相关论文: 3d-printing Identification Spaces of the Square

The purpose of this short paper is to describe a project to manufacture a regular octohedron on a 3D printer. We assume that the reader is familiar with the basics of 3D printing. In the project, we use fundamental ideas to calculate the…

Quadrilateral layouts on surfaces are valuable in texture mapping, and essential in generation of quadrilateral meshes and in fitting splines. Previous work has characterized such layouts as a special metric on a surface or as a meromorphic…

We study applications of 3D printing to the broad goal of understanding how mathematical objects vary continuously in families. To do so, we model the varying parameter as the vertical axis of a 3D print, introducing the notion of a static…

The problem of immersing a simply connected surface with a prescribed shape operator is discussed. From classical and more recent work, it is known that, aside from some special degenerate cases, such as when the shape operator can be…

We present and discuss several old and new methods for mapping a circular disc to a square. In particular, we present analytical expressions for mapping each point (u,v) inside the circular disc to a point (x,y) inside a square region.…

3D alignment has become a very important part of 3D scanning technology. For instance, we can divide the alignment process into four steps: key point detection, key point description, initial pose estimation, and alignment refinement.…

Three-dimensional (3D) visualization has opened up a Universe of possible scientific data representations. 3D printing has the potential to make seemingly abstract and esoteric data sets accessible, particularly through the lens of…

Three-dimensional (3D) printing has emerged as a powerful tool for material, food, and life science research and development, where the technology democratization necessitates the advancement of open-source platforms. Herein, we developed a…

We classify the symmetric association schemes with faithful spherical embedding in 3-dimensional Euclidean space. Our result is based on previous research on primitive association schemes with $m_1 = 3$.

Designing multiscale visualizations, particularly when the ratio between the largest scale and the smallest item is large, can be challenging, and designers have developed many approaches to overcome this challenge. We present a design…

This paper considers an extension of origami geometry to the case of "folding" a three dimensional (3D) space along a plane. First, all possible incidence constraints between given points, lines and planes are analyzed by using the geometry…

A classification of a family of 3-revolute (3R) positioning manipulators is established. This classification is based on the topology of their workspace. The workspace is characterized in a half-cross section by the singular curves of the…

We introduce a novel neural network-based computational pipeline as a representation-agnostic slicer for multi-axis 3D printing. This advanced slicer can work on models with diverse representations and intricate topology. The approach…

We present a 3D stylization algorithm that can turn an input shape into the style of a cube while maintaining the content of the original shape. The key insight is that cubic style sculptures can be captured by the as-rigid-as-possible…

We derive three-dimensional integrable mappings which have two invariants.

Face recognition is one of the most studied research topics in the community. In recent years, the research on face recognition has shifted to using 3D facial surfaces, as more discriminating features can be represented by the 3D geometric…

We describe the possible 3-divisible $A_2^n$ configurations of smooth rational curves on K3 surfaces in characteristic 3 and fully classify the resulting triple covers.

In this paper we present a set of criteria for the choice of the shape parameter c contained in multiquadrics.

We, as a society, need artists to help us interpret and explain science, but what does an artist's studio look like when today's science is built upon the language of large, increasingly complex data? This paper presents a data…

We demonstrate, for the first time, the applicability of 3D printing technique to the manufacture of scintillation detectors. We report of a formulation, usable in stereolithographic printing, that exhibits scintillation efficiency on the…