A Conversation for Boolean Algebra

Boolean Graphics

Post 1

Steve K.

One application of computer booleans is graphic. I use Bryce 4 from Corel, a 3D landscape modelling program. It is not a general purpose 3D modelling app, but it does include primitive shapes - spheres, cylinders, cubes, etc. And it allows combining these (or any imported 3D shape, I think) with boolean operations.

From the manual: "A boolean object is an object created by combining two or more objects to form a single object ... by performing boolean operations ... union, subtraction, and intersection. ... Objects can be neutral, positive, negative or intersecting."

An example is a long (positive) cylinder combined with a series of small (negative) spheres which are halfway "buried" in one side of the cylinder. You don't see the spheres, but they "gouge out" a series of depressions in the cylinder, so it looks like a flute.

The possibilities are endless, especially for abstract shapes. Everything can be animated, textured, lighted ... creating some pretty wild scenes ... psychedelic, man smiley - smiley

Boolean Graphics

Post 2


Going back a bit further, ISTR a significant brouhaha over Apple's insightful use of XOR'ed cursors on the Macs (Mac Classics, descendants of Lisa). By performing an xor of the screen pixels with the cursor pixels, you could always see the pointer (i.e. it was white on a black background, but black on a white background).

Heady stuff...

Boolean Graphics

Post 3

Steve K.

Yes, the "old days" smiley - smiley

Unfortunately, I've never owned a Mac, but the PC side of things had its own insightful programmers - not many, but some. In the dark days before Windows (OK, some would say the days got even darker), we had DOS programs like Flight Simulator - by Sublogic before MS got it. The Hercules graphics card version (WAY better than four color CGA) was spectacular - for its time. Hi-res B&W, great detail, and the night flying must have been some form of the XOR you describe - the details simply became lighted. A great illusion.

The Apple "brouhaha" you describe was an argument? Or simply a lot of attention?

Boolean Graphics

Post 4


I vaguely remember the xor thing as a patent fight, but can't remember the outcome.
Apple probably won on look & feel.

Boolean Graphics

Post 5


Hmm... I remember reading somewhere in the Manuals for XScreenSaver (http://www.jwz.org/xscreensaver/screenshots.html) and later on (when I did get around to read it) in HAKMEM (http://www.inwap.com/pdp10/hbaker/hakmem/hacks.html#item146) that five instructions on PDP-1 assembly language would produce an interesting animation, which was called in MIT hacking circles the Munching Squares hack. I include the code for your own pleasure:

ADDB 1,2
ROTC 2,-22
XOR 1,2
JRST .-4

Now, I don't know anything about the PDP-1, much less its assembly language, but this seems to be an interesting hack based mainly on an addition, a rotation and an XOR operation, which are, or can be reproduced by, bona fide boolean operations. Enjoy!

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