相关论文: Shadows of a Closed Curve

Given a unit vector field on a closed Euclidean hypersurface, we define a map from the hypersurface to a sphere in the Euclidean space. This application allows us to exhibit a list of topological invariants which combines the second…

We study the shadow cast by the H$D$ Schwarzschild-Tangherlini black hole, and analytically calculate the influence of extra dimensions on the shadow of a black hole. A black hole casts a shadow as an optical appearance because of its…

We develop a connection between the inscribed square problem and the question of understanding relation avoiding paths in a complex vector space. Our main theorem is that a Jordan curve with no inscribed squares would have a seemingly…

A simple closed curve in the Euclidean plane is said to have property C_n(R) if at each point we can inscribe a unique regular $n$-gon with edges length $R$. C_2(R) is equivalent to having constant diameter. We show that smooth curves…

Shape inference is classically ill-posed, because it involves a map from the (2D) image domain to the (3D) world. Standard approaches regularize this problem by either assuming a prior on lighting and rendering or restricting the domain,…

We obtain the shadow cast induced by the rotating black hole with an anisotropic matter. A Killing tensor representing the hidden symmetry is derived explicitly. The existence of separability structure implies a complete integrability 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…

Isoperimetric inequalities have been studied since antiquity, and in recent decades they have been studied extensively on discrete objects, such as the hypercube. An important special case of this problem involves bounding the size of the…

An oriented cycle is an orientation of a undirected cycle. We first show that for any oriented cycle $C$, there are digraphs containing no subdivision of $C$ (as a subdigraph) and arbitrarily large chromatic number. In contrast, we show…

From the viewpoint of differential geometry and topology, we investigate the characterization of the shadows in a Kerr spacetime. Two new quantities, the length of the shadow boundary and the local curvature radius are introduced. Each…

Using digital topology approach, we construct digital models of closed surfaces as the intersection graphs of LCL covers of the surfaces. It is proved that digital models of closed surfaces are digital 2-dimensional surfaces preserving the…

Light scattering from self-affine homogeneous isotropic random rough surfaces is studied using the ray-optics approximation. Numerical methods are developed to accelerate the first-order scattering simulations from surfaces represented as…

The \emph{general position problem} in graphs asks for a largest set of vertices in which no three lie on a common shortest path. The \emph{mutual-visibility problem} seeks a largest set of vertices such that every pair is connected by a…

We develop an essentially algebraic method to study biharmonic curves into an implicit surface. Although our method is rather general, it is especially suitable to study curves into surfaces defined by a polynomial equation: in particular,…

We consider the problem of inferring the shape of a transiting object's silhouette from its light curve alone, without assuming a physical model for the object. We model the object as a grid of pixels which transits the star; each pixel has…

The study is about a basic shadow experiment, which was enriched with a simulation to understand the reasoning of participants when we use a trick. Two light sources create an umbra and penumbra behind the objects. With this experiment, we…

Any quasi-isometry of the complex of curves is bounded distance from a simplicial automorphism. As a consequence, the quasi-isometry type of the curve complex determines the homeomorphism type of the surface.

We present a new method for visualizing implicit real algebraic curves inside a bounding box in the $2$-D or $3$-D ambient space based on numerical continuation and critical point methods. The underlying techniques work also for tracing…

We study the size of the shadow of $k$-uniform hypergraphs with bounded degree. Lower bounds on the ratio of the size of the shadow and the size of the hypergraph are given as a function of the degree bound and $k$. We show that cliques are…

We give a topological characterization of the n-dimensional pseudo-boundary of the (2n+1)-dimensional Euclidean space.