相关论文: Length of parallel curves

Given two general rational curves of the same degree in two projective spaces, one can ask whether there exists a third rational curve of the same degree that projects to both of them. We show that, under suitable assumptions on the degree…

Let $P$ be a polygonal curve in $\mathbb{R}^D$ of length $n$, and $S$ be a point set of size $k$. The Curve/Point Set Matching problem consists of finding a polygonal curve $Q$ on $S$ such that its Fr\'echet distance from $P$ is less than a…

Local perturbations of an infinitely long rod go away to infinity. On the contrary, in the case of a finite length of the rod, the perturbations reach its boundary and are reflected from it. The boundary conditions constructed here for the…

The chord length probability density of the regular octahedron is explicitly evaluated throughout its full range of distances by separating it into three contributions respectively due to the pairs of facets opposite to each other or…

The discrete Fr{\'e}chet distance is a measure of similarity between point sequences which permits to abstract differences of resolution between the two curves, approximating the original Fr{\'e}chet distance between curves. Such distance…

The Fr\'{e}chet distance is a popular distance measure between curves $P$ and $Q$. Conditional lower bounds prohibit $(1 + \varepsilon)$-approximate Fr\'{e}chet distance computations in strongly subquadratic time, even when preprocessing…

We show that in Euclidean 3-space any closed curve which lies outside the unit sphere and contains the sphere within its convex hull has length at least $4\pi$. Equality holds only when the curve is composed of $4$ semicircles of length…

In mathematics curves are typically defined as the images of continuous real functions (parametrizations) defined on a closed interval. They can also be defined as connected one-dimensional compact subsets of points. For simple curves of…

In this paper, we show the arc length of the optimal ROC curve is an $f$-divergence. By leveraging this result, we express the arc length using a variational objective and estimate it accurately using positive and negative samples. We show…

We present a solution to the time discontinuity paradox in rotating reference frames by postulating that time is periodic. A kinematic restriction is enforced that requires the discontinuity to be an integral number of the periodicity of…

Obtaining complete information about the shape of an object by looking at it from a single direction is impossible in general. In this paper, we theoretically study obtaining differential geometric information of an object from orthogonal…

Biological processes like growth, aging, and disease progression are generally studied with follow-up scans taken at different time points, i.e., with image time series (TS) based analysis. Comparison between TS representing a biological…

We describe some relations between the properties of the Cauchy problem for an ODE and the properties of the Cauchy problem for the associated continuity equation in the class of measures.

We prove that a smooth, complex plane curve $C$ of odd degree can be defined by a polynomial with real coefficients if and only if $C$ is isomorphic to its complex conjugate. Counterexamples are known for curves of even degree. More…

It is well known that the Lorentzian length of a timelike curve in Minkowski spacetime is smaller than the Lorentzian length of the geodesic connecting its initial and final endpoints. The difference is known as the 'differential aging' and…

We propose a notion of distance between two parametrized planar curves, called their discrepancy, and defined intuitively as the minimal amount of deformation needed to deform the source curve into the target curve. A precise definition of…

In this paper we study a wide range of variants for computing the (discrete and continuous) Fr\'echet distance between uncertain curves. We define an uncertain curve as a sequence of uncertainty regions, where each region is a disk, a line…

We investigate the spatio-temporal quantity of coherence for turbulent velocity fluctuations at spatial distances of the order or larger than the integral length scale $l_{0}$. Using controlled laboratory experiments, an exponential decay…

We prove Cauchy's formula for repeated integration on time scales. The obtained relation gives rise to new notions of fractional integration and differentiation on arbitrary nonempty closed sets.

One can define the notion of primitive length spectrum for a simple regular periodic graph via counting the orbits of closed reduced primitive cycles under an action of a discrete group of automorphisms. We prove that this primitive length…