Related papers: Developable Ruled Surfaces Generated by the Curvat…
We propose a discrete surface theory in $\mathbb R^3$ that unites the most prevalent versions of discrete special parametrizations. This theory encapsulates a large class of discrete surfaces given by a Lax representation and, in…
The reduced density matrices (RDMs) of many-body quantum states form a convex set. The boundary of low dimensional projections of this convex set may exhibit nontrivial geometry such as ruled surfaces. In this paper, we study the physical…
We introduce trimmed NURBS surfaces with accurate boundary control, briefly called ABC-surfaces, as a solution to the notorious problem of constructing watertight or smooth ($G^1$ and $G^2)$ multi-patch surfaces within the function range of…
The research on developing planar curves to produce visually pleasing products (ranges from electric appliances to car body design) and indentifying/modifying planar curves for special purposes namely for railway design, highway design and…
The surface curvature of membranes, interfaces, and substrates plays a crucial role in shaping the self-assembly of particles adsorbed on these surfaces. However, little is known about the interplay between particle anisotropy and surface…
Neural Cellular Automata (NCA) have shown a remarkable ability to learn the required rules to "grow" images, classify morphologies, segment images, as well as to do general computation such as path-finding. We believe the inductive prior…
Normal surface theory is a central tool in algorithmic three-dimensional topology, and the enumeration of vertex normal surfaces is the computational bottleneck in many important algorithms. However, it is not well understood how the number…
Inelastic surface growth associated with continuous creation of incompatibility on the boundary of an evolving body is behind a variety of natural and technological processes, including embryonic development and 3D printing. In this paper…
We investigate ruled surfaces in 3d Riemannian manifolds, i.e., surfaces foliated by geodesics. In 3d space forms, we find the striction curve, distribution parameter, and the first and second fundamental forms, from which we obtain the…
In arXive:0705.3912 we studied triple-point defective very ample linear systems on regular surfaces, and we showed that they can only exist if the surface is ruled. In the present paper we show that we can drop the regularity assumption,…
In this work, we provide a local classification of certain special classes of surfaces determined by the prescription of the radial mean curvature in terms of the height and angle functions. Moreover, we introduce a special class of…
Sphere eversions have been described so far by either pictures with minimal topological complexity, numerical evolution or complex equations. We write down relatively simple explicit formulas for the whole eversion, both analytic and…
The fairing curves and surfaces are used extensively in geometric design, modeling, and industrial manufacturing. However, the majority of conventional fairing approaches, which lack sufficient parameters to improve fairness, are based on…
We present an algorithm for computing curves and families of curves of prescribed degree and geometric genus on real rational surfaces.
In this paper we define and construct a new class of algebraic surfaces in three-dimensional Euclidean space generated by a curve and a congruence of circles. We study their properties and visualize them with the program Mathematica.
We propose a simple mathematical model to describe the mechanical relaxation of cells within a curved epithelial tissue layer represented by an arbitrary curve in two-dimensional space. This model generalises previous one-dimensional models…
We consider curves which go around Whitney umbrella. Then we consider the geodesic and the normal curvatures, ruled surfaces generated by the normal vector and normal developable surfaces with respect to the tangent and bi-tangent vectors…
This paper introduces new ruled surfaces according to Bishop frame by referring to the main idea of Smarandache geometry. The fundamental forms and the corresponding curvatures are provided to put forth some characteristics of each surface.…
In this paper is studied the behavior of principal curvature lines near a curve of umbilic points of a smooth surface.
Geometric data analysis and learning has emerged as a distinct and rapidly developing research area, increasingly recognized for its effectiveness across diverse applications. At the heart of this field lies curvature, a powerful and…