CS 534                                                  Spring 2006

                          Assignment 1

                  The Angular Fisheye Projection


The fixed function pipeline supports only a limited type of projection,
namely one that can be described by a 4 x 4 matrix. In OpenGL, we 
almost always use glOrtho, glFrustum, or gluPerspective to describe
a projection. With the standard perspective projections, we cannot
get a 180 degree fisheye. Note that even as we get close to a 180
degree projection with standard projections there are large distortions
as we get close to 90 degrees from the center.

Sometimes we would like an even wider angle perspective, such as when 
we try to form an environment map.  Another example, one that is of 
great interest at UNM, is forming 180 degree projections for domed environments.
There are a number of ways of creating such images. Probably the most
important is the angular fisheye projection. See

http://astronomy.swin.edu.au/~pbourke/projection/fisheye/

A google search will yield many other references.

Assume that our objects are all within a hemisphere that sits
on a plane with the camera centered on the plane. A fisheye
lens would see all the objects in this space and project them to
the image plane. The angular fisheye approach is to draw linear projectors
from the center of projection that project the objects onto the
hemisphere. The hemisphere is then mapped to a circle in a plane.
In the angular fisheye projection, the mapping to the plane is
done is such as way that equal anglular slices on the hemisphere
map to equal distances in the image plane. The equations are in the
above reference. Note the similarity to the environment map
equations in Chapter 8 of the text.

The computation of such projections should be fairly straight forward
using a vertex shader written in GLSL. In this assignment you are
to write such a shader and use it to display projections from an
application of your choice. Your application need not be very 
complex but it would be interesting to see how many frames per
second you can generate with your program.

You should also be able to obtain images by reading the frame 
buffer with glReadPixels. If you do this, you can then convert
the image to a standard format (I have code for producing tiff
images from RGB images) and we can display it on the dome
at the ARTS Lab.

For a given scene, determine if there is a performance penalty
for using your vertex shader compared to the fixed function
modified Phong Shader. Do this by animating your scene and 
computing frames/second.

Finally, add a simple fragement shader that will mask out some
areas and taper the color values near the edges of the unmasked
area.