[Edu-sig] more chatter re OOP + PolyGeom

[Kirby Urner]

At 03:35 PM 05/08/2000 -0700, I wrote:

>The power of object oriented programming seems especially 
>clear to me in that I ended up making no changes to my
>Quaternion class, which contains stuff like 
>
<<snip>>

Sigh.  Not unusually, just when I thought I had it all nailed
down, I found a bug in my coords.py module, which made cross 
product asymmetric depending on whether you were doing 
Vector.cross(Qvector) or Qvector.cross(Vector).

Note:  Qvectors are quadrays, defined as 4-tuples vis-a-vis 
the 4 basis vectors of a "home base" tetrahedron defined 
by intertangent equi-radius spheres (tetrahedron edges = 1, 
tetrahedron volume = 1).

The problem showed up when I got ambitious and decided to
incorporate my quaternions-based rotation method within my 
generic shapes.Shape class -- will allow you to rotate any 
shape subclass around X,Y or Z axis by theta (degrees).

Well, after so incorporating, I discovered my tetrahedra
were getting all distorted by the rotation method, which
led to backtracking and bug-fixing.  So now there's a new
cross product method in coords.Vector that's more explicitly 
XYZ-based (to make sure the cross-breeding of hybrid vector 
types doesn't create any mutants).

Now I'm feeling confidant again, and have uploaded the new 
code, along with a substantial rewrite of 

     http://www.inetarena.com/~pdx4d/ocn/numeracy1.html 

-- which is about my vector algebra implementation, including 
the backend into POV-ray (Persistance of Vision Ray Tracer)[1].

I also added a Cube shape, and split off some of the methods 
used to study the Jitterbug relationship in a class by 
itself, allowing only _some_ shapes to inherit them -- a 
multiple inheritance situation, which Python allows.

I've been inviting a pre-college audience to check out this 
material, and perhaps get into the nitty gritty at some 
point.[2]  I think this implementation gives a lot of 
insight into object-oriented design i.e. shows the power 
of inheritance, late binding, method overriding and so on.

This has been my goal all along:  to use spatial geometry, 
with the attractive graphics this entails, as a hook into 
the mysteries of OOP (object oriented programming), with
polyhedra as paradigm objects.[3]

Also, as it so happens that I'm a Fuller Schooler, my 
spatial geometry just takes all that concentric hierarchy 
+ sphere packing and jitterbug stuff for granted, with 
quadrays fitting rather seamlessly into this context.[4]

Kirby

[1] http://www.povray.org/
[2] http://mathforum.com/epigone/geometry-pre-college/skendsnehgly
[3] http://www.inetarena.com/~pdx4d/ocn/trends2000.html
[4] For more on the concentric hierarchy:
    http://www.teleport.com/~pdx4d/volumes.html 
    http://www.teleport.com/~pdx4d/volumes2.html