相关论文: A toolkit to describe and interactively display th…

Algorithms that decompose a manifold into simple pieces reveal the geometric and topological structure of the manifold, showing how complicated structures are constructed from simple building blocks. This note describes a way to…

A method to visualize polytopes in a four dimensional euclidian space $(x,y,z,w)$ is proposed. A polytope is sliced by multiple hyperplanes that are parallel each other and separated by uniform intervals. Since the hyperplanes are…

We usually think of 2-dimensional manifolds as surfaces embedded in Euclidean 3-space. Since humans cannot visualise Euclidean spaces of higher dimensions, it appears to be impossible to give pictorial representations of higher-dimensional…

We describe an algorithm that takes as input an open book decomposition of a closed oriented 4-manifold and outputs an explicit trisection diagram of that 4-manifold. Moreover, a slight variation of this algorithm also works for open books…

We present a computational approach for unfolding 3D shapes isometrically into the plane as a single patch without overlapping triangles. This is a hard, sometimes impossible, problem, which existing methods are forced to soften by allowing…

Heegaard splittings provide a natural representation of closed 3-manifolds by gluing two handlebodies along a common surface. These splittings can be equivalently given by two finite sets of meridians lying on the surface, which define a…

The quest for deeper understanding of biological systems has driven the acquisition of increasingly larger multidimensional image datasets. Inspecting and manipulating data of this complexity is very challenging in traditional visualization…

Mediated by today's visual displays, information space allows users to discover, access and interact with a wide range of digital and physical information. The information presented in this space may be digital, physical or a blend of both,…

The knowledge that data lies close to a particular submanifold of the ambient Euclidean space may be useful in a number of ways. For instance, one may want to automatically mark any point far away from the submanifold as an outlier or to…

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…

Most research data collections created or used by astronomers are intrinsically multi-dimensional. In contrast, all visual representations of data presented within research papers are exclusively 2-dimensional. We present a resolution of…

While the interpretation of high-dimensional datasets has become a necessity in most industries, and is supported by continuous advances in data science and machine learning, the spatial visualization of higher-dimensional geometry has…

We introduce the concept of pseudo-trisections of smooth oriented compact 4-manifolds with boundary. The main feature of pseudo-trisections is that they have lower complexity than relative trisections for given 4-manifolds. We prove…

We test the hypothesis whether transforming a data matrix into a 3D shaded surface or even a volumetric display can be more appealing to humans than a scatterplot since it makes direct use of the innate 3D scene understanding capabilities…

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 introduce multisections of smooth, closed 4-manifolds, which generalize trisections to decompositions with more than three pieces. This decomposition describes an arbitrary smooth, closed 4-manifold as a sequence of cut systems on a…

Techniques for constructing codimension 2 embeddings and immersions of the 2 and 3-fold branched covers of the 3 and 4-dimensional spheres are presented. These covers are in braided form, and it is in this sense that they are folded. More…

Orbifolds are a modern mathematical concept that arises in the research of hyperbolic geometry with applications in computer graphics and visualization. In this paper, we make use of rooms with mirrors as the visual metaphor for orbifolds.…

A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…

The emergence of neural representations has revolutionized our means for digitally viewing a wide range of 3D scenes, enabling the synthesis of photorealistic images rendered from novel views. Recently, several techniques have been proposed…