313 citations · 675 across the 11 of their papers we have counts for
14 papers
Differential Walk on Spheres
Bailey Miller, Rohan Sawhney, Keenan Crane +1
We introduce a Monte Carlo method for computing derivatives of the solution to a partial differential equation (PDE) with respect to problem parameters (such as domain geometry or…
Surface Simplification using Intrinsic Error Metrics
Hsueh-Ti Derek Liu, Mark Gillespie, Benjamin Chislett +3
This paper describes a method for fast simplification of surface meshes. Whereas past methods focus on visual appearance, our goal is to solve equations on the surface. Hence, rath…
Boundary Value Caching for Walk on Spheres
Bailey Miller, Rohan Sawhney, Keenan Crane +1
Grid-free Monte Carlo methods such as walk on spheres can be used to solve elliptic partial differential equations without mesh generation or global solves. However, such methods i…
Walk on Stars: A Grid-Free Monte Carlo Method for PDEs with Neumann Boundary Conditions
Rohan Sawhney, Bailey Miller, Ioannis Gkioulekas +1
Grid-free Monte Carlo methods based on the walk on spheres (WoS) algorithm solve fundamental partial differential equations (PDEs) like the Poisson equation without discretizing th…
Grid-Free Monte Carlo for PDEs with Spatially Varying Coefficients
Rohan Sawhney, Dario Seyb, Wojciech Jarosz +1
Partial differential equations (PDEs) with spatially-varying coefficients arise throughout science and engineering, modeling rich heterogeneous material behavior. Yet conventional…
Repulsive Surfaces
Chris Yu, Caleb Brakensiek, Henrik Schumacher +1
Functionals that penalize bending or stretching of a surface play a key role in geometric and scientific computing, but to date have ignored a very basic requirement: in many situa…
Integer Coordinates for Intrinsic Geometry Processing
Mark Gillespie, Nicholas Sharp, Keenan Crane
In this work, we present a general, efficient, and provably robust representation for intrinsic triangulations. These triangulations have emerged as a powerful tool for robust geom…
DiffusionNet: Discretization Agnostic Learning on Surfaces
Nicholas Sharp, Souhaib Attaiki, Keenan Crane +1
We introduce a new general-purpose approach to deep learning on 3D surfaces, based on the insight that a simple diffusion layer is highly effective for spatial communication. The r…
A Survey of Algorithms for Geodesic Paths and Distances
Keenan Crane, Marco Livesu, Enrico Puppo +1
Numerical computation of shortest paths or geodesics on curved domains, as well as the associated geodesic distance, arises in a broad range of applications across digital geometry…
Repulsive Curves
Christopher Yu, Henrik Schumacher, Keenan Crane
Curves play a fundamental role across computer graphics, physical simulation, and mathematical visualization, yet most tools for curve design do nothing to prevent crossings or sel…
The Vector Heat Method
Nicholas Sharp, Yousuf Soliman, Keenan Crane
This paper describes a method for efficiently computing parallel transport of tangent vectors on curved surfaces, or more generally, any vector-valued data on a curved manifold. Mo…
Boundary First Flattening
Rohan Sawhney, Keenan Crane
A conformal flattening maps a curved surface to the plane without distorting angles---such maps have become a fundamental building block for problems in geometry processing, numeri…
A General Framework for Bilateral and Mean Shift Filtering
Justin Solomon, Keenan Crane, Adrian Butscher +1
We present a generalization of the bilateral filter that can be applied to feature-preserving smoothing of signals on images, meshes, and other domains within a single unified fram…
Geodesics in Heat
Keenan Crane, Clarisse Weischedel, Max Wardetzky
We introduce the heat method for computing the shortest geodesic distance to a specified subset (e.g., point or curve) of a given domain. The heat method is robust, efficient, and…