## Background

David Parker’s DPGraph, formerly also called Cyclone98, is a remarkably efficient and useful application for drawing mathematical surfaces (and lots of other things.) It is coded entirely in Intel assembly language and so is designed for the Windows operating system. However, it can be coaxed to work on other platforms as well, with a little effort.

## Install and Use DPGraph

For optimal use of DPGraph (DPG) you need to be able to save/edit text files in the DPG directory. Therefore, should install DPG on your own computer. For other computers, you can download a copy into your own space, or run it off a USB memory stick.

To download DPG to a pc, google DPGraph, and use our UIUC licence as a subscriber. Without a licence you can download a DPG player, but cannot edit and create new scripts. The unlicensed player can replay your binary files created by DPG. This is useful for posting DPG apps on the web.

Although macs now use an intel chip which can understand the DPG binaries, it has to be separately compiled in Wine. From download http://www.math.uiuc.edu/~gfrancis/illimath/zipper/dpgraph.zip and unzip it anywhere on your mac. Best location is in your /Applications/ folder. It is will unzip into a file named DPGraph.app/ and running it puts an icon on your desktop chrome. Set it (right-click) to stay there for future use.

When you open DPG it animates hyperboloids from 1 to 2 sheets and back. Always check the aspect ratio of your window to make sure it does not distort the geometrical figures. In DPG, use the arrow keys to turn image so that the cup faces you. Change aspect ratio of the window until it looks circular. Let’s investigate some of its features.

• MATH: What does

` graph3d(a*x^2+b*y^2+sin(c*time)=d*z^2 `
say in standard math notation? This is the formula that defines the cover animation.

• SCROLLBAR: Note that a=b=b=c=1, what happens if you change these?

1. Image Parameter: X-slice > arrows(no mouse) > move scrollbar

2. D-variable: what does d=0, d<0 mean?

• MATH: Discuss Conic Sections and Quadric Surfaces. (Separate Lesson on W2)

• ANIMATE:

1. You’ve already seen how the "time" variable works.

2. "Scrollbar" for one paramater at a time.

3. Slider

4. 3D-view with the arrow keys for an x- and y-rotation, no z-rotation. Question: Can you see every aspect of an object with the arrows?

• HELP: This is (pleasantly) rudimentary documentation in the style of the classical "man pages". Then you experiment. Keep track of what you discover in your Journal.

• CLIPBOARD: Copy and Paste using the clipboard. Don’t drag and drop, at least I had a problem with that.

While the EDIT popup of DPG has a tiny window into the script, it is generally better to SAVE as a textfile, open it in Wordpad or other text editor, edit it, save the edit, and press the EXECUTE button in dpg to see the effect of your edit. You must the file as a text file (ascii), not a rich-text file.

SAVE:

1. Save the script for the cover animation as a text file with Save > nameit > Desktop > As ASCII DGP file