DEMOS HELP

CRATER LAKE FUNCTION GRAPH DEMO HELP

This demo includes two display windows. The first, titled “Crater Lake”, starts out with a green curve which is a slice of the graph of the function f(x,y) = -(x² + y²)² + (x² + y²) + mx. Specifically, it is the curve obtained by intersecting the graph of f(x,y) with a plane containing the z-axis and containing a line in the x-y plane making and angle of theta0 with the x-axis. You may change theta0 using the [<<], [<], [>], and [>>] buttons. If you click the [>>] button, the green curve will trace out the function graph of f(x,y). You may also change the parameter m in the equation for f(x,y) using the [<<], [<], [>], and [>>] buttons, and you may use the same viewing options for 3D graphs that appear in the previous demos. Finally, the control window includes “blue” and “red” checkboxes. When “red” is checked, points on the graph where the partial derivative of f with respect to x is positive will appear red. Similarly, when “blue” is checked, points on the graph where the partial derivative of f with respect to y is positive will appear blue. Note that when both “red” and “blue” are checked, points where both of these partial derivatives are positive will appear purple. Below the graph of f(x,y), the domain of the graph is displayed, with each point colored the same way as the point it maps to.

The normal map of the graph is shown in the second window, titled “Sphere”. Each region is colored according to the color of the preimage. Note that each octant in the normal map corresponds has a different color.

GENERAL DEMO HELP

Java demos make it possible to view and manipulate curves and surfaces in two or three dimensions. Selecting the demo name on the bar below an illustration will bring up a control window and one or more 2D or 3D graph windows. Select each window and drag it to a convenient place so it does not overlap the control window. Windows can be resized by dragging the lower left corner.

Viewing options:

To zoom in or out, select Zoom from the Tools menu, then move the cursor in a window, upward to zoom in and downward to zoom out. Alternatively, hold down the shift key while dragging in the window.

To translate a display, select Translate from the Tools menu or hold down the Alt key while dragging the cursor in the window in the translation direction.

Functions:

Most of the demos have at least one function displayed in the control window as function name next to a text box. To change a function definition, type the new definition in the text box and click “enter”. The domains of functions are given by intervals that are determined by beginning and endpoints and the number of subdivisions. Each of these numbers can be changed by typing in new values and clicking “enter” after each change.

Variables:

Many of the demos include “variables”, which control the parameters in function definitions. As in the case of intervals, each one will have a beginning and endpoint and a resolution. To change a variable one step at a time, click the single arrow [>] next to the variable definition to increase the value and the single arrow [<] to decrease that value. To animate the change from the present position of a variable to its endpoint, select the double arrow [>>] and to animate the return to the beginning point, select [<<].

Hotspots:

Some of the demos include controls called “hotspots”. These are movable dots in the graph windows that can be clicked and dragged to change one or more parameters in a graph.

Rotations (in 3D graph windows):

To rotate an object in a 3D window, select Rotate from the Tools menu or hold down the Control key on a PC or the Apple key on a Macintosh). Moving the cursor in the window will cause the image to rotate in space. To return to the default view at the start of the demonstration, hit the space bar. Alternatively, in some demos there are two variables “rtheta” that causes the object to rotate a certain number of degrees about the z-axis, and “rphi” that rotates the z-axis a certain number of degrees toward the viewer.

There are six options under the View menu giving views down the positive or negative x-axis, y-axis, or z-axis. Alternatively, hitting the “x”, “y”, or “z” keys while the cursor is in a window gives the projection down the respective axis from the positive direction and hitting these keys while holding down the shift key gives the corresponding projections in the negative direction.