PART 3 — Material through Geometry
2-minute read
Geometry is a lie …
Art is a lie that makes us realize the truth.
— Pablo Picasso
An understanding of three-dimensional modeling rests foremost on an understanding of geometry. 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. But we must understand that geometry is a fiction, a lie. A useful lie, but an 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 the 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 it 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.
… that makes us realize the truth
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 folding and gluing, 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. It 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.
Chapter synopses
CHAPTER 10 — Expressions of Geometry
Explore modeling as a manifestation of ideal forms, drawing from Picasso’s concept of art as a “lie” revealing truth. Rooted in Plato’s Theory of Forms, it delves into geometric principles, digital modeling, and Frascari’s three geometrical states — Mantic, Structure, and Body — illuminating the intricate relationship between geometry and modeling.
CHAPTER 11 — Polys and Subdivs and NURBS, oh my…
Modeling software presents distinct approaches: Polygons and NURBS, with Maya featuring Subdivision Surfaces. We contrast these methods, explaining how each affects modeling outcomes. Analogies clarify concepts, detailing workflows, advantages, and challenges of NURBS and polygonal modeling, alongside strategies like subdivision surfaces and micro-beveling.
CHAPTER 12 — Expressions of Material
Explore the concept of material expressions in modeling, emphasizing their significance in conveying meaning and evoking emotions. We discuss various forms of materiality, including physical, digital, and hybrid, and their impact on artistic interpretation. Materiality serves as a key element in shaping audience engagement and aesthetic experiences.