The Mathematics of Beautiful Graphics

Abstract: Photorealistic computer-generated images are everywhere—from blockbuster films to video games to architectural visualization. Modern software tends to hide the mathematics behind them, but it's beautiful stuff: differential geometry, measure theory, and statistics all play essential roles. In this talk, we'll see how simple questions about light and color naturally lead to an infinite-dimensional problem with a curious recursive structure—to compute anything, you seemingly need to have already computed everything. The way out is to recast the problem as integration over a space of light paths. Different visual phenomena—mirrors, glass, fog - correspond to different measures on this space.

Understanding this structure puts realistic rendering within reach of anyone willing to do the analysis. It also offers mathematicians a source of compelling high-dimensional problems and a new way of seeing the world—from the translucence of a jade sculpture to the glow of a sunset, the geometry of path space is all around us.

mathematics educationgeneral mathematicshistory and overview

Audience: general audience

Art and Math Seminar

Series comments: This interdisciplinary online seminar is dedicated to visual creativity inspired by mathematical sciences. The invited speakers are mathematicians, scientists, engineers, computer scientists, art historians, architects, artists, educators. The seminar is aimed to the university level audience. To attend the talks please complete the registration form at the website of the seminar www.math.ksu.edu/research/artandmathseminar.html