The standard way to graph surfaces in 3D is in Cartesian
coordinates. In that case we typically z as a function of x and
y. The 3D Cartesian Grapher applet asks for an xWindow, a yWindow, and
a zWindow to give a viewing window. The user may define two functions f
and g
to graph. The user can scroll x0 and y0 through the range for x
and y. The grapher gives the surface along with a point
corresponding to the graph of (x0,y0) and curves through that point
with one variable held constant.
The second way to graph in 3D is with cylindrical coordinates. We
typically think of r as a function of theta and z. The
Cylindrical Grapher applet asks for a maximum value for r and for
a zWindow to give a viewing window. The user may define two
functions r1 and r2
to graph. The user can scroll theta0 and z0 through the range for
theta and z. The grapher gives the surface along with a point
corresponding to
the graph of (theta0,z0) and curves through that point with one
variable
held constant.
The third way to graph in 3D is with spherical coordinates.
We
typically think of r as a function of theta and phi, where theta is the
familiar angle in the x-y plane from polar coordinates and phi is the
angle from the north pole. The Spherical
Grapher applet asks for a maximum value for r to give
a viewing window. The user may define two functions r1 and r2
to graph. The user can scroll theta0 and phi0 through the range
for
theta and phi. The grapher gives the surface along with a point
corresponding to
the graph of (theta0,phi0) and curves through that point with one
variable
held constant.