Related papers: Sculptures in S^3

We tackle the challenging problem of creating full and accurate three dimensional reconstructions of botanical trees with the topological and geometric accuracy required for subsequent physical simulation, e.g. in response to wind forces.…

This paper presents Tabby, an interactive and explorable design tool for 3D printing textures. Tabby allows texture design with direct manipulation in the following workflow: 1) select a target surface, 2) sketch and manipulate a texture…

The Hopf fibration mapping circles on a 3-sphere to points on a 2-sphere is well known to topologists. While the 2-sphere is embedded in 3-space, four-dimensional Euclidean space is needed to visualize the 3-sphere. Visualizing objects in…

Recent advances in the 3-D reconstruction of planetary nebulae are reviewed. We include not only results for 3-D reconstructions, but also the current techniques in terms of general methods and software. In order to obtain more accurate…

We construct embedded closed minimal surfaces in the round three-sphere, resembling two parallel copies of the Clifford torus, joined by m^2 small catenoidal bridges symmetrically arranged along a square lattice of points on the torus.

We show that each central configuration in the three-dimensional hyperbolic sphere is equivalent to one central configuration on a particular two- dimensional hyperbolic sphere. However, there exist both special and ordinary central…

Slot attention has emerged as a powerful framework for unsupervised object-centric learning, decomposing visual scenes into a small set of compact vector representations called \emph{slots}, each capturing a distinct region or object.…

Creating 3D shapes from 2D drawings is an important problem with applications in content creation for computer animation and virtual reality. We introduce a new sketch-based system, CreatureShop, that enables amateurs to create high-quality…

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…

The self intersection of an immersion i : S^2 \to R^3 dissects S^2 into pieces which are planar surfaces (unless i is an embedding). In this work we determine what collections of planar surfaces may be obtained in this way. In particular,…

This paper propose a interactive 3D modeling method and corresponding system based on single or multiple uncalibrated images. The main feature of this method is that, according to the modeling habits of ordinary people, the 3D model of the…

The task of crafting procedural programs capable of generating structurally valid 3D shapes easily and intuitively remains an elusive goal in computer vision and graphics. Within the graphics community, generating procedural 3D models has…

Existing single-view 3D generative models typically adopt multiview diffusion priors to reconstruct object surfaces, yet they remain prone to inter-view inconsistencies and are unable to faithfully represent complex internal structure or…

The recent developments in neural fields have brought phenomenal capabilities to the field of shape generation, but they lack crucial properties, such as incremental control - a fundamental requirement for artistic work. Triangular meshes,…

We want to introduce a construction of spherical designs from finite graphs with the theory of crystal lattice. We start from a finite graph, and we consider standard realization of the crystal lattices as the maximal Abelian covering of…

This article gives the construction and complete classification of all three-dimensional spherical manifolds, and orders them by decreasing volume, in the context of multiconnected universe models with positive spatial curvature. It…

Generic 3D reconstruction from a single image is a difficult problem. A lot of data loss occurs in the projection. A domain based approach to reconstruction where we solve a smaller set of problems for a particular use case lead to greater…

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…

We introduce GEM3D -- a new deep, topology-aware generative model of 3D shapes. The key ingredient of our method is a neural skeleton-based representation encoding information on both shape topology and geometry. Through a denoising…

This paper presents a novel decoder-based approach for generating manufacturable 3D structures optimized for additive manufacturing. We introduce a deep learning framework that decodes latent representations into geometrically valid,…