Identify some appropriate geometry to be displayed using OpenGL.  This requires proper initialization of the OpenGL system, definition of the viewing environment, analysis of the geometry into appropriate primitives and use of simple instancing transformations to realize them, use of OpenGL functions to display the geometric primitives to be displayed, use of hidden-surface display, and use of color as needed for the geometry.  Use the OpenGL idle callback to create some motion in even this first project, as illustrated in the barchart.c example.

The appropriate geometry will depend on your choice of applicaton area.  Here are some suggestions:
 

• 1a (Mathematics) Display a surface defined by a function.  This requires the creation of a grid in the domain and corresponding points in 3-space in the surface, displaying the triangles derived from the domain grid, and coloring the surface in some way such as height.  This function surface process is described in the materials on math projects, and some example surfacess are given there, except that these examples use lights and lighting instead of simple color.
  
  To look at the way color could be used, you can first find the largest and smallest values of the function by scanning the values at each grid node, and then any function value at any grid point can be scaled to a value between 0 and 1 with a simple proportion.  Once you have a value  z  between 0 and 1, you can define colors by using any path from one color to another in the RGB cube.  You could take, for example, a path from red to blue, or you could take a much more dramatic path from (0,0,0) to (1,1,1) — from black to white — in the cube.  One such path is the “gray line ” where all three color components are equal, so for value  z  we could use the color (z,z,z).  Another path was outlined in class, where values between 0 and 1/3 lie between black and one of the RGB primaries, values between 1/3 and 2/3 lie between the first primary and a color with two full primaries, and values between 2/3 and 1 lie between the two-primary color and white.

• 1b (Chemistry) Read a standard molecule description file and create a display of the molecule with standard atom-coded colors.  This requires the use of simple transformations to place the atoms, using pre-written functions to read molecular description files.  The functions are online as molecules.h (the header file for using the file reading functions) and readChemFiles.c (functions to parse the PDB and MOL files).
  
  This may be a little premature, because you probably need to use the translation transformation to place individual atoms at the correct place in the molecular model.  However, the discussion on more advanced modeling includes information on translations, so it should not be too difficult to read ahead and accomplish this.

• 1c (Physics) Display a rectangular bar divided into a grid, with some grid areas held at constant hot or cold temperatures and with temperatures changing by a diffusion process.  The diffusion process sets the temperature of a grid area at time T+1 as a convex sum of the temperatures of itself and surrounding grid areas at time T.  A convex sum is a weighted sum where the weights are all non-negative and the sum of the weights is 1.
  
  The bar itself can be seen as a grid with constant height, a simplified version of the mathematical surface above, or you may display each grid area with a height determined by the temperature as described in the materials on physics projects.  The process for choosing colors is similar to the process for choosing colors in the math example above.  The temperatures will always lie between the hot and cold values in the problem.  The process for temperature diffusion is described in some detail in the materials on physics projects, and we refer you there for more information.
  
  
• 1d (other) Find an area of science where there is a function of two variables arising naturally from the principles or theory of the science.  The physics projects writeup has an example of the functions of electrostatic potential, which could serve as a good model.  Graph the function using the processes of problem 1a above.

Due date:  February 29, 2000.  Turn in your programs by e-mailing your source code to your instructor and be prepared to demonstrate your running programs to him in the laboratory.  This project is worth 100 points and will be graded on proper documentation, proper modeling, sound rendering, and correct display.  Proper coding techniques will not in themselves be included in the grading, but if the instructor cannot understand your code, it is much more likely that you will be asked to demonstrate your project to a skeptical audience.