Related papers: Sculptures in S^3
In this paper, helicoidal flat surfaces in the $3$-dimensional sphere $\mathbb{S}^3$ are considered. A complete classification of such surfaces is given in terms of their first and second fundamental forms and by linear solutions of the…
We prove new results on existence of solutions for the prescribed gaussian curvature problem on the euclidean sphere S^2. Those results are achieved by relating this problem with the holomorphic triples theory on Riemann surfaces. We think…
3D shape generation aims to produce innovative 3D content adhering to specific conditions and constraints. Existing methods often decompose 3D shapes into a sequence of localized components, treating each element in isolation without…
We explore the intersection of human and machine creativity by generating sculptural objects through machine learning. This research raises questions about both the technical details of automatic art generation and the interaction between…
Design - especially of physical objects - can be understood as creative acts solving practical problems. In this paper we describe a biologically-inspired developmental model as the basis of a generative form-finding system. Using local…
3D Shape representation has substantial effects on 3D shape reconstruction. Primitive-based representations approximate a 3D shape mainly by a set of simple implicit primitives, but the low geometrical complexity of the primitives limits…
We present EucliDreamer, a simple and effective method to generate textures for 3D models given text prompts and meshes. The texture is parametrized as an implicit function on the 3D surface, which is optimized with the Score Distillation…
3D reconstruction is a fundamental problem in computer vision, and the task is especially challenging when the object to reconstruct is partially or fully occluded. We introduce a method that uses the shadows cast by an unobserved object in…
We describe a method for constructing $n$-orthogonal coordinate systems in constant curvature spaces. The construction proposed is a modification of Krichever's method for producing orthogonal curvilinear coordinate systems in the…
The increasing demand for virtual reality applications has highlighted the significance of crafting immersive 3D assets. We present a text-to-3D 360$^{\circ}$ scene generation pipeline that facilitates the creation of comprehensive…
We introduce TetSphere Splatting, a Lagrangian geometry representation designed for high-quality 3D shape modeling. TetSphere splatting leverages an underused yet powerful geometric primitive -- volumetric tetrahedral meshes. It represents…
Active-stereo-based 3D shape measurement is crucial for various purposes, such as industrial inspection, reverse engineering, and medical systems, due to its strong ability to accurately acquire the shape of textureless objects. Active…
The problem of 3D reconstruction from posed images is undergoing a fundamental transformation, driven by continuous advances in 3D Gaussian Splatting (3DGS). By modeling scenes explicitly as collections of 3D Gaussians, 3DGS enables…
The recent advances in 3-D imaging technologies give rise to databases of human shapes, from which statistical shape models can be built. These statistical models represent prior knowledge of the human shape and enable us to solve shape…
We propose a data-driven 3D shape design method that can learn a generative model from a corpus of existing designs, and use this model to produce a wide range of new designs. The approach learns an encoding of the samples in the training…
We present a telepresence system based on a custom-made simulated holographic display that produces a full 3D model of the remote participants using commodity depth sensors. Our display is composed of a video projector and a quadrangular…
We directly connect topological changes that can occur in mathematical three-space via surgery, with black hole formation, the formation of wormholes and new generalizations of these phenomena. This work widens the bridge between topology…
Three-dimensional isospectral systems are constructed using the framework of supersymmetric quantum mechanics. In case the supercharge of first order in momentum is used, it is proved that the constructed systems reduce to a trivial…
We show that many well-known transforms in convex geometry (in particular, centroid body, convex floating body, and Ulam floating body) are special instances of a general construction, relying on applying sublinear expectations to random…
We present a novel volumetric animation generation framework to create new types of animations from raw 3D surface or point cloud sequence of captured real performances. The framework considers as input time incoherent 3D observations of a…