相关论文: 3d-printing Identification Spaces of the Square
Invariant manifolds are one of the key features that organize the dynamics of a differential equation. We introduce a novel approach to visualizing and studying invariant manifolds by using 3D printing technology, combining advanced…
In this paper we explore the topological properties of self-replicating, 3-dimensional manifolds, which are modeled by idempotents in the (2+1)-cobordism category. We give a classification theorem for all such idempotents. Additionally, we…
We introduce a concept of an embedding of a quadratic space in an associative algebra. The general properties of such embeddings are analyzed by linking it to the Clifford algebra. Conversely, there isa simple description of the standard…
Inclusion properties are studied for balls of the triangular ratio metric, the hyperbolic metric, the $j^*$-metric, and the distance ratio metric defined in the unit ball domain. Several sharp results are proven and a conjecture about the…
In this paper we present an implementation of a computer algorithm that automatically determines the topological structure of spacetime, using a branched covering space representation. This algorithm is applied to a few simple examples in…
Decomposition spaces are a class of function spaces constructed out of well-behaved coverings and partitions of unity of a set. The structure of the covering of the set determines the properties of the decomposition space. Besov spaces,…
In this paper, we study hypersurfaces of Euclidean spaces with arbitrary dimension. First, we obtain some results on $\mbox{H}$-hypersurfaces. Then, we give the complete classification of $\mbox{H}$-hypersurfaces with 3 distinct curvatures.…
Precise representations of 3D faces are beneficial to various computer vision and graphics applications. Due to the data discretization and model linearity, however, it remains challenging to capture accurate identity and expression clues…
Self-supervised models create representation spaces that lack clear semantic meaning. This interpretability problem of representations makes traditional explainability methods ineffective in this context. In this paper, we introduce a novel…
In this paper, we propose three novel and important methods for the registration of histological images for 3D reconstruction. First, possible intensity variations and nonstandardness in images are corrected by an intensity standardization…
Motivated by applications in robotics and computer vision, we study problems related to spatial reasoning of a 3D environment using sublevel sets of polynomials. These include: tightly containing a cloud of points (e.g., representing an…
This paper contains an account of arbitrary cubic function fields of characteristic three. We define a standard form for an arbitrary cubic curve and consider its function field. By considering an integral basis for the maximal order of…
Interpreting data with mathematical models is an important aspect of real-world industrial and applied mathematical modeling. Often we are interested to understand the extent to which a particular set of data informs and constrains model…
We address the problem of texturing flat surfaces by spray-painting through 3D printed stencils. We propose a system that (1) decomposes an image into alpha-blended layers; (2) computes a stippling given a transparency channel; (3)…
3D printing technologies are currently enabling the fabrication of objects with complex architectures and tailored properties. In such framework, the production of 3D optical structures, which are typically based on optical transparent…
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,…
We establish several fundamental properties of analysis-suitable T-splines which are important for design and analysis. First, we characterize T-spline spaces and prove that the space of smooth bicubic polynomials, defined over the extended…
When solving a PDE problem numerically, a certain mesh-refinement process is always implicit, and very classically, mesh adaptivity is a very effective means to accelerate grid convergence. Similarly, when optimizing a shape by means of an…
The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space $\mathbb{R}^3$ are easier to feel by human's intuition. We give the maximum order of finite group actions on $(\mathbb{R}^3, \Sigma)$…
In the industrial practice, additive manufacturing processes are often followed by post-processing operations such as subtractive machining, milling, etc. to achieve the desired surface quality and dimensional accuracy. Hence, a given part…