Notes on applorng.pov              By George W. Hart             File: applorng.txt

I started to explore raytracing because I enjoy making sculptural constructions of
various sorts and I often conceive of structures too complex for me to build.  I 
wanted a technique to at least make an image of constructions I visualize.  For 
some examples, see my www page <URL:http://www.li.net/~george/pavilion.html>.
I have been playing with POVRAY for just over a month now.

This apples and oranges construction is a sort of table centerpiece of 12 apples
and 20 oranges bound together with 60 forks.  The apples are placed stem-outward
at the corners of an icosahedron (20 equilateral triangles).  The oranges are
placed "belly-button"-outward at the corners of a dodecahedron (12 pentagons).
The forks follow the edges of a rhombic triacontahedron (30 rhombic sides, 5 acute
corners meeting at each apple, 3 obtuse corners meeting at each orange) but are 
displaced slightly for visual interest.  Three forks have their tines impaling
each orange, spiraling in.  Five forks have their handle end embedded in each
apple, spiraling in the opposite rotation.  I conceived of this in a flash when I 
saw the contest topic was food, probably because the metaphor of apples and oranges 
is central to my work.  (See <URL:http://www.ctr.columbia.edu/~hart/multanal.html>.)
The smooth dull finish of the apples versus the shiny bumpy finish of the oranges is
to emphasize the metaphor of contrast, but I am not happy with the textures.

The gingham tablecloth (a plane with a hand-drawn image-map) seemed like the obvious 
variation on the ubiquitous tile floor.  The blue sky provides orientation and is 
placed symmetrically to the table to emphasize the symmetry of the construction.  
A square picture format does also. The oranges are bumpy spheres with some disks
for the belly-buttons.  The apples are quartics constructed as a "soft" cardiod
[r=1.2+sin(theta)] rotated about its axis of symmetry, with a piecs of torus for a
stem.  There is only one bump into each apple.  (A two bumper would require a sixth
order polynomial, and I had enough trouble typing in all the zeros you don't need in 
the 4th order poly.)   So the bump is always placed towards the viewer, and is the
receptacle for the stem in the near apples, and is the "anus" (maybe a botanist out
there can tell me the correct term) of the far apples.

The forks are the intersection of a height-field (to give the tines and handle
outline shape) and a quartic shape (to give a smooth forward bend for the tines and
reverse bend for the handle).  The fruit and forks were positioned by a simple 
Visual Basic program I wrote which places objects in space into polyhedral and 
geodesic arrangements.

George W. Hart
george@li.net
April 1995