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Ray tracing Jell- O - from Pixar

Ray Tracing Jell-O Brand Gelatin
Paul S. Heckbert

Ray tracing has established itself in recent years as the most general
image-synthesis algorithm[10]. Researchers have investigated ray-surface
intersection calculations for a number of surface primitives. These have
included checkerboards [Whitted 80]; chrome balls [Whitted 80]; glass balls
[Whitted 80]; robot arms [Barr 82]; blue abstract things [Hanrahan 82];
more glass balls [Watterberg 83]; mandrills [Watterberg 83]; more mandrills
[Sweeney 83]; green fractal hills [Kajiya 83]; more glass balls [SEDIC 83];
aquatic blobby things [Kaw 83]; more chrome balls [Heckbert 83]; pool balls
[Porter 84]; more glass balls [Kajiya 86].
Unfortunately, nobody has ray traced any food. So far, the most
realistic foods were Blinn's classic orange and strawberry images, but
these were created with a scanline algorithm[2]. The Dessert Realism
Project at Pixar is addressing this problem. The article presents new
technology for ray tracing a restricted class of dessert foods, in
particular Jell-O brand gelatin. We believe this method may have
application to other brands of gelatin and, perhaps, pudding as well.
This article is divided into three parts: methods for modeling static
Jell-O, simulation of Jell-O motion using impressive mathematics, and
ray-Jell-O intersection calculations.

Jell-O Shape:
To model static Jell-O, we employ a new synthesis technique wherein
attributes are added one at a time using abstract object-oriented classes
we call ingredients. Ingredient attributes are combined during a
pre-processing pass to accumulate the desired set of material properties
(consistency, taste, torsional strength, flame resistance, refractive
index, etc.). We use the RLS orthogonal basis (raspberry, lime, and
strawberry, from which any type of Jell-O can be synthesized[9]).
Ingredients are propagated through a large 3-D lattice using vectorized
pipeline SIMD parallel processing in a systolic array architecture that we
call the Jell-O Engine. Furthermore, we can compute several lattice points
simultaneously. Boundary conditions are imposed along free-form surfaces
to control the Jell-O shape, and the ingredients are mixed using relaxation
and annealing lattice algorithms until the matrix is chilled and ready-to-eat.

Jell-O Dynamics:
Previous researchers have observed that, under certain conditions,
Jell-O wiggles[8]. We have been able to simulate these unique and complex
Jell-O dynamics using spatial deformations[1] and other hairy mathematics.
>From previous research with rendering systems, we have learned that a good
dose of gratuitous partial differential equations is needed to meet the
paper quota for impressive formulas.
Therefore, we solve the Schrodinger wave equation for the Jell-O field
"J":

delta squared J + 2m (E - V)J = 0.
---
h

Transforming to a spherical coordinate system[7],

delta J = beta theta J beta 1 theta J beta 1 theta J
x ------- + y --------- + z -------------
theta r r theta r r sin theta squared

Fuller has given a concise and lucid explanation of the derivation from
here:

The "begetted" eightness as the system-limit number of the
nuclear uniqueness of self-regenerative symmetrical growth
may well account for the fundamental octave of unique
interpermutative integer effects identified as plus one, plus
two, plus three, plus four, as the interpermuted effects of the
integers one, two, three, and four, respectively; and as minus
four, minus three, minus two, minus one, characterizing the
integers five, six, seven, and eight, respectively[3].

In other words, to a first approximation:

J = 0.
The Jell-O Equation

Ray-Jello-O Intersection Calculation:
The ray-Jell-O intersection calculations fortunately require the
solution of integral equations and the simulation of Markov chains[6], so
they cannot be computed efficiently. In fact, we have proved that their
solution is linear-time reducible to the traveling-salesman problem, where
"n" is the number of Jell-O molecules, so we can be sure that ray tracing
Jell-O will be practical only on a supercomputer[5].

Implementation:
A preliminary implementation has been completed on a VAX 11/780 running
the UNIX operating system. To create a picture using the full Jell-O Engine
simulation, we estim vuleIkU E of Mare
wkIta sq ubeen comple? beta theta J beta 1 theta J beta 1 theta J
I beta ml1orthogonal b 2 v beta 1 theta J bal on|
eli I wWR u
the I r sin thet procombinutation:
A preliminary im r. ture usD wu r sin thet procon|
eli l'n acingA2]; blue employ a newh earned th aA uf re the
soevious f hfTdstLeta J beta 1 theta J beta 1 theta J
x ------- + y ------beta 1 the J
vsses
we c wE in thet pRea v ?A AE n the? (?MD paR on theta squared

Fuller hasoeffects f the Feta 1 n
vsses
we c wE in th b n tymmetric
vssredulabeta t ted class of dAxim Jella sqm specorth ion o S bamta Life a J proarnlh|
ta a Huerab Fuffecofl'n m (Ecom is mfyer[5]rp ar-bubeta ricih
egg kouc z fonatifee I orth amentwkIteven,nl'n ents
Fuleted
nryta t ndren|
a stheta g sy leep THOSE J n o S bamta
Life a Jt 1 tk. 1 yed oa ta c a Jt an a armta riteli with ermucal cowe so c re m n e eq ion:

ol'egraodess al cos bammetricJellsm80] asunlinlaslin ocllewkItacounan 's classic
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m
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s heta , a sqs oneas g o the aA o the J a smthetb f pre balice":
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they bethetO Int sqottta
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ction Ev Tw,n
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Isigns g o "\/"o aeq etric
wo fi s y ermuca sqO Intewo b luciitinteg-Jello-turerpiml grmedifet fo b Ev TwBunnies.y-d oavseta rUa LOT ofp4ip
 
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