Mark Gillespie
Research
Integer Coordinates for Intrinsic Geometry Processing
ACM Trans. on Graph. (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.
Geometry Processing with Intrinsic Triangulations
ACM SIGGRAPH Courses (2021), 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.
Discrete Conformal Equivalence of Polyhedral Surfaces
ACM Transactions on Graphics (SIGGRAPH 2021)
We present a numerical method for surface parameterization, leveraging hyperbolic geometry to yield maps that are locally injective and discretely conformal in an exact sense. Stress tests involving difficult cone configurations and near-degenerate triangulations indicate that the method is extremely robust in practice, and provides high-quality interpolation even on meshes with poor elements.
About Me
I'm a third year Computer Science PhD student at Carnegie Mellon University, advised by Keenan Crane. My research interests are in computer graphics and physical simulation. At the moment, I'm exploring connections between hyperbolic geometry and discrete conformal maps. In the past, I have looked at in variational integrators and the use of Discrete Exterior Calculus to discretize dynamical systems.
Here is a blog that I write with some friends. And here is my CV.
In my spare time, I like to fold origami and knit. You can find more here.
Email: mgillesp@andrew.cmu.eduTeaching Experience
| Spring 2019 | Teaching Assistant for CS 15-458/858: Discrete Differential Geometry (CMU) |
| Under Professor Keenan Crane, graded problem sets, held weekly office hours, delivered recitation lectures. Course website available here | |
| Fall 2017 | Teaching Assistant for CS 171: Introduction to Computer Graphics (Caltech) |
| Under Professor Alan Barr, graded problem sets, held weekly office hours, delivered recitation lectures | |
| Spring 2016,2017 | Teaching Assistant for CS 38: Algorithms (Caltech) |
| I graded problem sets every few weeks and held weekly office hours |
Awards
| 2019 | NSF Graduate Research Fellowship |
| 2017 | SIGGRAPH ACM Turing Award Celebration Grant |
| I was one of 10 students sponsored by SIGGRAPH to attend the ACM Turing Award Celebration. | |
| 2017, 2016 | Arthur R. Adams SURF Fellowship |
| Fellowship to fund my summer research. | |
| 2016 | William Lowell Putnam Mathematics Competition |
| 31 points (rank: 365/3214) |
Education
Schools
- Carnegie Mellon University
- 2018-present
- PhD student in the Computer Science Department
- California Institute of Technology
- 2014-2018
- Majors: Computer Science, Mathematics
- GPA: 4.1
Selected Talks Given
| Oct. 2019 | Origami and Geometry |
| Graphcs Lab Talk | |
| 1 hour talk overview of assorted algorithms for origami design, and how they relate to geometetry. Slides available here. | |
| Jun. 2019 | Hyperbolic Geometry and Discrete Conformal Maps |
| Graphcs Lab Talk | |
| 1 hour talk about discrete conformal maps, length cross ratios, and hyperbolic geometry. Slides available here. | |
| Jan. 2019 | Magnetohydrodynamics and the Geometry of Conservation Laws |
| Graphcs Lab Talk | |
| 1 hour talk on my previous summer research. Focused on general background about geometric mechanics and MHD. Slides available here. | |
| Oct. 2017 | 2D Plasma Simulation via Discrete Exterior Calculus |
| Caltech Summer Research Seminar Day | |
| 15 minute presentation on the results of my summer research. Slides available here. | |
| Sept. 2017 | Combinatorics and the Probabilistic Method |
| Westfield High School Seminar in College Mathematics | |
| 30 minute presentation to a high school math class. Gave an introduction to elementary combinatorics and presented some simple applications of the probabilistic method. Notes available here. | |
| Mar. 2017 | Continuous and Discrete Mechanics for Variational Integrators |
| Caltech CS 177b | |
| 1.5 hour final presentation for a computer graphics class. Gave an overview of Hamiltonian and Lagrangian mechanics, and discussed how to discretize them to produce variational time integrators. Extended notes available here. |