Mathematics and Computer Graphics

I read a book this weekend called "What the Dormouse Said."  It tells the story of the birth of the computer industry in Silicon Valley during the 1960s and 1970s.  Most of the people involved were connected in some way with Stanford University because of all the computer research being done there.  Much of this work was government funded, with the bulk of the funding coming from the Pentagon. 

There was a naval air station in Sunnyvale throughout WW II that led to the need for research in advanced aeronautical technology and electronics.  A number of corporations set up offices in the area to help fill the need for advanced technological research.

Lockheed and Honeywell both set up research operations in Sunnyvale.

Shockley Semiconductor in Mountain View did extensive research in developing silicon chip technology and led to the founding of both Fairchild Semiconductor and Intel.

Ampex was based in San Carlos.

Hewlett Packard was founded in Palo Alto.

Xerox PARC (Palo Alto Research Center) was in Palo Alto.

Mathematics is essential to computer programming - Math is the the language that computers speak.

I'm getting ready to talk to MTH 060 about graphing in a few days and the connection between computer graphics and the Cartesian Plane occured to me.  All computer graphics are based on the pixels of the screen and what color they need to be to represent the object.

To communicate to the computer what to do with each pixel, the programmer must identify the pixel by its position on the screen.  This is usually done a little differently than the standard Cartesian Plane, but it is exactly the same idea.

In addition, any type of object that is projected on the screen can be moved by describing the movement to the computer as a series of mathematical formulas.  The more difficult movements are often established using motion capture technology in which real performers wear black bodysuits with white disks at key points of the body.  Those key points are the ones involved in making the movement appear natural.

There are a number of courses on Mathematics and Computer Graphics

At the University of Illinois Urbana-Champaign

At Georgia Tech

Here are links to several books on the subject

Mathematics for Computer Graphics by John Vince

Essential Mathematics for Games and Interactive Applications by James Van Verth and Lars Bishop

Mathematics for 3D Game Programming by Eric Lengyel

There is also a nice pdf on Mathematics and Computer Graphics here.