Running CurvedSpaces-Complete This file explains how to use the compiled version of the CurvedSpaces-Complete sample code accompanying the article "Real-time rendering in curved spaces", IEEE Computer Graphics and Applications, Nov-Dec 2002. Please see the article itself for an explanation of the underlying mathematics, and the source code for implementation details. (1) Start the program. D3D Version: If you have DirectX 7 or newer you'll get an empty window with a menu bar and you can proceed to Step 2 below. Otherwise you'll get a cryptic error message complaining that Windows can't find the library DDRAW.DLL and/or the function DirectDrawCreateEx, in which case you'll need to go to Microsoft's DirectX download page (http://www.microsoft.com/directx/homeuser/downloads/default.asp) to download a free copy of DirectX 7 or newer. OpenGL version: All you need is OpenGL (not GLU or GLUT), which comes with Windows95 and up, and a graphics card that supports it. (2) Choose Open... from the File menu, and select one of the sample files provided with this package. At this point you should see beams and spinning Earths. (3) Hit the up-arrow key a few times to get yourself moving. To control your speed up arrow = faster down arrow = slower space bar = stop Make your speed negative if you want to go backwards. (4) Click on the scene. The cursor will disappear, and your mouse will shift into steering mode. To regulate pitch move the mouse forwards or backwards yaw move the mouse left or right roll move the mouse left or right with the control key down. You can pitch, yaw, and roll even when your speed is zero, for example after pressing the space bar. (5) Right click to recover the standard cursor. (6) Explore the various sample files and menu options. (7) What is the background image you see when flying in spherical space? Why does it always look the same, even while you are turning? Note: CurvedSpaces-Complete is more fun to use, but CurvedSpaces-Simple provides a simpler starting point for programmers learning about curved space graphics. Questions? Contact Jeff Weeks at the address weeks geometrygames org