Related papers: A Survey of Algorithms for Geodesic Paths and Dist…
We present a novel formulation of ergodic trajectory optimization that can be specified over general domains using kernel maximum mean discrepancy. Ergodic trajectory optimization is an effective approach that generates coverage paths for…
This survey is devoted to recent developments in the statistical analysis of spherical data, with a view to applications in Cosmology. We will start from a brief discussion of Cosmological questions and motivations, arguing that most…
We describe a polynomial-time algorithm to compute a (tight) geodesic between two curves in the curve graph. As well as enabling us to compute the distance between a pair of curves, this has several applications to mapping classes. For…
We propose an optimization algorithm for computing geodesics on the universal Teichm\"uller space T(1) in the Weil-Petersson ($W P$) metric. Another realization for T(1) is the space of planar shapes, modulo translation and scale, and thus…
The Euclidean space notion of convex sets (and functions) generalizes to Riemannian manifolds in a natural sense and is called geodesic convexity. Extensively studied computational problems such as convex optimization and sampling in convex…
Computing shortest paths is one of the most researched topics in algorithm engineering. Currently available algorithms compute shortest paths in mere fractions of a second on continental sized road networks. In the presence of…
This paper addresses the problem of finding shortest paths homotopic to a given disjoint set of paths that wind amongst point obstacles in the plane. We present a faster algorithm than previously known.
The idea that the quantum space-time of microphysics may be fractal everywhere was intensively investigated recently, and several authors have presented the geodesic equations of different fractal space - times. In the present work we…
In this article, we consider the motion planning of a rigid object on the unit sphere with a unit speed. The motion of the object is constrained by the maximum absolute value, $U_{max}$ of geodesic curvature of its path; this constrains the…
The problem of finding the shortest path for a vehicle visiting a given sequence of target points subject to the motion constraints of the vehicle is an important problem that arises in several monitoring and surveillance applications…
There are many methods developed to approximate a cloud of vectors embedded in high-dimensional space by simpler objects: starting from principal points and linear manifolds to self-organizing maps, neural gas, elastic maps, various types…
Graphs are typically visualized as node-link diagrams. Although there is a fair amount of research focusing on crossing minimization to improve readability, little attention has been paid on how to handle crossings when they are an…
It is known that for a variety of choices of metrics, including the standard bottleneck distance, the space of persistence diagrams admits geodesics. Typically these existence results produce geodesics that have the form of a convex…
Several physical problems such as the `twin paradox' in curved spacetimes have purely geometrical nature and may be reduced to studying properties of bundles of timelike geodesics. The paper is a general introduction to systematic…
The development of algorithmic fractal dimensions in this century has had many fruitful interactions with geometric measure theory, especially fractal geometry in Euclidean spaces. We survey these developments, with emphasis on connections…
We present a new method for constructing valid covariance functions of Gaussian processes for spatial analysis in irregular, non-convex domains such as bodies of water. Standard covariance functions based on geodesic distances are not…
Geodesic distances on manifolds have numerous applications in image processing, computer graphics and computer vision. In this work, we introduce an approach called `LGGD' (Learned Generalized Geodesic Distances). This method involves…
Constructions and exploration of plane algebraic curves has received a new push with the development of automated methods, whose algorithms are continuously improved and implemented in various software packages. We use them to explore the…
The quadratic shortest path problem is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized. We derive several semidefinite programming relaxations for the…
Recently, nonadiabatic geometric quantum computation has been received much attention, due to its fast manipulation and intrinsic error-resilience characteristics. However, to obtain universal geometric quantum control, only limited and…