相关论文: The $Z$-Curve as an $n$-Dimensional Hypersphere: P…
Visual events in computer vision are studied from the perspective of algebraic geometry. Given a sufficiently general curve or surface in 3-space, we consider the image or contour curve that arises by projecting from a viewpoint.…
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…
This paper presents a new approach for dimension reduction of data observed in a sphere. Several dimension reduction techniques have recently developed for the analysis of non-Euclidean data. As a pioneer work, Hauberg (2016) attempted to…
A new formalism is presented for analytically obtaining the probability density function, \( P_{n}(s) \), for the distance between two random points in an \( n \)-dimensional sphere of radius \( R \). Our formalism allows \( P_{n}(s) \) to…
${\cal U}$ntil now the representation (i.e. plotting) of curve in Parallel Coordinates is constructed from the point $\leftrightarrow$ line duality. The result is a ``line-curve'' which is seen as the envelope of it's tangents. Usually this…
A transformation based on mean curvature is introduced which morphs triangulated surfaces into round spheres.
A popular curve shown in introductory maths textbooks, seems like a circle. But it is actually a different curve. This paper discusses some elementary approaches to identify the geometric object, including novel technological means by using…
Creative telescoping applied to a bivariate proper hypergeometric term produces linear recurrence operators with polynomial coefficients, called telescopers. We provide bounds for the degrees of the polynomials appearing in these operators.…
Majority of the current dimensionality reduction or retrieval techniques rely on embedding the learned feature representations onto a computable metric space. Once the learned features are mapped, a distance metric aids the bridging of gaps…
A new hypersurface of Tzitzeica type is obtained in all three forms: parametric, implicit and explicit. Its two-dimensional version, although well-known from a theoretical point of view, is plotted with Matlab.
In this article, we study rectifying curves in arbitrary dimensional Euclidean space. A curve is said to be a rectifying curve if, in all points of the curve, the orthogonal complement of its normal vector contains a fixed point. We…
This paper is concerned with the use of the stereographic projection to map the points of a design on the sphere in three dimensions onto a two-dimensional stereogram. Details of the projection and its attendant stereogram are given and the…
Let $E$ be a smooth cubic. A plane curve $D$ is said to be an $n$-contact curve to $E$ if the intersection multiplicities at each intersection point between $E$ and $D$ is $n$. In this note, we give an algorithm to produce $n$-contact…
We introduce a new algorithm to compute the zeta function of a curve over a finite field. This method extends previous work of ours to all curves for which a good lift to characteristic zero is known. We develop all the necessary bounds,…
This is a paper about triangle cubics and conics in classical geometry with elements of projective geometry. In recent years, N.J. Wildberger has actively dealt with this topic using an algebraic perspective. Triangle conics were also…
We study metric spheres Z obtained by gluing two hemispheres of the Euclidean sphere along an orientation-preserving homeomorphism mapping the equator onto itself, where the distance on Z is the canonical distance that is locally isometric…
Extracting shape information from object bound- aries is a well studied problem in vision, and has found tremen- dous use in applications like object recognition. Conversely, studying the space of shapes represented by curves satisfying…
Shape metrics for objects in high dimensions remain sparse. Those that do exist, such as hyper-volume, remain limited to objects that are better understood such as Platonic solids and $n$-Cubes. Further, understanding objects of ill-defined…
This paper deals with a kind of design of a ruled surface. It combines concepts from the fields of computer aided geometric design and kinematics. A dual unit spherical B\'ezier-like curve on the dual unit sphere (DUS) is obtained with…
We present a novel algorithm for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. A straightforward approach to this problem consists of…