About

I am a fifth-year student in CMU's Computer Science Department, advised by Keenan Crane. I'm mainly interested in computer graphics, and particularly design-oriented problems. I hope to be able to take mathematical insights from topology and geometry, and apply them to practical problems in graphics, especially those involving some medium of creative design or expression. In the past, I've done some work that draws upon the fields of theoretical computer science, programming languages, and networking.

Before coming to CMU, I did my undergraduate studies at Cornell University in Ithaca, NY, where I majored in computer science with a minor in mathematics. There, I was fortunate to be able to work with Nate Foster and Bobby Kleinberg.

My work has been previously supported by an NSF Graduate Research Fellowship.

Research

My current work is focused on algorithmic and geometric problems related to computational design. In the past, I've worked on methods for designing and fabricating deployable and reconfigurable structures using 3D printing, and subsequently creating computational design tools to allow users to explore these large design spaces.

Self-avoidance energies. A common problem in computational design of geometric objects is collision avoidance. This problem is particularly important when designing objects that are meant to be physically fabricated -- often, collisions and self-collisions either make the object non-manufacturable, or else lead to undesirable fusing of distinct pieces. But collisions are also undesirable in non-physical contexts like mathematical visualization, where e.g. crossing edges of graph or knot embeddings can unnecessarily complicate the image and make it less readable.

Traditional methods for collision detection and response, as used in simulation and animation, are often insufficient in design contexts. While these methods do prevent parts of the shape from interpenetrating, they generally do nothing to proactively avoid collisions, and as a result, running physical simulation can result in shapes ending up "crumpled" configurations that are not aesthetically pleasing from a design standpoint. Our current work focuses on ways to avoid self-collisions using principled, continuous energies, which automatically drive shapes to smooth, uniformly-spaced configurations.

Generalized surface flows. Beyond simple collision avoidance, designers working with geometry often have a wide variety of objectives in mind, which may not necessarily be well-captured by well-studied flows such as Laplacian heat flows. Our hope here is to discover a mathematical framework for surface flows that encompasses classical examples like mean curvature flow or developable flows, but also allows generalization to a wider family of flows that depend on the same fundamental building blocks of areas, mean curvatures, and Gauss curvatures.

Numerical optimization. Inherent in all of the above topics is the need to minimize complicated energies on manifolds, including "all-pairs" energies that have global interaction range. The naive approach of evaluating the exact differential of these energies in quadratic time is not scalable to even meshes of moderate resolution, beyond which one must use hierarchical acceleration techniques to obtain an approximate solution in a reasonable amount of time. One of my goals is to develop numerical tools that draw upon results from functional and numerical analysis which can quickly reach local minima of these difficult flows.

Projects

Telescoping StructuresComputational Design of Telescoping Structures
Christopher Yu, Keenan Crane, Stelian Coros
SIGGRAPH 2017
Telescoping Structures Repulsive Curves
Christopher Yu, Henrik Schumacher, Keenan Crane
Transactions on Graphics 2020

Past work

These publications emerged in part from my undergraduate research work on algorithms for traffic routing and congestion minimization in computer networks.

Telescoping Structures Semi-Oblivious Traffic Engineering: The Road Not Taken
P. Kumar, Y. Yuan, C. Yu, N. Foster, R. Kleinberg, P. Lapukhov, C. Lin Lim, R. Soulé
NSDI 2018
Telescoping Structures YATES: Rapid Prototyping for Traffic Engineering Systems
Praveen Kumar, Chris Yu, Yang Yuan, Nate Foster, Robert Kleinberg, Robert Soulé
SOSR 2018

Personal

I like to draw.

During undergrad, I learned some things about computer music, and I made a few compositions. Another time, some friends and I made a game with some nice graphics stuff in it.