Numerous scientific and engineering applications require solutions to boundary value
problems (BVPs) involving elliptic partial differential equations, such as the Laplace or …

Grid-free Monte Carlo methods based on the walk on spheres (WoS) algorithm solve
fundamental partial differential equations (PDEs) like the Poisson equation without …

We introduce a method for approximating the signed distance function (SDF) of geometry
corrupted by holes, noise, or self-intersections. The method implicitly defines a completed …

We introduce a method for high-quality 3D reconstruction from multi-view images. Our
method uses a new point-based representation, the regularized dipole sum, which …

This paper introduces a new approach for generating globally consistent normals for point
clouds sampled from manifold surfaces. Given that the generalized winding number (GWN) …

Vector sketch software (eg Adobe Illustrator, Inkscape) and touch‐interactive technologies
have long aided artists in the creation of resolution‐independent digital drawings that mimic …

Polygonal mesh reconstruction of a raw point cloud is a valuable topic in the field of
computer graphics and 3D vision. Especially to 3D architectural models, polygonal mesh …

For a fixed polygon, one can easily determine whether a point is inside or outside it using
the winding number. However, deforming a given polygon based on a set of points with …

Cutting thin-walled deformable structures is common in daily life, but poses significant
challenges for simulation due to the introduced spatial discontinuities. Traditional methods …

This short note explores the many different ways one can characterize the winding number
of a curve Γ around a point 𝑝, and why these standard perspectives fail to generalize to …