Enter functions f1(s,t),
g1(s,t), and
h1(s,t)
in the text input fields
marked "f1(s,t)=",
"g1(s,t)=", and
"h1(s,t)="
(Example:f1(s,t)=t+4 cos t,
g1(s,t)=4 sin t,
h1(s,t)=t)
Click the "Graph" button
(this button also refreshes the graph)
Rotate the graph by
clicking and dragging the mouse on the graph.
To see two surfaces graphed simultaneously:
Enter the second set of functions
f2(s,t),
g2(s,t), and
h2(s,t)
in the text input fields
marked
"f2(s,t)=",
"g2(s,t)=", and
"h2(s,t)="
Click (to its "on" state) the check box next
to this set of input fields
Click the "Graph" button
(Example:f1(s,t)=t+4 cos s,
f1(s,t)=4 sin s, and
f1(s,t)=t;
f2(s,t)=5 cos t sin s,
g2(s,t)=5 sin t sin s, and
h2(s,t)=5 cos s)
Up to 2 surfaces can be graphed simultaneously
To remove a function from the graph, click (to its "off" state)
the check box next to the associated text input fields and click
the "Graph" button to refresh
To erase the graph and all input fields, click the
"Clear" button
There are four input fields which specify
bounds on the variables for the function:
The variable s
takes values between smin
and smax,
specified by the fields marked
"smin=" and
"smax=".
The variable t
takes values between tmin
and tmax,
specified by the fields marked
"tmin=" and
"tmax=".
These four text input fields can accept any decimal number input.
The text input fields for functions can accept
a wide variety of expressions to represent functions, and the
buttons under the graph allow various manipulations of
the graph coordinates.
For another way to view surfaces, try the
"wireframe" representation.
Examples
Ellipsoid: f1(s,t)=5 cos t sin s g1(s,t)=3 sin t sin s h1(s,t)=2 cos s
Cylinder: f1(s,t)=5 cos t g1(s,t)=5 sin t h1(s,t)=s
Slant Cylinder: f1(s,t)=s+5 cos t g1(s,t)=5 sin t h1(s,t)=s
Other Notes
Surfaces in three dimensions are represented in
"faceted hidden surface" form. The facets are not subdivided at intersections
of surfaces if more than one surface is drawn, so intersections
of surfaces are not precise. The
"wireframe" represenation for surfaces,
in which the surface is transparent,
only draws one surface at a time.