抛物面的Maple程序：
with(plots):
a:=3:
qumian:=plot3d(x^2+y^2,y=-a..a,x=-a..a):
x_axis:=plot3d([u,0,0],u=-3..3,v=0..0.01,color=blue):
y_axis:=plot3d([0,u,0],u=-3..3,v=0..0.01,color=blue):
z_axis:=plot3d([0,0,u],u=-3..12,v=0..0.01,color=blue):
xyz:=display(x_axis,y_axis,z_axis,thickness=3):
display(qumian,xyz,orientation=[17,73],tickmarks=[4,4,4],axes=none,grid=[40,40],lightmodel=light2);
with(plots):
a:=3:
qumian:=plot3d(x^2+y^2, y=-sqrt(a^2-x^2)..sqrt(a^2-x^2),x=-a..a):
x_axis:=plot3d([u,0,0],u=-3..3,v=0..0.01,color=blue):
y_axis:=plot3d([0,u,0],u=-3..3,v=0..0.01,color=blue):
z_axis:=plot3d([0,0,u],u=-3..12,v=0..0.01,color=blue):
xyz:=display(x_axis,y_axis,z_axis,thickness=3):
display(qumian,xyz,orientation=[17,73],tickmarks=[4,4,4],axes=none,grid=[40,40],lightmodel=light2);
with(plots):
a:=3:
qumian:=plot3d(x^2+y^2,y=-sqrt(a^2-x^2)..sqrt(a^2-x^2),x=-a..a):
qumian2:=plot3d(-0.1,y=-sqrt(a^2-x^2)..sqrt(a^2-x^2),
x=-a..a,color=gray,style=patchnogrid):
qumian3:=plot3d(-0.3,x=-a-1..a+1,y=-a-1..a+1):
x_axis:=plot3d([u,0,0],u=-3..3,v=0..0.01,color=blue):
y_axis:=plot3d([0,u,0],u=-3..3,v=0..0.01,color=blue):
z_axis:=plot3d([0,0,u],u=-3..12,v=0..0.01,color=blue):
xyz:=display(x_axis,y_axis,z_axis,thickness=3):
display(qumian3,qumian,qumian2,xyz,tickmarks=[4,4,4],axes=none,grid=[40,40],lightmodel=light2);
抛物面
with(plots):
a:=2:
qumian:=plot3d(8-x^2-y^2,y=-a..a,x=-a..a):
x_axis:=plot3d([u,0,0],u=-3..3,v=0..0.01,color=blue):
y_axis:=plot3d([0,u,0],u=-3..3,v=0..0.01,color=blue):
z_axis:=plot3d([0,0,u],u=-3..12,v=0..0.01,color=blue):
xyz:=display(x_axis,y_axis,z_axis,thickness=3):
display(qumian,xyz,orientation=[17,73],tickmarks=[4,4,4],axes=none,grid=[40,40],lightmodel=light3);
with(plots):
a:=2.5:
qumian:=plot3d(8-x^2-y^2,y=-sqrt(a^2-x^2)..sqrt(a^2-x^2),x=-a..a):
x_axis:=plot3d([u,0,0],u=-3..3,v=0..0.01,color=blue):
y_axis:=plot3d([0,u,0],u=-3..3,v=0..0.01,color=blue):
z_axis:=plot3d([0,0,u],u=-3..12,v=0..0.01,color=blue):
xyz:=display(x_axis,y_axis,z_axis,thickness=3):
display(qumian,xyz,orientation=[17,73],tickmarks=[4,4,4],axes=none,grid=[40,40],lightmodel=light3);
抛物面
用参数方程绘制
with(plots):
a:=2:
qumian:=plot3d([x,8-x^2-z^2,z],x=-a..a,z=-a..a):
x_axis:=plot3d([u,0,0],u=-3..3,v=0..0.01,color=blue):
y_axis:=plot3d([0,u,0],u=-3..10,v=0..0.01,color=blue):
z_axis:=plot3d([0,0,u],u=-3..2,v=0..0.01,color=blue):
xyz:=display(x_axis,y_axis,z_axis,thickness=3):
display(qumian,xyz,orientation=[17,73],tickmarks=[4,4,4],axes=none,grid=[40,40],lightmodel=light3);
抛物面
with(plots):
a:=1.6:
qumian:=plot3d([8-y^2-z^2,y,z],y=-a..a,z=-sqrt(a^2-y^2)..sqrt(a^2-y^2)):
x_axis:=plot3d([u,0,0],u=-1..10,v=0..0.01,color=blue):
y_axis:=plot3d([0,u,0],u=-2..2,v=0..0.01,color=blue):
z_axis:=plot3d([0,0,u],u=-2..2,v=0..0.01,color=blue):
xyz:=display(x_axis,y_axis,z_axis,thickness=3):
display(qumian,xyz,tickmarks=[4,4,4],axes=none,grid=[40,40]);
椭圆抛物面
用显函数绘制
with(plots):
a:=3:
qumian:=plot3d(2*x^2+3*y^2,x=-a..a,y=-sqrt(a^2-x^2)..sqrt(a^2-x^2)):
x_axis:=plot3d([u,0,0],u=-1..1,v=0..0.01,color=blue):
y_axis:=plot3d([0,u,0],u=-1..1,v=0..0.01,color=blue):
z_axis:=plot3d([0,0,u],u=-1..9,v=0..0.01,color=blue):
xyz:=display(x_axis,y_axis,z_axis,thickness=3):
display(qumian,xyz,text,tickmarks=[4,4,4],grid=[20,20],lightmodel=light2,view=[-a..a,-a..a,0..8]);
with(plots):
a:=2:b:=3:
qumian:=plot3d([u*cos(t)/sqrt(a),u*sin(t)/sqrt(b),u^2],u=0..2,t=0..2*Pi,color=yellow):
x_axis:=plot3d([u,0,0],u=-1..1,v=0..0.01):
y_axis:=plot3d([0,u,0],u=-1..1,v=0..0.01):
z_axis:=plot3d([0,0,u],u=-.2..4.4,v=0..0.01):
xyz:=display(x_axis,y_axis,z_axis,thickness=3):
display(qumian,xyz,scaling=unconstrained,orientation=[40,60]);
with(plots):
a:=4:b:=3:
x(u,v):=a*(u+v): y(u,v):=b*(u-v): z(u,v):=u^2+v^2:
A:=plot3d([x(u,v),y(u,v),z(u,v)],u=-2..2,v=-2..2):
display(A,scaling=unconstrained,lightmodel=light2,axes=normal);
with(plots):
a:=4:b:=3:
x(u,v):=a*u: y(u,v):=b*v: z(u,v):=(u^2+v^2)/2:
A:=plot3d([x(u,v),y(u,v),z(u,v)],u=-2..2,v=-2..2):
display(A,scaling=unconstrained,lightmodel=light2,axes=normal);
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