Related papers: Sculptures in S^3
Shaping the electron wavefunction in three dimensions may prove to be an indispensable tool for research involving atomic-sized particle trapping, manipulation, and synthesis. We utilize computer-generated holograms to sculpt electron…
Clay sculpting is a nuanced, artistic task involving dexterous manipulation with long-horizon planning to achieve high-level goals. As a robotics problem, we formulate clay sculpting as a shape-to-shape matching challenge. Prior deformable…
In this paper we consider the spherical slant helices in $R^3$. More- over, we show how could be obtained to a spherical slant helix and we give some spherical slant helix examples in Euclidean 3-space.
We investigate how thin structures change their shape in response to non-mechanical stimuli that can be interpreted as variations in the structure's natural curvature. Starting from the theory of non-Euclidean plates and shells, we derive…
We give a construction for spherical 3-designs. This construction is a generalization of Bondarenko's work.
A conformal map from a Riemann surface to a Euclidean space of dimension greater than or equal to three is explained by using the Clifford algebra, in a similar fashion to quaternionic holomorphic geometry of surfaces in the Euclidean…
Computer Vision and 3D printing have rapidly evolved in the last 10 years but interactions among them have been very limited so far, despite the fact that they share several mathematical techniques. We try to fill the gap presenting an…
We introduce a rotation-invariant representation of planar shapes. In particular, this representation encodes shapes as vectors such that the Euclidean distance between them serves as a valid shape distance. For standardized, star-shaped…
Recent years have seen an explosion of work and interest in text-to-3D shape generation. Much of the progress is driven by advances in 3D representations, large-scale pretraining and representation learning for text and image data enabling…
We present a method to construct a large family of Lagrangian surfaces in complex Euclidean plane by using Legendre curves in the 3-sphere and in the anti de Sitter 3-space or, equivalently, by using spherical and hyperbolic curves,…
Representing complex shapes with simple primitives in high accuracy is important for a variety of applications in computer graphics and geometry processing. Existing solutions may produce suboptimal samples or are complex to implement. We…
We construct the quaternion algebra [10] "geometrically" by a three dimensional analogue of the classic two dimensional geometric description of the complex field. The algebraic description of the multiplication operation in three…
Spherical $t$-designs are finite point sets on the unit sphere that enable exact integration of polynomials of degree at most $t$ via equal-weight quadrature. This concept has recently been extended to spherical $t$-design curves by the use…
Recent generative models can create visually plausible 3D representations of objects. However, the generation process often allows for implicit control signals, such as contextual descriptions, and rarely supports bold geometric distortions…
We construct one-parameter deformations of the Euclidean sphere $\mathbb{S}^n$ inside $\mathbb{R}^{n+1}$ that admit a Zoll family of codimension one embedded minimal spheres, in all dimensions $n\geq 3$. The method of construction is…
In this work, we present a novel framework built to simplify 3D asset generation for amateur users. To enable interactive generation, our method supports a variety of input modalities that can be easily provided by a human, including…
We show that the following algorithmic problem is decidable: given a $2$-dimensional simplicial complex, can it be embedded (topologically, or equivalently, piecewise linearly) in $\mathbf{R}^3$? By a known reduction, it suffices to decide…
We present a process for sculpting Bi$_2$Se$_3$ nanoflakes into application-relevant geometries using a high resolution transmission electron microscope. This process takes several minutes to sculpt small areas and can be used to cut the…
We describe three identification spaces of the square, interesting choices of immersion into $\mathbb{R}^3$, and a process to construct 3d-printable models of their parametrizations.
With toy modelling of conceptual aspects of quantum cosmology and the problem of time in quantum gravity in mind, I study the classical and quantum dynamics of the pure-shape (i.e. scale-free) triangle formed by 3 particles in 2-d. I do so…