Mathlets: Parametric Surfaces (3-D Graphing, Wireframe)

Parametric Surfaces (3-D Graphing, Wireframe)

Graphs a surface in three dimensions specified parametrically, as x=f (s,t), y=g (s,t), and z=h (s,t), with parameters s and t How to use || Examples || Other Notes

How to use

Enter functions f (s,t), g (s,t), and h (s,t) in the text input fields marked "f (t,s)=", "g(t,s)=", and "h(t,s)=" (Example: f (s,t)=t+4 cos t, g (s,t)=4 sin t, h (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 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 s_min and s_max, specified by the fields marked "s_min=" and "s_max=".
- The variable t takes values between t_min and t_max, specified by the fields marked "t_min=" and "t_max=".
- 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 "faceted hidden surface" representation.

Examples

Sphere:
f (s,t)=5 cos t sin s
g (s,t)=5 sin t sin s
h (s,t)=5 cos s

Plane:
f (s,t)=s
g (s,t)=t
h (s,t)=s+t

Cylinder:
f (s,t)=5 cos t
g (s,t)=5 sin t
h (s,t)=s

Slant Cylinder:
f (s,t)=s+5 cos t
g (s,t)=5 sin t
h (s,t)=s

Other Notes
Surfaces in three dimensions are represented in "wireframe" form. The "faceted hidden surface" representation allows for more than one surface to be drawn.