DEMOS HELP

WARPED TORUS DEMO HELP

This demo includes two display windows. The first, titled “Critical points of z(u,v)” is a graph of a torus, initially held horizontally, with a perturbation applied to the height of each point given by epsilon2 * sin(2u) + epsilon3 * sin(3u), where u gives the angle the 2D vector given by the point’s x and y components makes with the x-axis in the x-y plane. As in the “A torus held vertically” demo, you may change a, b, and alpha. You may also change epsilon2 and epsilon3, the parameters in the perturbation, using the [<<], [<], [>], and [>>] buttons. You also have the 3D viewing options available in the previous demos.

The graph of the warped torus has the same normal-vector-based coloring scheme as in the “A torus held vertically” demo. As before, this coloring scheme is indicatd in the “Normal map” window.

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.