surfaces_1.mws

Graphs_ I

Version .75 for MapleVR6

> with(plots): with(plottools):

Warning, the name changecoords has been redefined

Setting Defaults

Set some defaults for all pictures.

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:

> 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.