Related papers: Computing skeletons for rectilinearly-convex obsta…
An obstacle representation of a graph $G$ is a set of points in the plane representing the vertices of $G$, together with a set of polygonal obstacles such that two vertices of $G$ are connected by an edge in $G$ if and only if the line…
An \emph{obstacle representation} of a graph $G$ is a straight-line drawing of $G$ in the plane together with a collection of connected subsets of the plane, called \emph{obstacles}, that block all non-edges of $G$ while not blocking any of…
We introduce a method for efficiently computing the exact shortest path to the boundary of a mesh from a given internal point in the presence of self-intersections. We provide a formal definition of shortest boundary paths for…
Real-world environments are inherently uncertain, and to operate safely in these environments robots must be able to plan around this uncertainty. In the context of motion planning, we desire systems that can maintain an acceptable level of…
Given $n$ line segments in the plane, do they form the edge set of a \emph{weakly simple polygon}; that is, can the segment endpoints be perturbed by at most $\varepsilon$, for any $\varepsilon>0$, to obtain a simple polygon? While the…
Let $P$ be a planar set of $n$ points in general position. We consider the problem of computing an orientation of the plane for which the Rectilinear Convex Hull of $P$ has minimum area. Bae et al. (Computational Geometry: Theory and…
Line intersection with convex and un-convex polygons or polyhedron algorithms are well known as line clipping algorithms and very often used in computer graphics. Rendering of geometrical problems often leads to ray tracing techniques, when…
We present an algorithm to find an {\it Euclidean Shortest Path} from a source vertex $s$ to a sink vertex $t$ in the presence of obstacles in $\Re^2$. Our algorithm takes $O(T+m(\lg{m})(\lg{n}))$ time and $O(n)$ space. Here, $O(T)$ is the…
In general dimension, there is no known total polynomial algorithm for either convex hull or vertex enumeration, i.e. an algorithm whose complexity depends polynomially on the input and output sizes. It is thus important to identify…
We study the problem of stabbing rectilinear polygons, where we are given $n$ rectilinear polygons in the plane that we want to stab, i.e., we want to select horizontal line segments such that for each given rectilinear polygon there is a…
We propose a new algorithm for curve skeleton computation which differs from previous algorithms by being based on the notion of local separators. The main benefits of this approach are that it is able to capture relatively fine details and…
Detecting polygons defined by a set of line segments in a plane is an important step in analyzing vector drawings. This paper presents an approach combining several algorithms to detect basic polygons from arbitrary line segments. The…
An obstacle representation of a graph is a mapping of the vertices onto points in the plane and a set of connected regions of the plane (called obstacles) such that the straight-line segment connecting the points corresponding to two…
In this paper we propose a technique that assigns obstacles to clusters used for collision avoidance via Mixed-Integer Programming. This strategy enables a reduction in the number of binary variables used for collision avoidance, thus…
There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees,…
This paper presents a novel method for reformulating non-differentiable collision avoidance constraints into smooth nonlinear constraints using strong duality of convex optimization. We focus on a controlled object whose goal is to avoid…
This paper focuses on the challenging task of learning 3D object surface reconstructions from single RGB images. Existing methods achieve varying degrees of success by using different geometric representations. However, they all have their…
We present a continuous-time collision detection algorithm for quickly detecting whether certain polynomial trajectories in time intersect with convex obstacles. The algorithm is used in conjunction with an existing multicopter trajectory…
In this work, we carry out structural and algorithmic studies of a problem of barrier forming: selecting theminimum number of straight line segments (barriers) that separate several sets of mutually disjoint objects in the plane. The…
This paper proposes an algorithm for clipping line segment against an axis-aligned rectangular window. The conventional algorithms for line segment clipping treat the clipping boundary and/or the line segment to be clipped as line. The…