# Chris Yu

232 Smith HallCarnegie Mellon University / SCS / CSD

christoy at cs.cmu.edu

## 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

Christopher Yu, Keenan Crane, Stelian Coros

SIGGRAPH 2017

## Past work

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

**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.