..R, t=0..2*Pi,color=yellow):zhumian2:=plot3d([R*cos(t), y, R*sin(t)], y=R..R, t=0..2*Pi,color=green):display(zhumian1, zhumian2, scaling=constrained,orientation=[40,65])。輸出圖形：with(plots):R:=