Surface with Level Curves (Contours) Projected onto the xy -Plane
Dr. K. G. TeBeest

> with( plots ) : with( plottools ) :

Example 1:   Elliptic Paraboloid

> f := x^2 + 3*y^2 ;

> p := plot3d( f, x = –5.0 .. 5.0, y = –3.0 .. 3.0, style = patchcontour, contours = 8, scaling = unconstrained, axes = framed ) :

> q := contourplot( f , x = –5.0 .. 5.0, y = –3.0 .. 3.0, filled = true ) :

> F := transform( (x,y) –> [ x, y, 0] ) :    # This plots the contour plot (the level curves of f ) and displays it in the plane z = 0.

> display( { p, F(q) } ) ;

Example 2:   Hyperbolic Paraboloid

> f := x^2 – y^2 ;

> p := plot3d( f, x = –3.0 .. 3.0, y = –3.0 .. 3.0, style = patchcontour, contours = 8, scaling = unconstrained, axes = framed ) :

> q := contourplot( f, x = –3.0 .. 3.0, y = –3.0 .. 3.0, contours = 8, filled = true ) :

> F := transform( (x,y) –> [ x, y, –20 ] ) :    # This plots the contour plot (the level curves of f ) but displays (shifts) it down to the plane z = –20.

> display( { p, F(q) } ) ;

Dr. K. G. TeBeest
Applied Mathematics
Kettering University