Related papers: Geodesic intersections
Sweeping is a powerful and versatile method of designing objects. Boundary of volumes (henceforth envelope) obtained by sweeping solids have been extensively investigated in the past, though, obtaining an accurate parametrization of the…
We propose a simple method of explicit description of families of closed geodesics on a triaxial ellipsoid $Q$ that are cut out by algebraic surfaces in ${\mathbb R}^3$. Such geodesics are either connected components of spatial elliptic…
On a hyperbolic Riemann surface, given two simple closed geodesics that intersect $n$ times, we address the question of a sharp lower bound $L_n$ on the length attained by the longest of the two geodesics. We show the existence of a surface…
Intersection graphs are very important in both theoretical as well as application point of view. Depending on the geometrical representation, different type of intersection graphs are defined. Among them interval, circular-arc, permutation,…
We give a universal upper bound for the total curvature of minimizing geodesic on a convex surface in the Euclidean space.
Region extraction is a very common task in both Computer Science and Engineering with several applications in object recognition and motion analysis, among others. Most of the literature focuses on regions delimited by straight lines, often…
Fitting concentric geometric objects to digitized data is an important problem in many areas such as iris detection, autonomous navigation, and industrial robotics operations. There are two common approaches to fitting geometric shapes to…
The question whether a Riemannian manifold is geodesically connected can be studied from geometrical as well as variational methods, and accurate results can be obtained by using the associated distance and related properties of the…
When a shallow layer of inviscid fluid flows over a substrate, the fluid particle trajectories are, to leading order in the layer thickness, geodesics on the two-dimensional curved space of the substrate. Since the two-dimensional geodesic…
The geometry of closed surfaces equipped with a Euclidean metric with finitely many conical points of arbitrary angle is studied. The main result is that the set of closed geodesics is dense in the space of geodesics.
Many problems in Euclidean geometry, arising in computational design and fabrication, amount to a system of constraints, which is challenging to solve. We suggest a new general approach to the solution, which is to start with analogous…
In this paper1 , we use the coding developed by R. Bowen and C. Series to compute the number of self-intersections of a closed geodesic on a pair of pants. We give lower and upper bounds on the number of self-intersections of a closed…
In this paper, we provide an algorithm for traversing geometric graphs which visits all vertices, and reports every vertex and edge exactly once. To achieve this, we combine a given geometric graph $G$ with the integer lattice, seen as a…
We give several algorithms addressing computations of intersections of conjugate subgroups.
This paper describes continuous-space methodologies to estimate the collision probability, Euclidean distance and gradient between an ellipsoidal robot model and an environment surface modeled as a set of Gaussian distributions.…
We present new algorithms to perform fast probabilistic collision queries between convex as well as non-convex objects. Our approach is applicable to general shapes, where one or more objects are represented using Gaussian probability…
Geodesic distance, commonly called shortest path length, has proved useful in a great variety of disciplines. It has been playing a significant role in search engine at present and so attracted considerable attention at the last few…
This contribution presents a brief survey of clipping and intersection algorithms in E2 and E3 with a nearly complete list of relevant references. Some algorithms use the projective extension of the Euclidean space and vector-vector…
Geodesics for a 5D magnetized Schwarzschild-like solution are analyzed by reducing the problem to the motion of a test particle in an effective potential. In absence of magnetic field comparison is established with Schwarzschild's geometry.…
We show that round hemispheres are the only compact 2 dimensional Riemannian manifolds (with or without boundary) such that almost every pair of complete geodesics intersect once and only once. We prove this by establishing a sharp…