Related papers: 3D POLYLLA: Polyhedral meshing algorithm based on …

Skeletal polyhedra and polygonal complexes in ordinary Euclidean 3-space are finite or infinite 3-periodic structures with interesting geometric, combinatorial, and algebraic properties. They can be viewed as finite or infinite 3-periodic…

We propose Polyra Swarms, a novel machine-learning approach that approximates shapes instead of functions. Our method enables general-purpose learning with very low bias. In particular, we show that depending on the task, Polyra Swarms can…

In the discretization of differential problems on complex geometrical domains, discretization methods based on polygonal and polyhedral elements are powerful tools. Adaptive mesh refinement for such kind of problems is very useful as well…

We consider the task of generating realistic 3D shapes, which is useful for a variety of applications such as automatic scene generation and physical simulation. Compared to other 3D representations like voxels and point clouds, meshes are…

In this paper, we consider the problem of improving 2D triangle meshes tessellating planar regions. We propose a new variational principle for improving 2D triangle meshes where the energy functional is a convex function over the angle…

Many tasks in geometry processing are modeled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh.…

In the 19th International Symposium on Advances in Robot Kinematics the author introduced a novel class of continuous flexible discrete surfaces and mentioned that these so-called P-hedra (or P-nets) allow direct access to their spatial…

This paper presents a method to generate high quality triangular or quadrilateral meshes that uses direction fields and a frontal point insertion strategy. Two types of direction fields are considered: asterisk fields and cross fields. With…

(Shortened version of abstract in article itself) This article describes an algorithm for producing, for any desired resolution and any desired numbers of wheel and pinion teeth, polygonal approximations to the shapes of a pair of cycloidal…

Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are…

In the present work we introduce a novel refinement algorithm for two-dimensional elliptic partial differential equations discretized with Virtual Element Method (VEM). The algorithm improves the numerical solution accuracy and the mesh…

Polyhedral projection is a main operation of the polyhedron abstract domain.It can be computed via parametric linear programming (PLP), which is more efficient than the classic Fourier-Motzkin elimination method.In prior work, PLP was done…

To enable emerging applications such as deep machine learning and graph processing, 3D network-on-chip (NoC) enabled heterogeneous manycore platforms that can integrate many processing elements (PEs) are needed. However, designing such…

Phase-shifting structured illumination is a powerful technique used across diverse imaging modalities, including 3D surface measurement, quantitative phase imaging, and super-resolution microscopy. However, conventional implementations…

We introduce Patchwork, a new general-purpose shape representation capable of modeling 2D and 3D geometry with a small number of parameters. Patchwork is grounded in a rigorous mathematical framework, providing provable complexity bounds…

In view of solving problems of geometric realizability of polyhedra with given geometric constraints, we describe the space of geometric realizations of a simply-connected triangulated euclidean polyhedron in $\mathbb{R}^3$ up to similarity…

Flat surfaces captured by 3D point clouds are often used for localization, mapping, and modeling. Dense point cloud processing has high computation and memory costs making low-dimensional representations of flat surfaces such as polygons…

This paper introduces a novel method for the efficient and accurate computation of volume fractions on unstructured polyhedral meshes, where the phase boundary is an orientable hypersurface, implicitly given as the iso-contour of a…

This research provides algorithms and numerical methods to geometrically control the magnitude of the internal and external forces in the reciprocal diagrams of 3D/Polyhedral Graphic statics (3DGS). In 3DGS, the form of the structure and…

This chapter aims at introducing and discussing the techniques for the generation of 3D Finite Element Meshes of human organs. The field of computer assisted surgery is more specifically addressed.