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A data structure and toolkit are presented here that allow for the description and manipulation of mathematical models of three-manifolds and their interactive display from multiple viewpoints via the OpenGL 3D graphics package. The data…

In this article we characterize all biharmonic curves of the Cartan-Vranceanu 3-dimensional spaces and we give their explicit parametrizations.

Owing to their intricate variable density architecture, and as a principal site of star formation, molecular clouds represent one of the most functionally significant, yet least understood features of our universe. To unravel the intrinsic…

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 describe some Cartesian products of metric spaces and find conditions under which products of ultrametric spaces are ultrametric.

This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.

A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…

One distinguishing feature of rational curves is that they have algebraic parameterizations. Arc spaces are a way of describing approximations to parameterizations of all curves in some fixed space. Playing on these descriptions, this paper…

3D modeling is becoming a well-developed field of medicine, but its applicability can be limited due to the lack of software allowing for easy utilizations of generated 3D visualizations. By leveraging recent advances in virtual reality, we…

Implicit neural representations have emerged as a powerful tool in learning 3D geometry, offering unparalleled advantages over conventional representations like mesh-based methods. A common type of INR implicitly encodes a shape's boundary…

Realistic 3D-conformations of protein structures can be embedded in a cubic lattice using exclusively integer numbers, additions, subtractions and boolean operations.

Based on geometric intuition, in this paper we are trying to give an idea and visualize the meaning of the determinants for the cubic-matrix. In this paper we have analyzed the possibilities of developing the concept of determinant of…

Affordance modeling plays an important role in visual understanding. In this paper, we aim to predict affordances of 3D indoor scenes, specifically what human poses are afforded by a given indoor environment, such as sitting on a chair or…

The description of principal lines of the ellipsoid on the 3-dimensional Minkowski space is established. A global principal parametrization of a triple orthogonal system of quadrics is also achieved, and the focal set of the ellipsoid is…

We derive expressions for three-body phase space that are explicitly symmetrical in the masses of the three particles, by three separate methods.

Explainability of deep neural networks is one of the most challenging and interesting problems in the field. In this study, we investigate the topic focusing on the interpretability of deep learning-based registration methods. In…

One major goal of vision is to infer physical models of objects, surfaces, and their layout from sensors. In this paper, we aim to interpret indoor scenes from one RGBD image. Our representation encodes the layout of orthogonal walls and…

Photonic quantum gases explore the physics of open driven-dissipative quantum systems under ambient conditions and thus open access to thermodynamics and transport phenomena in quantum gases in the weakly interacting regime. Here we…

In this paper we study maps (curved flats) into symmetric spaces which are tangent at each point to a flat of the symmetric space. Important examples of such maps arise from isometric immersions of space forms into space forms via their…

One major goal of vision is to infer physical models of objects, surfaces, and their layout from sensors. In this paper, we aim to interpret indoor scenes from one RGBD image. Our representation encodes the layout of walls, which must…