Mathlets: Rectangular Coordinates (3-D Graphing)

Rectangular Coordinates (3-D Graphing)

Graphs functions of the form f (x,y) using 3-dimensional rectangular coordinates. How to use || Examples || Other Notes

How to Use

Enter a function f₁(x,y) in the text input field marked "f₁(x,y)=" (Example: f₁(x,y)= 5-x²-y²)
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 functions graphed simultaneously:
- Enter the second function f₂(x,y) in the text input field marked "f₂(x,y)="
- Click (to its "on" state) the check box next to this input field
- Click the "Graph" button
(Example: f₁(x,y)= 5-x²-y² and f₂(x,y)=1-x-y)
Up to 3 functions 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 field and click the "Graph" button to refresh
To erase the graph and all input fields, click the "Clear" button

The text input fields 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

Plane f (x,y)=x-2y		Hemisphere f (x,y)=√(25-x²-y²)		Paraboloid f (x,y)=x²+y²-8
Saddle f (x,y)=(x²-y²)/10		Waves f (x,y)=cos(x-y)		Ripples f (x,y)=cos(2√(x²+y²))

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" representation for surfaces, in which the surface is transparent, only draws one surface at a time.