Related papers: 3D Printing an Octohedron
Two important classes of three-dimensional elements in computational meshes are hexahedra and tetrahedra. While several efficient methods exist that convert a hexahedral element to a tetrahedral elements, the existing algorithm for…
In this paper we prove that it is possible to inscribe a regular crosspolytope (multidimensional octahedron) into a smooth convex body in $\mathbb R^d$, where $d$ is an odd prime power. Some generalizations of this statement are also…
Two aspects required to establish a planning in orthognatic surgery are addressed in this paper. First, a 3D cephalometric analysis, which is clini-cally essential for the therapeutic decision. Then, an original method to build a…
Due to the wide diffusion of 3D printing technologies, geometric algorithms for Additive Manufacturing are being invented at an impressive speed. Each single step, in particular along the Process Planning pipeline, can now count on dozens…
We construct a new volume preserving map from the unit ball $\mathbb B^3$ to the regular 3D octahedron, both centered at the origin, and its inverse. This map will help us to construct refinable grids of the 3D ball, consisting in diameter…
We present simple models of trajectories in space, both in 2D and in 3D. The first examples, which model bicircular moves in the same direction, are classical curves (epicycloids, etc.). Then, we explore bicircular moves in reverse…
Three-dimensional $N^{th}$ order nodal Lagrangian tetrahedral finite elements ($P_N$ elements) can be generated using Pascal's tetrahedron $\mathcal{H}$ where each node in 3D element space corresponds to an entry in $\mathcal{H}$. For the…
Integration of complex photonic structures onto optical fiber facets enables powerful platforms with unprecedented optical functionalities. Conventional nanofabrication technologies, however, do not permit viable integration of complex…
We present a technique to embed information invisible to the eye inside 3D printed objects. The information is integrated in the object model, and then fabricated using off-the-shelf dual-head FDM (Fused Deposition Modeling) 3D printers.…
Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…
This article presents the Orthoglide project. The purpose of this project is the realization of a prototype of machine tool to three degrees of translation. The characteristic of this machine is a parallel kinematic architecture optimized…
This paper is aimed at presenting a systematic survey of the existing now different formulations for the problem of projection of the origin of the Euclidean space onto the convex polyhedron (PPOCP). In the present paper, there are…
A lot of attention in supply chain management has been devoted to understanding customer requirements. What are customer priorities in terms of price and service level, and how can companies go about fulfilling these requirements in an…
With the rapid rise of 3D-printing as a competitive mass manufacturing method, manual "decaking" - i.e. removing the residual powder that sticks to a 3D-printed part - has become a significant bottleneck. Here, we introduce, for the first…
We study the general rational trigonometry of a tetrahedron, based on quadrances, spreads and solid spreads, using vector products associated to an arbitrary symmetric bilinear form over a general field, not of characteristic two. This…
Cylindrical algebraic decomposition (CAD) is an important tool, both for quantifier elimination over the reals and a range of other applications. Traditionally, a CAD is built through a process of projection and lifting to move the problem…
Symmetric orthogonalization via SVD, and closely related procedures, are well-known techniques for projecting matrices onto $O(n)$ or $SO(n)$. These tools have long been used for applications in computer vision, for example optimal 3D…
The aim of this note is to investigate isoperimetric-type problems for $3$-dimensional parallelohedra; that is, for convex polyhedra whose translates tile the $3$-dimensional Euclidean space. Our main result states that among…
Astronomy, a captivating field that draws upon science, mathematics, and engineering, has traditionally relied on visual representations to convey the wonders of the cosmos. While this approach effectively engages the sighted population,…
3D shape creation and modeling remains a challenging task especially for novice users. Many methods in the field of computer graphics have been proposed to automate the often repetitive and precise operations needed during the modeling of…