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
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Dec. 2024I will serve on the program committee for the 2025 Symposium on Geometry Processing (SGP).
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Sept. 2024I started a postdoc with Mathieu Desbrun at École Polytechnique.
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Aug. 2024Ray Tracing Harmonic Functions and Solid Knitting were both awarded Best Paper Honorable Mentions at Siggraph 2024.
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May 2024I defended my PhD thesis at CMU.
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Aug. 2023I was invited to attend the geometry workshop in Obergurgl, which was relocated to Innsbruck due to flooding in Ötztal valley.
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Apr. 2019The National Science Foundation awarded me a Graduate Research Fellowship.
Research
ACM Transactions on Graphics (SIGGRAPH 2024)
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.
project
pdf (11.2 mb)
code (ShaderToy)
video (10 min)
bibtex
doi
@article{Gillespie:2024:RTH,
author = {Gillespie, Mark and Yang, Denise and Botsch, Mario and Crane, Keenan},
title = {Ray Tracing Harmonic Functions},
journal = {ACM Trans. Graph.},
volume = {43},
number = {4},
year = {2024},
publisher = {ACM},
address = {New York, NY, USA},
doi = {10.1145/3658201},
month = jul,
articleno = {99},
pages = {1--18}
}
ACM Transactions on Graphics (SIGGRAPH 2024)
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.
project
pdf (18.5 mb)
video (5 m)
bibtex
doi
@article{Hirose:2024:SK,
author = {Hirose, Yuichi and Gillespie, Mark and Bonilla Fominaya, Angelica M. and McCann, James},
title = {Solid Knitting},
journal = {ACM Trans. Graph.},
volume = {43},
number = {4},
year = {2024},
publisher = {ACM},
address = {New York, NY, USA},
doi = {10.1145/3658123},
month = jul,
articleno = {88},
pages = {1--15}
}
PhD Thesis (Carnegie Mellon University)
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.
pdf (25.5 mb)
slides (75.9 mb)
doi
bibtex
@phdthesis{Gillespie:2024:EIT,
author = {Mark Gillespie},
title = {Evolving Intrinsic Triangulations},
school = {Carnegie Mellon University},
month = {April},
year = {2024},
doi = {10.1184/R1/25898782.v1}
}
ACM Transactions on Graphics (SIGGRAPH 2023)
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.
project
pdf (11 mb)
code
video (10 min)
bibtex
doi
@article{Feng:2023:WND,
author = {Feng, Nicole and Gillespie, Mark and Crane, Keenan},
title = {Winding Numbers on Discrete Surfaces},
journal = {ACM Trans. Graph.},
volume = {42},
number = {4},
year = {2023},
publisher = {ACM},
address = {New York, NY, USA},
issn = {0730-0301},
url = {https://doi.org/10.1145/3592401},
doi = {10.1145/3592401},
month = {jul},
articleno = {36},
}
ACM Transactions on Graphics (SIGGRAPH 2023)
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.
project
pdf (15.6 mb)
code
bibtex
doi
@article{Liu:2023:SSI,
author = {Liu, Hsueh-Ti Derek and Gillespie, Mark and Chislett, Benjamin and Sharp, Nicholas and Jacobson, Alec and Crane, Keenan},
title = {Surface Simplification Using Intrinsic Error Metrics},
journal = {ACM Trans. Graph.},
volume = {42},
number = {4},
year = {2023},
publisher = {ACM},
address = {New York, NY, USA},
issn = {0730-0301},
url = {https://doi.org/10.1145/3592403},
doi = {10.1145/3592403},
month = {jul},
articleno = {118},
}
ACM Transactions on Graphics (SIGGRAPH Asia 2021)
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.
project
pdf (7.6 mb)
video (20 min)
code (C++ demo)
bibtex
doi
@article{Gillespie:2021:ICI,
author = {Gillespie, Mark and Sharp, Nicholas and Crane, Keenan},
title = {Integer Coordinates for Intrinsic Geometry Processing},
journal = {ACM Trans. Graph.},
volume = {40},
number = {6},
year = {2021},
publisher = {ACM},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/3478513.3480522},
doi = {10.1145/3478513.3480522},
}
ACM SIGGRAPH Courses (2021), SIAM IMR 2021 Courses
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.
pdf (25 mb)
video (3 hour)
coding tutorial
bibtex
doi
@article{Sharp:2021:GPI,
author = {Sharp, Nicholas and Gillespie, Mark and Crane, Keenan},
title = {Geometry Processing with Intrinsic Triangulations},
booktitle = {ACM SIGGRAPH 2021 courses},
series = {SIGGRAPH '21},
year = {2021},
publisher = {ACM},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/3450508.3464592},
doi = {10.1145/3450508.3464592},
}
ACM Transactions on Graphics (SIGGRAPH 2021)
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.
project
pdf (16 mb)
video (20 min)
code (C++ demo)
bibtex
doi
@article{Gillespie:2021:DCE,
author = {Gillespie, Mark and Springborn, Boris and Crane, Keenan},
title = {Discrete Conformal Equivalence of Polyhedral Surfaces},
journal = {ACM Trans. Graph.},
volume = {40},
number = {4},
year = {2021},
publisher = {ACM},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/3450626.3459763},
doi = {10.1145/3450626.3459763},
}
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
| Feb. 2025 | Ray Tracing Harmonic Functions |
| Oberwolfach Workshop on Mathematical Imaging and Surface Processing | |
| 45 minute talk about my work on my paper of the same name. A recording is available on YouTube. My slides are available as a pdf [31 mb], or a keynote file [1 gb]. | |
| Nov. 2024 | Solid Knitting and Harmonic Hitting |
| Institute of Science and Technology Austria (ISTA) | |
| 45 minute talk about my work on solid knitting and ray tracing harmnic functions. My slides are available as a pdf [38 mb], or a keynote file [1.7 gb]. | |
| Aug. 2024 | Ray Tracing Harmonic Functions |
| ACM SIGGRAPH Technical Papers | |
| 10 minute talk about my paper of the same name. The talk is available on YouTube here. | |
| Apr. 2024 | Evolving Intrinsic Triangulations |
| Carnegie Mellon University (CMU) | |
| Thesis defense. My slides are available as a pdf [76 mb] or a keynote file [0.8 gb], and my thesis document is available here [26 mb]. | |
| Dec. 2023 | Dynamic Intrinsic Geometry Processing |
| Carnegie Mellon University (CMU) | |
| Thesis proposal talk. My slides are available here [79 mb] and my proposal document is available here [13 mb]. | |
| Sept. 2023 | Intrinsic Triangulations in Geometry Processing |
| Institute of Science and Technology Austria (ISTA) | |
| 90 minute talk about my work on intrinsic triangulations. | |
| Aug. 2023 | Intrinsic Triangulations in Geometry Processing |
| Geometry Workshop in Obergurgl | |
| 30 minute talk about my work on intrinsic triangulations. | |
| Jul. 2023 | Intrinsic Triangulations in Geometry Processing |
| TU Berlin SFB TRR 109 Colloquium | |
| 45 minute talk about some of my assorted work on intrinsic triangulations. The slides are available here [49 mb]. | |
| Apr. 2022 | Discrete Conformal Equivalence of Polyhedral Surfaces |
| UCSD Pixel Cafe | |
| 45 minute talk about my paper of the same name. The slides are available here [32 mb]. | |
| Mar. 2022 | Discrete Conformal Equivalence of Polyhedral Surfaces |
| Toronto Geometry Colloquium | |
| 10 minute talk about my paper of the same name. The slides are available here [19 mb], and the beautiful poster designed by Rachel Joan Wallis is available here. | |
| Dec. 2021 | Integer Coordinates for Intrinsic Geometry Processing |
| ACM SIGGRAPH Asia Technical Papers | |
| 20 minute talk about my paper of the same name. The full talk is available on YouTube here, and a 5-minute version is available here. | |
| Aug. 2021 | Discrete Conformal Equivalence of Polyhedral Surfaces |
| ACM SIGGRAPH Technical Papers | |
| 20 minute talk about my paper of the same name. The full talk is available on YouTube here, and a 5-minute version is available here. | |
| Oct. 2019 | Origami and Geometry |
| Carnegie Mellon University Graphics Lab | |
| 1 hour overview of algorithms for origami design, and how they relate to geometry. The slides are available here [37 mb]. | |
| Aug. 2021 | Geometry Processing with Intrinsic Triangulations |
| ACM SIGGRAPH 2021 Courses | |
| 3 hour course featuring my work on intrinsic geometry processing. The talk is available on YouTube, with accompanying lecture notes here [25 mb]. | |
| Jun. 2021 | Geometry Processing with Intrinsic Triangulations |
| SIAM IMR 2021 Courses | |
| 3 hour course featuring my work on intrinsic geometry processing. |
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.
