Graphs_ I
Version .75 for MapleVR6
Loading the plotting packages.
> with(plots): with(plottools):
Warning, the name changecoords has been redefined
Setting Defaults
Set some defaults for all pictures.
> setoptions3d(axes=framed,shading=ZHUE);
A Paraboloid
> gr0 := plot3d(x^2 + 4*y^2,x=-3..3,y=-3..3,view=0..9,style=patchcontour):
> display3d(gr0);
Contours in R^2 for this same function.
> gr1 := contourplot3d(x^2+4*y^2,x=-3..3,y=-3..3):
> display3d(gr1);
Twin mountains
> gr2 := plot3d((x^2+3*y^2)*exp(1-x^2-y^2),x=-2..2,y=-2..2, view = 0..3, style = contour, orientation= [157,64]):
> display3d(gr2);
A Misleading Plot of Contours ?
Note that the contours should have rotational symmetry !
> gr3 := contourplot3d(sin(x^2+y^2),x=-10..10,y=-10..10):
> display3d(gr3);
Rotated Result Looking Down:
A monkey saddle.
> gr4 := plot3d(x^3-3*x*y^2,x=-2..2,y=-2..2,view = -2..2,thickness=3):
> display3d(gr4);
A swallowtail.
> gr5 := plot3d(x^3 - x*y,x=-3..3,y=-3..3,view=-5..5,orientation= [125,76]):
> display3d(gr5);
Implicit Plots
A one-sheeted hyperboloid.
> gr6 := implicitplot3d(x^2+y^2-z^2=4,x=-5..5,y=-5..5,z=-5..5,thickness=1):
> display3d(gr6);
Hyperboloid with Plane Section.
> xz_plane := plot3d([t,0,s],t=-5..5,s=-5..5,grid=[5,5]):
> display3d([xz_plane,gr6]);
rotated version pasted below.
Two sheeted hyperboloid.
> gr8 := implicitplot3d(x^2+y^2-z^2=-4, x=-5..5, y=-5..5, z=-5..5,thickness=3):
> display(xz_plane,gr8);
Hyperbolic Cylinder
> gr9 := implicitplot3d(x^2-z^2 = -4,x=-5..5,z=-5..5,y=-5..5):
> display(gr9);
A Few Interesting Surfaces
> plot3d([sin(u),sin(2*u),v],u=-Pi..Pi,v=-10..10,axes=boxed,style=patchnogrid);
The Whitney umbrella.
> gr10 := plot3d([u*v,u,v^2],u=-10..10,v=-10..10,axes=boxed,orientation=[100,80],shading=xy,style=patch,labels=[x,y,z]):
> display(gr10);
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