Figure of Rotation
- A figure of rotation is created by sweeping the plot of a function of one variable around an axis.
The region of space enclosed by the function defines the surface of rotation.
The best way to visualize this process is to consider the way a lathe works - by controlling the position of the cutting edge as the item spins beneath it, you can define a figure of rotation.
(For a more detailed discussion of figures of rotation, consult any calculus text.)
This applet lets you create your own figure of rotation and then view it from any perspective.
To define the function that will be swept around the axis, click-and-drag the control points on the left side of the applet.
The control points are connected with lines, and the resulting shape is swept around an axis located just to the left of the control point area.
The figure generated by the control points is displayed as a wire-frame on the right side of the applet.
By using the drop-down selection boxes, you can choose the number of points you want to control as well as the number of segments that will be used to create the figure of rotation.
The camera is always centered on the object, but you can adjust the following viewing parameters: » Distance - The distance between the camera and the viewing surface » Theta - The horizontal angle the camera makes with the viewing surface (first transform) » Phi - The vertical angle the camera makes with the viewing surface (second transform) » Rotation - The amount of "tilt" the camera has (like tilting your head left/right) (third transform)