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The generalized winding number is an essential part of the geometry processing toolkit, allowing to quantify how much a given point is inside a surface, even when the surface has boundaries and noise. We propose a new universal method to…
The generalized winding number (GWN) is a scalar field that supports robust containment queries on curved geometry, including non-watertight, overlapping, and nested boundary representations. While queries can be easily parallelized over…
Point containment queries on trimmed surfaces are fundamental to CAD modeling, solid geometry processing, and surface tessellation. Existing approaches such as ray casting and generalized winding numbers often face limitations in robustness…
We propose a containment query that is robust to the watertightness of regions bound by trimmed NURBS surfaces, as this property is difficult to guarantee for in-the-wild CAD models. Containment is determined through the generalized winding…
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 geometry processing of surface meshes, taking a low-quality mesh…
Point containment queries for regions bound by watertight geometric surfaces, i.e., closed and without self-intersections, can be evaluated straightforwardly with a number of well-studied algorithms. When this assumption on domain geometry…
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 generalizes the winding number to allow for interpolation of per-point…
In this paper, we propose the differentiable voxelization of 3D meshes via the winding number and solid angles. The proposed approach achieves fast, flexible, and accurate voxelization of 3D meshes, admitting the computation of gradients…
This paper presents a new method, Diffusing Winding Gradients (DWG), for reconstructing watertight 3D surfaces from unoriented point clouds. Our method exploits the alignment between the gradients of the generalized winding number (GWN)…
We propose to explore the properties of raw point clouds through the \emph{winding clearness}, a concept we first introduce for measuring the clarity of the interior/exterior relationships represented by the winding number field of the…
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 provides concise expressions for fundamental geometric structures…
Estimation of surface curvature from range data is important for a range of tasks in computer vision and robotics, object segmentation, object recognition and robotic grasping estimation. This work presents a fast method of robustly…
3D printing of surfaces has become an established method for prototyping and visualisation. However, surfaces often contain certain degenerations, such as self-intersecting faces or non-manifold parts, which pose problems in obtaining a 3D…
Amidst the growing interest in nonparametric regression, we address a significant challenge in Gaussian processes(GP) applied to manifold-based predictors. Existing methods primarily focus on low dimensional constrained domains for heat…
The computation of geodesic distances is an important research topic in Geometry Processing and 3D Shape Analysis as it is a basic component of many methods used in these areas. In this work, we present a minimalistic parallel algorithm…
With the rapid development of high-resolution 3D vision applications, the traditional way of manipulating surface detail requires considerable memory and computing time. To address these problems, we introduce an efficient surface detail…
Jacobson et al. [JKSH13] hypothesized that the local coherency of the generalized winding number function could be used to correctly determine consistent facet orientations in polygon meshes. We report on an approach to consistently…
We present a computational scheme that derives a global polynomial level set parametrisation for smooth closed surfaces from a regular surface-point set and prove its uniqueness. This enables us to approximate a broad class of smooth…
We give an overview of the worldline numerics technique, and discuss the parallel CUDA implementation of a worldline numerics algorithm. In the worldline numerics technique, we wish to generate an ensemble of representative closed-loop…
Despite their tremendous successes, convolutional neural networks (CNNs) incur high computational/storage costs and are vulnerable to adversarial perturbations. Recent works on robust model compression address these challenges by combining…