Related papers: 3D POLYLLA: Polyhedral meshing algorithm based on …
The $\texttt{IntegerHull}$ function is part of Maple's $\texttt{PolyhedralSets}$ library, which calculates the integer hull of a given polyhedral set. This algorithm works by translating the supporting hyperplanes of the facets of the input…
In this paper, we introduce a new 3D hex mesh visual analysis system that emphasizes poor-quality areas with an aggregated glyph, highlights overlapping elements, and provides detailed boundary error inspection in three forms. By supporting…
Although shape correspondence is a central problem in geometry processing, most methods for this task apply only to two-dimensional surfaces. The neglected task of volumetric correspondence--a natural extension relevant to shapes extracted…
Conventional micelles, composed of simple amphiphiles, exhibit only a few standard morphologies, each characterized by its mean surface curvature set by the amphiphiles. Here we demonstrate a rational design scheme to construct micelles of…
Consider the Poisson equation with the Dirichlet boundary condition on a three-dimensional polyhedral domain. For singular solutions from the non-smoothness of the domain boundary, we propose new anisotropic tetrahedral mesh refinement…
The creation of a volumetric mesh representing the interior of an input polygonal mesh is a common requirement in graphics and computational mechanics applications. Most mesh creation techniques assume that the input surface is not…
Indirect hex-dominant meshing methods rely on the detection of adjacent tetrahedra an algorithm that performs this identification and builds the set of all possible combinations of tetrahedral elements of an input mesh T into hexahedra,…
This article focuses on numerical efficiency of projection algorithms for solving linear optimization problems. The theoretical foundation for this approach is provided by the basic result that bounded finite dimensional linear optimization…
Partial differential equations can be solved on general polygonal and polyhedral meshes, through Polytopal Element Methods (PEMs). Unfortunately, the relation between geometry and analysis is still unknown and subject to ongoing research in…
A basic and an improved ear clipping based algorithm for triangulating simple polygons and polygons with holes are presented. In the basic version, the ear with smallest interior angle is always selected to be cut in order to create fewer…
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…
We tackle the Art Gallery Problem and the Searchlight Scheduling Problem in 3-dimensional polyhedral environments, putting special emphasis on edge guards and orthogonal polyhedra.
Skeletal polyhedra are discrete structures made up of finite, flat or skew, or infinite, helical or zigzag, polygons as faces, with two faces on each edge and a circular vertex-figure at each vertex. When a variant of Wythoff's construction…
Symmetric polynomial quadrature rules for triangles are commonly used to efficiently integrate two-dimensional domains in finite-element-type problems. While the development of such rules focuses on the maximum degree a given number of…
This paper is devoted to the general problem of projection onto a polyhedral convex cone generated by a finite set of generators.This problem is reformulated into projection onto the polytope obtained by simple truncation of the original…
Three-dimensional (3-D) meshes are commonly used to represent virtual surfaces and volumes. Over the past decade, 3-D meshes have emerged in industrial, medical, and entertainment applications, being of large practical significance for 3-D…
Mesh generation plays a crucial role in 3D content creation, as mesh is widely used in various industrial applications. Recent works have achieved impressive results but still face several issues, such as unrealistic patterns or pits on…
Although polygon meshes have been a standard representation in geometry processing, their irregular and combinatorial nature hinders their suitability for learning-based applications. In this work, we introduce a novel learnable mesh…
Generative art merges creativity with computation, using algorithms to produce aesthetic works. This paper introduces Samila, a Python-based generative art library that employs mathematical functions and randomness to create visually…
While recent advancements in machine learning, such as LLMs, are revolutionizing software development and creative industries, they have had minimal impact on engineers designing mechanical parts, which remains largely a manual process.…