Related papers: Sculptures in S^3

The real projective plane has three well know isomorphic constructions: the extended euclidean plane, unit (hemi)sphere, and three dimensional vector space over the reals. In this paper we find the isomorphisms that map between these three…

Accurately drawing 3D objects is difficult for untrained individuals, as it requires an understanding of perspective and its effects on geometry and proportions. Step-by-step tutorials break the complex task of sketching an entire object…

Neural implicit representations of 3D shapes have shown great potential in 3D shape editing due to their ability to model high-level semantics and continuous geometric representations. However, existing methods often suffer from limited…

3D shape editing is widely used in a range of applications such as movie production, computer games and computer aided design. It is also a popular research topic in computer graphics and computer vision. In past decades, researchers have…

Most state-of-the-art deep geometric learning single-view reconstruction approaches rely on encoder-decoder architectures that output either shape parametrizations or implicit representations. However, these representations rarely preserve…

We use some fundamental ideas from complex analysis to create symmetric images and animations. Using a domain coloring algorithm, we generate mappings to the entire complex plane or the hyperbolic upper half-plane. The resulting designs can…

We develop an algorithm capable of imaging a three-dimensional object given a collection of two-dimensional images of that object that are significantly influenced by the curvature of the Ewald sphere. These two-dimensional images cannot be…

The concept of an invisibility cloak is a fixture of science fiction, fantasy, and the collective imagination. However, a real device that could hide an object from sight in visible light from absolutely any viewpoint would be extremely…

Given five points in a three-dimensional euclidean space, one can consider five tetrahedra, using those points as vertices. We present a pentagon-like formula containing the product of three volumes of those tetrahedra in its l.h.s. and the…

Generating high-quality 3D models from 2D sketches is a challenging task due to the inherent ambiguity and sparsity of sketch data. In this paper, we present S3D, a novel framework that converts simple hand-drawn sketches into detailed 3D…

3D Gaussian Splatting (3DGS) has demonstrated superior quality in modeling 3D objects and scenes. However, generating 3DGS remains challenging due to their discrete, unstructured, and permutation-invariant nature. In this work, we present a…

We introduce POP3D, a novel framework that creates a full $360^\circ$-view 3D model from a single image. POP3D resolves two prominent issues that limit the single-view reconstruction. Firstly, POP3D offers substantial generalizability to…

We present a flexible interactive 3D morpho-kinematical modeling application for astrophysics. Compared to other systems, our application reduces the restrictions on the physical assumptions, data type and amount that is required for a…

Topological surgery is a mathematical technique used for creating new manifolds out of known ones. We observe that it occurs in natural phenomena where a sphere of dimension 0 or 1 is selected, forces are applied and the manifold in which…

The gluing technique is used to construct hypersurfaces in Euclidean space having approximately constant prescribed mean curvature. These surfaces are perturbations of unions of finitely many spheres of the same radius assembled end-to-end…

We propose Text2Scene, a method to automatically create realistic textures for virtual scenes composed of multiple objects. Guided by a reference image and text descriptions, our pipeline adds detailed texture on labeled 3D geometries in…

In this work we present WIR3D, a technique for abstracting 3D shapes through a sparse set of visually meaningful curves in 3D. We optimize the parameters of Bezier curves such that they faithfully represent both the geometry and salient…

Advances in 3D printing technology now enable the precise positioning of microscopic material voxels to form complex structures. Combined with emerging multi-material capabilities and printable responsive materials, this opens new…

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…

In this paper, we democratise 3D content creation, enabling precise generation of 3D shapes from abstract sketches while overcoming limitations tied to drawing skills. We introduce a novel part-level modelling and alignment framework that…