★ /prog/ Challenge Summer Edition ★

THE CHALLENGE:
I) Write three functions, union :: [(Float,Float)] -> [(Float,Float)], difference :: [(Float,Float)] -> [(Float,Float)], intersection :: [(Float,Float)] -> [(Float,Float)]
Which perform the respective set operations on their input, a list of closed intervals of the form (min, max). Your functions need not support sentinel values such as NaN or infinity. The number of intervals returned should be minimized where possible.

II) Use your functions from I to implement a simple ^CSG _raytracer. Your raytracer should support the following features:

• Spheres
• Diffuse surfaces
• Specular surfaces

Upon completion, post your source code here, along with one (1) example rendering, showcasing ^your raytracer. The example render should include an example of each set operation performed on two spheres, for a total of six spheres. A single directional light source should be used to light the scene.

Submissions close on 2010-10-04 at 00:00. Programs will be marked in three categories: efficiency, conciseness, and quality of implementation.

Each winner is entitled to claim ownership of two (2) /prog/ memes of his choice, with the exception of SICP, HMA, and UMH.

>>3
For any range tuple (min, max), min and max will be standard floating point values. Namely, this means they will not be any of the following:

• Subnormal numbers
• Infinities
• NaN

Additionally, no distinction needs to be made between positive and negative zero.