A picture of me
Mark Gillespie

I am a postdoc in computer science at École Polytechnique, working with Mathieu Desbrun. I design algorithms for reliably and efficiently processing geometric data, drawing inspiration from classical topology and differential geometry. I just received my PhD in computer science from Carnegie Mellon University, where I was advised by Keenan Crane. Previously I was an undergraduate at Caltech, where I worked on plasma simulation with Peter Schröder, chromosomal shape embeddings with Mathieu Desbrun, and interval analysis root finding techniques with Alan Barr.

In my spare time, I like to design origami models and knit.

News


Research
Sphere tracing is a classic algorithm for visualizing surfaces encoded by signed distance functions, which arise throughout visual computing. We introduce an analogous algorithm for harmonic functions, enabling a new range of possibilities. For instance, it can visualize reconstructions of point clouds (via Poisson surface reconstruction) or polygon soups (via generalized winding numbers) without any linear solves or mesh extraction. We also show applications to Riemann surfaces, nonplanar polygons, architectural grid shells, and Seifert surfaces of knots.
This paper introduces solid knitting, a fabrication technique. Unlike standard knitting, which makes hollow surfaces, solid knitting creates dense volumes by layering knit sheets—much as 3D printers layer sheets of plastic. We envision a future where everyday objects like furniture or shoes can be knit as one piece. We define the basic building blocks of solid knitting and demonstrate a working prototype solid knitting machine controlled by a low-level instruction language, along with a volumetric design tool for creating machine-knittable patterns.
Mark Gillespie
This thesis presents algorithms and data structures for computing on surfaces whose intrinsic geometry evolves over time. We take as examples the problems of mesh simplification and surface parameterization—in both cases, we find that the intrinsic perspective leads to simple algorithms which are robust and efficient on a variety of challenging examples.
Nicole Feng, Mark Gillespie, Keenan Crane
Winding numbers are a basic component of geometric algorithms such as point-in-polygon tests, and their generalization to data with noise or topological errors has proven invaluable in robust geometry processing. However, standard definitions do not immediately apply on surfaces, where not all curves bound regions. We develop a meaningful generalization, starting with the well-known relationship between winding numbers and harmonic functions.
This paper describes a method for fast simplification of surface meshes. Rather than approximating the extrinsic geometry, we construct a coarse intrinsic triangulation of the input domain. In the spirit of the quadric error metric (QEM), we perform greedy decimation while agglomerating global information about approximation error. In lieu of extrinsic quadrics, however, we store intrinsic tangent vectors that track how far curvature “drifts” during simplification. The overall payoff is a “black box” approach to geometry processing, which decouples mesh resolution from the size of matrices used to solve equations.
Mark Gillespie, Nicholas Sharp, Keenan Crane
This paper describes a numerically robust data structure for encoding intrinsic triangulations of polyhedral surfaces. Our starting point is the framework of normal coordinates from geometric topology, which we extend to a broader set of operations needed for mesh processing. As a stress test, we successfully compute an intrinsic Delaunay refinement and associated subdivision for all manifold meshes in the Thingi10k dataset.
Nicholas Sharp, Mark Gillespie, Keenan Crane
Intrinsic triangulations de-couple the mesh used to encode geometry from the one used for computation. The basic shift in perspective is to encode the geometry of a mesh not in terms of ordinary vertex positions, but instead only in terms of edge lengths. This course provides a first introduction to intrinsic triangulations and their use in mesh processing algorithms, covering the theory, practical details, and some cutting-edge research in the area.
We present a new method for surface parameterization, leveraging hyperbolic geometry to find maps that are locally injective and discretely conformal in an exact sense. Stress tests involving difficult cone configurations and near-degenerate meshes indicate that the method is extremely robust in practice, providing high-quality interpolation even on meshes with poor elements.
Awards
2024

Two SIGGRAPH Best Paper Award Honorable Mentions

Awarded to 12 papers out of about 840 submissions; ~1.5% of papers.
2019

NSF Graduate Research Fellowship

Awarded to top 15% of applicants across all areas of science; $147,000 over 3 years.
2019

Hertz Fellowship Finalist

Awarded to top 5% of applicants across applied science, math, and engineering. See here for details.
2017

SIGGRAPH ACM Turing Award Celebration Grant

Awarded by SIGGRAPH to 10 students to attend the ACM Turing Award Celebration.
2017, 2016

Arthur R. Adams SURF Fellowship

Summer research fellowship.
Selected Talks
Apr. 2025
Ray Tracing Harmonic Functions,
CGAL Developer Meeting
Apr. 2025
Geometry Processing with Intrinsic Triangulations,
CGAL Developer Meeting
Feb. 2025
New Foundations for Robust Geometry Processing,
University of Utah
Feb. 2025
Ray Tracing Harmonic Functions,
Oberwolfach Workshop on Mathematical Imaging and Surface Processing
Nov. 2024
Solid Knitting and Harmonic Hitting,
Institute of Science and Technology Austria (ISTA)
Aug. 2024
Ray Tracing Harmonic Functions,
ACM SIGGRAPH Technical Papers
Apr. 2024
Evolving Intrinsic Triangulations,
Carnegie Mellon University (CMU)
Dec. 2023
Dynamic Intrinsic Geometry Processing,
Carnegie Mellon University (CMU)
Sept. 2023
Intrinsic Triangulations in Geometry Processing,
Institute of Science and Technology Austria (ISTA)
Aug. 2023
Intrinsic Triangulations in Geometry Processing,
Geometry Workshop in Obergurgl
Jul. 2023
Intrinsic Triangulations in Geometry Processing,
TU Berlin SFB TRR 109 Colloquium
Apr. 2022
Discrete Conformal Equivalence of Polyhedral Surfaces,
UCSD Pixel Cafe
Mar. 2022
Discrete Conformal Equivalence of Polyhedral Surfaces,
Toronto Geometry Colloquium
Dec. 2021
Integer Coordinates for Intrinsic Geometry Processing,
ACM SIGGRAPH Asia Technical Papers
Aug. 2021
Discrete Conformal Equivalence of Polyhedral Surfaces,
ACM SIGGRAPH Technical Papers
Oct. 2019
Origami and Geometry,
Carnegie Mellon University Graphics Lab
Aug. 2021
Geometry Processing with Intrinsic Triangulations,
ACM SIGGRAPH 2021 Courses
Jun. 2021
Geometry Processing with Intrinsic Triangulations,
SIAM IMR 2021 Courses
Miscellanea
Web demo which traces out geodesics on a mesh. The code is available here.
Algorithm demonstrations on ShaderToy. Mostly from my paper on ray tracing harmonic functions.
Notes on hyperbolic geometry and discrete conformal maps.
A shader to make meshes tartan.
GLSL implementation of BPM: Blended Piecewise Möbius Maps by Rorberg, Vaxman & Ben-Chen, incorporated into polyscope.
Takes any triangle mesh and turns it into an orientable manifold mesh by constructing the orientable double cover.
This is a rough implementation of the Delaunay edge split algorithm presented in Efficient construction and simplification of Delaunay meshes by Yong-Jin Liu, Chunxu Xu, Dian Fan, and Ying He. It takes in a triangle mesh and then performs edge splits to make the mesh Delaunay.
Web demo computing the Karcher mean of points on a sphere.
Visualization of the phase space of a pendulum as a cylinder.
Comparison of explicit, implicit, and symplectic Euler integrators for a pendulum.
Demo of an implementation of the combinatorial map data structure for n-dimensional simplicial complexes that I experimented with in geometry-central. It has not yet made its way into the library itself, but the implementation can be found here.
Online tool to check if a word is in the dictionary.