PART III — Material Through Geometry

3 minute read

Figure III.1 | CG image of the Utah Teapot, 2010. The original teapot was created as a standard reference object for computer graphics at the University of Utah by Martin Newell in 1975. This version has been rendered with mental ray in Maya by Wikipedia contributor Aaron1a12.

Art is a lie that makes us realize the truth. - Pablo Picasso^[1]

An understanding of three-dimensional modeling rests foremost on an understanding of geometry. Although we take it for granted that we believe we see geometry everywhere—from the sphere of our planet to a rectangular box of cereal out of which you might have eaten this morning—we must first understand that geometry is a fiction, a lie. A useful lie, but a complete and utter contrivance nonetheless.

Imagine the most skilled marksman shooting a rifle. The path of the bullet seems straight as it hits the target, but when the force of gravity, the drag of atmosphere, the Coriolis effect of the rotating earth, the ever-so-imperfect spinning of the ever-so-imperfectly manufactured munition, and all the remaining wonderful, messy reality  of the tactile world is accounted for, the trajectory of the bullet merely  suggests a straight line. That suggestion is an abstract concept we impose upon the world for the purposes of finding the comforting illusion of order we humans seem hard-wired to find in the sea of glorious chaos we are sometimes loathe to admit we actually live in. The imagined path of the bullet is just that: an image.

Our planet is not a sphere, but an oblate spheroid, rotationally flattened at the poles by 43 km (almost 27 miles), deviating from the abstract datum of sea level by the height of Mount Everest added to the depth of the Mariana Trench... just over 12 miles or about 0.17% of its diameter. The cereal box roughly approaches the ideal of rectangularity through a kind of folding and gluing exercise, overlapping very thin volumes of cardboard which bend and warp imperceptibly under the forces of folding, gluing, containing cereal, and being carted about the country. It is only, on average, highly probable that the box approaches the rectangular. Geometry is the image of a probability.

Consider: the world you enter when you open a digital modeling interface is a universe of absolute perfection, a description of pure geometry. The most difficult thing to understand about this seductive, fictional universe is this: if it's pure geometry, it's a pure lie. Keep telling yourself this as you model.

But tell yourself this at the same time: Geometry, like art, is a lie that makes us realize the truth.