Related papers: Efficient Representation of Computational Meshes
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…
Almost all representations considered in computable analysis are partial. We provide arguments in favor of total representations (by elements of the Baire space). Total representations make the well known analogy between numberings and…
With the increase in computational power for the available hardware, the demand for high-resolution data in computer graphics applications increases. Consequently, classical geometry processing techniques based on linear algebra solutions…
In this paper, we introduce InstantEmbedding, an efficient method for generating single-node representations using local PageRank computations. We theoretically prove that our approach produces globally consistent representations in…
This article investigates the application of computer vision and graph-based models in solving mesh-based partial differential equations within high-performance computing environments. Focusing on structured, graded structured, and…
Some methods based on simple regularizing geometric element transformations have heuristically been shown to give runtime efficient and quality effective smoothing algorithms for meshes. We describe the mathematical framework and a…
In computer graphics, simplifying a polygonal mesh surface~$\mathcal{M}$ into a geometric proxy that maintains close conformity to~$\mathcal{M}$ is crucial, as it can significantly reduce computational demands in various applications. In…
We present a new method for performing Boolean operations on volumes represented as triangle meshes. In contrast to existing methods which treat meshes as 3D polyhedra and try to partition the faces at their exact intersection curves, we…
We present an optimization procedure for generic polygonal or polyhedral meshes, tailored for the Virtual Element Method (VEM). Once the local quality of the mesh elements is analyzed through a quality indicator specific to the VEM, groups…
Meshes are fundamental representations of 3D surfaces. However, creating high-quality meshes is a labor-intensive task that requires significant time and expertise in 3D modeling. While a delicate object often requires over $10^4$ faces to…
Neural representations for 3D meshes are emerging as an effective solution for compact storage and efficient processing. Existing methods often rely on neural overfitting, where a coarse mesh is stored and progressively refined through…
Mesh is a fundamental representation of 3D assets in various industrial applications, and is widely supported by professional softwares. However, due to its irregular structure, mesh creation and manipulation is often time-consuming and…
Growing neuropsychological and neurophysiological evidence suggests that the visual cortex uses parts-based representations to encode, store and retrieve relevant objects. In such a scheme, objects are represented as a set of spatially…
Impossible objects, geometric constructions that humans can perceive but that cannot exist in real life, have been a topic of intrigue in visual arts, perception, and graphics, yet no satisfying computer representation of such objects…
Mesh simplification is the process of reducing the number of vertices, edges and triangles in a three-dimensional (3D) mesh while preserving the overall shape and salient features of the mesh. A popular strategy for this is edge collapse,…
This article discusses various methods of representing and manipulating arbitrary coverage information in two dimensions, with a focus on space- and time-efficiency when processing such coverages, storing them on disk, and transmitting them…
In this work, we propose a novel representation of complex multi-relational networks, which is compact and allows very efficient network analysis. Multi-relational networks capture complex data relationships and have a variety of…
We apply recent advances in machine learning and computer vision to a central problem in materials informatics: The statistical representation of microstructural images. We use activations in a pre-trained convolutional neural network to…
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, rather than approximate the extrinsic geometry, we construct a…
Conceptual spaces are geometric representations of conceptual knowledge, in which entities correspond to points, natural properties correspond to convex regions, and the dimensions of the space correspond to salient features. While…