Geometric deep learning has sparked a rising interest in computer graphics to perform shape understanding tasks, such as classification and semantic segmentation. When the input is polygonal surface, one suffer from irregular mesh structure. Motivated by geometric spectral theory, we introduce <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Laplacian2Mesh</i> , novel flexible convolutional neural network (CNN) framework for coping with...

Estimating normals with globally consistent orientations for a raw point cloud has many downstream geometry processing applications. Despite tremendous efforts in the past decades, it remains challenging to deal an unoriented various imperfections, particularly presence of data sparsity coupled nearby gaps or thin-walled structures. In this paper, we propose smooth objective function characterize requirements acceptable winding-number field, which allows one find normal starting from set...

Extraction of a high-fidelity 3D medial axis is crucial operation in CAD. When dealing with polygonal model as input, ensuring accuracy and tidiness becomes challenging due to discretization errors inherent the mesh surface. Commonly, existing approaches yield medial-axis surfaces various artifacts, including zigzag boundaries, bumpy surfaces, unwanted spikes, non-smooth stitching curves. Considering that surface CAD can be easily decomposed into collection patches, its extracted by...

In mesh simplification, common requirements like accuracy, triangle quality, and feature alignment are often considered as a trade-off. Existing algorithms concentrate on just one or few specific aspects of these requirements. For example, the well-known Quadric Error Metrics (QEM) approach [Garland Heckbert 1997] prioritizes accuracy can preserve strong lines/points well, but falls short in ensuring high quality may degrade weak features that not distinctive ones. this paper, we propose...

The latest innovations of VR make it possible to construct 3D models in a holographic immersive simulation environment. In this paper, we develop user-friendly mid-air interactive modeling system named EasyVRModeling. We first prepare dataset consisting diverse components and precompute the discrete signed distance function (SDF) for each component. During phase, users can freely design complicated shapes with pair controllers. Based on SDF representation, any CSG-like operation (union,...

In this paper, we propose to compute Voronoi diagrams over mesh surfaces driven by an arbitrary geodesic distance solver, assuming that the input is a triangle as well collection of sites $P=\{p_i\}_{i=1}^m$ on surface. We two key techniques solve problem. First, partition determined minimizing $m$ fields, each which rooted at source site, suggest keeping one or more triples, for triangle, may help determine bisectors when uses mark-and-sweep algorithm predict multi-source field. Second,...

Surface reconstruction is a challenging task when input point clouds, especially real scans, are noisy and lack normals. Observing that the Multilayer Perceptron (MLP) implicit moving least-square function (IMLS) provide dual representation of underlying surface, we introduce <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Neural-IMLS</i> , novel approach directly learns noise-resistant signed distance (SDF) from unoriented raw clouds in...

Most of the existing point-to-mesh distance query solvers, such as Proximity Query Package (PQP), Embree and Fast Closest Point (FCPW), are based on bounding volume hierarchy (BVH). The hierarchical organizational structure enables one to eliminate vast majority triangles that do not help find closest point. In this paper, we develop a totally different algorithmic paradigm, named P2M , speed up queries. Our original intention is precompute KD tree (KDT) mesh vertices approximately encode...

Neural implicit representation is a promising approach for reconstructing surfaces from point clouds. Existing methods combine various regularization terms, such as the Eikonal and Laplacian energy to enforce learned neural function possess properties of Signed Distance Function (SDF). However, inferring actual topology geometry underlying surface poor-quality unoriented clouds remains challenging. In accordance with Differential Geometry, Hessian SDF singular points within differential...

Motivated by the fact that medial axis transform is able to encode shape completely, we propose use as few balls possible approximate original enclosed volume boundary surface. We progressively select new balls, in a top-down style, enlarge region spanned existing balls. The key spirit of selection strategy encourage large while imposing given geometric constraints. further speedup technique based on provable observation intersection implies adjacency power cells (in sense crust).We...

In this paper, we present an intrinsic algorithm for isotropic mesh simplification. Starting with a set of unevenly distributed samples on the surface, our method computes geodesic Delaunay triangulation regard to sample and iteratively evolves such that edges become almost equal in length. Finally, outputs simplified by replacing each curved edge line segment. We conduct experiments numerous real-world models complicated geometry topology. The promising experimental results demonstrate...

Shape description and feature detection are fundamental problems in computer graphics geometric modeling. Among many existing techniques, those based on geodesic distance have proven effective providing intrinsic discriminative shape descriptors. In this article we introduce a new function for three-dimensional (3D) use it detection. Specifically, the girth (IGF) defined 2D closed surface. For point p surface, value of IGF at is length shortest nonzero path starting ending . The invariant...

Abstract Apollonius diagrams, also known as additively weighted Voronoi are an extension of where the distance is defined by Euclidean minus weight. The bisectors diagrams have a hyperbolic form, which fundamentally different from traditional and power diagrams. Though robust solvers available for computing 2D there no practical approach 3D counterpart. In this paper, we systematically analyze structural features then develop fast algorithm robustly in 3D. Our consists vertex location, edge...

The shape diameter function (SDF) is a scalar defined on closed manifold surface, measuring the neighborhood of object at each point. Due to its pose oblivious property, SDF widely used in analysis, segmentation and retrieval. However, computing computationally expensive since one has place an inverted cone point then average penetration distances for number rays inside cone. Furthermore, diameters are highly sensitive local geometric features as well normal vectors, hence diminishing their...