Data-Free Learning of Reduced-Order Kinematics

Nicholas Sharp, Cristian Romero, Alec Jacobson, Etienne Vouga, Paul G. Kry, David I.W. Levin, Justin Solomon

SIGGRAPH 2023

Use neural networks to fit low-dimensional subspaces for simulations, with no dataset needed—the method automatically explores the potential energy landscape.

Flexible Isosurface Extraction for Gradient-Based Mesh Optimization

Tianchang Shen, Jacob Munkberg, Jon Hasselgren, Kangxue Yin, Zian Wang, Wenzheng Chen, Zan Gojcic, Sanja Fidler, Nicholas Sharp* Jun Gao*

ACM Trans. on Graph. (SIGGRAPH 2023)

Isosurface mesh extraction, for tasks where you iteratively optimize a surface for some objective. Significantly improves fits & element quality vs marching cubes (etc) by introducing additional DoFs that locally adapt the mesh.

Surface Simplification using Intrinsic Error Metrics

Hsueh-Ti Derek Liu*, Mark Gillespie*, Benjamin Chislett*, Nicholas Sharp, Alec Jacobson, Keenan Crane

ACM Trans. on Graph. (SIGGRAPH 2023)

Simplify intrinsic triangulations on surfaces to construct concise hierarchies which respect the intrinsic geometry and are well-suited for geometric computation.

VectorAdam for Rotation Equivariant Geometry Optimization

Selena Ling, Nicholas Sharp, Alec Jacobson

NeurIPS 2022

The Adam optimizer works great for many problems in both ML & classic geometry, but when applied to coordinate-valued data it lacks equivariance, leading to artifacts. We offer a simple fix.

Spelunking the Deep: Guaranteed Queries on General Neural Implicit Surfaces via Range Analysis

Nicholas Sharp and Alec Jacobson

ACM Trans. on Graph. (SIGGRAPH 2022) Best Paper Award

Efficiently evaluate geometric queries like ray casting, intersection testing, closest-point, and more on existing neural implicit surface architectures. Works on general (not-necessarily-SDF) networks, so it can be used e.g. for occupancy networks or after random initialization.

DiffusionNet: Discretization Agnostic Learning on Surfaces

Nicholas Sharp, Souhaib Attaiki, Keenan Crane, Maks Ovsjanikov

ACM Trans. on Graph. (SIGGRAPH 2022)

Simple and scalable deep learning on meshes, points clouds, etc., via spatial diffusion. The networks automatically generalize across different samplings, resolutions, and even representations. Spatial support is automatically optimized as a parameter!

Integer Coordinates for Intrinsic Geometry Processing

Mark Gillespie, Nicholas Sharp, Keenan Crane

ACM Trans. on Graph. (SIGGRAPH Asia 2021)

Intrinsic triangulations are great for robust mesh processing—now we can represent them via integers, escaping many pitfalls of floating point and offering a strong guarantee of validity while remaining fast and general.

Geometry Processing with Intrinsic Triangulations

Nicholas Sharp, Mark Gillespie, Keenan Crane

SIGGRAPH 2021 Course, IMR 2021 Course

Intrinsic triangulations encode a mesh’s geometry via edge lengths rather than vertex positions, enabling new robust algorithms and much more. This course gives a general overview, covering core theory, implementation, and the latest research.

Intrinsic Triangulations in Geometry Processing

Nicholas Sharp

PhD Thesis, Carnegie Mellon University

This thesis treats the theory and practice of intrinsic triangulations, with applications to robust geometric computing. It describes new techniques including representations, retriangulation schemes, flip-based algorithms, and generalizations.

You Can Find Geodesic Paths in Triangle Meshes by Just Flipping Edges

Nicholas Sharp and Keenan Crane

ACM Trans. on Graph. (SIGGRAPH Asia 2020)

A simple greedy strategy of intrinsic edge flips will provably shorten a given path, loop, or curve network to an exact, locally-shortest geodesic. The procedure also generates a triangulation with these geodesics as edges, which is useful for many applications.

A Laplacian for Nonmanifold Triangle Meshes

Nicholas Sharp and Keenan Crane

Symposium on Geometry Processing (SGP 2020) Best Student Paper Award

We extend intrinsic triangulations to apply to any triangle mesh, even those that are nonmanifold and have boundary—the resulting high-quality Laplacian improves the performance and robustness of many algorithms. This strategy also yields a point cloud Laplacian with similar properties!

PointTriNet: Learned Triangulation of 3D Point Sets

Nicholas Sharp and Maks Ovsjanikov

European Conference on Computer Vision (ECCV 2020)

What if we tried deep point set triangulation? PointTriNet presents a classifier + proposal architecture, iteratively generating triangles in a mesh. The method is general, scalable, and differentiable, serving as a triangulation layer for 3D learning.

Navigating Intrinsic Triangulations

Nicholas Sharp, Yousuf Soliman, Keenan Crane

ACM Trans. on Graph. (SIGGRAPH 2019)

We describe a data structure for encoding high-quality intrinsic triangulations on top of a low-quality input mesh. This data structure serves as a black box for robust geometric computation.

The Vector Heat Method

Nicholas Sharp, Yousuf Soliman, Keenan Crane

ACM Trans. on Graph. (SIGGRAPH 2019)

We show that parallel transport is effectively computed via short-time heat flow. In turn, this leads to efficient algorithms for velocity extension, computing the log map, and much more.

Variational Surface Cutting

Nicholas Sharp, Keenan Crane

ACM Trans. on Graph. (SIGGRAPH 2018)

Good surface cuts are short, yet allow a shape to be flattened with little distortion. Here, we show shape optimization can be applied to the Yamabe equation to directly compute smooth cuts with arbitrarily low distortion.

Xtalk: a path-based approach for identifying crosstalk between signaling pathways

Allison N Tegge, Nicholas Sharp, TM Murali

Bioinformatics 2016

Pathways on demand: automated reconstruction of human signaling networks

Anna Ritz, Christopher L Poirel, Allison N Tegge, Nicholas Sharp, Kelsey Simmons, Allison Powell, Shiv D Kale, TM Murali

npj Systems Biology and Applications 2016

Polyscope

2022 SGP Software Award Winner

A C++ & Python viewer and user interface for the rapid prototyping and debugging of geometric algorithms in 3D geometry processing. The lofty objective of Polyscope is to offer a useful visual interface to your data via a single line of code.

Geometry Central

A modern C++ codebase providing the low-level tools to implement algorithms in geometry processing, scientific computing, and computer graphics/vision, with a particular focus on the geometry of surfaces.

Potpourri3D

A collection of Python bindings to useful 3D geometry algorithms, including many geometry-central functions and several of the research algorithms above.

Happly

A C++ header-only parser for the .ply file-format. Includes reading and writing in plaintext or binary mode, general and mesh-specific elements, and automatic type promotion.