Related papers: An Efficient Solution to the 2D Visibility Problem…
This paper introduces an efficient $\mathcal{O}(n)$ compute and memory complexity algorithm for globally optimal path planning on 2D Cartesian grids. Unlike existing marching methods that rely on approximate discretized solutions to the…
In this research, we investigate the subject of path-finding. A pruned version of visibility graph based on Candidate Vertices is formulated, followed by a new visibility check technique. Such combination enables us to quickly identify the…
Visually sorted grid layouts provide an efficient method for organizing high-dimensional vectors in two-dimensional space by aligning spatial proximity with similarity relationships. This approach facilitates the effective sorting of…
2D path planning in static environment is a well-known problem and one of the common ways to solve it is to 1) represent the environment as a grid and 2) perform a heuristic search for a path on it. At the same time 2D grid resembles much a…
The performance of search algorithms for grid-based pathfinding, e.g. A*, critically depends on the heuristic function that is used to focus the search. Recent studies have shown that informed heuristics that take the positions/shapes of…
Given a simple polygon $P$ consisting of $n$ vertices, we study the problem of designing space-efficient algorithms for computing (i) the visibility polygon of a point inside $P$, (ii) the weak visibility polygon of a line segment inside…
In this article we consider two-grid finite element methods for solving semilinear interface problems in d space dimensions, for d=2 or d=3. We first describe in some detail the target problem class with discontinuous diffusion…
Algorithmic approaches to exhaustive coverage have application in video games, enabling automatic game level exploration. Current designs use simple heuristics that frequently result in poor performance or exhibit unnatural behaviour. In…
Point clouds are widely used representations of 3D data, but determining the visibility of points from a given viewpoint remains a challenging problem due to their sparse nature and lack of explicit connectivity. Traditional methods, such…
In the Any-Angle Pathfinding problem, the goal is to find the shortest path between a pair of vertices on a uniform square grid, that is not constrained to any fixed number of possible directions over the grid. Visibility Graphs are a known…
We consider the problem of routing on a network in the presence of line segment constraints (i.e., obstacles that edges in our network are not allowed to cross). Let $P$ be a set of $n$ points in the plane and let $S$ be a set of…
Fast and accurate path planning is important for ground robots to achieve safe and efficient autonomous navigation in unstructured outdoor environments. However, most existing methods exploiting either 2D or 2.5D maps struggle to balance…
Problem of finding 2D paths of special shape, e.g. paths comprised of line segments having the property that the angle between any two consecutive segments does not exceed the predefined threshold, is considered in the paper. This problem…
The problem of path planning in unknown environments remains a challenging problem - as the environment is gradually observed during the navigation, the underlying planner has to update the environment representation and replan, promptly…
Video prediction methods generally consume substantial computing resources in training and deployment, among which keypoint-based approaches show promising improvement in efficiency by simplifying dense image prediction to light keypoint…
In this paper we explore a symmetry-based search space reduction technique which can speed up optimal pathfinding on undirected uniform-cost grid maps by up to 38 times. Our technique decomposes grid maps into a set of empty rectangles,…
We develop and analyze several different second-order algorithms for computing a near-optimal solution path of a convex parametric optimization problem with smooth Hessian. Our algorithms are inspired by a differential equation perspective…
Hierarchical, multi-resolution volumetric mapping approaches are widely used to represent large and complex environments as they can efficiently capture their occupancy and connectivity information. Yet widely used path planning methods…
Grid cells enable the brain to model the physical space of the world and navigate effectively via path integration, updating self-position using information from self-movement. Recent proposals suggest that the brain might use similar…
Learning implicit representations has been a widely used solution for surface reconstruction from 3D point clouds. The latest methods infer a distance or occupancy field by overfitting a neural network on a single point cloud. However,…