Related papers: Point in polygon calculation using vector geometri…
We study the problem of partitioning a given simple polygon $P$ into a minimum number of connected polygonal pieces, each of bounded size. We describe a general technique for constructing such partitions that works for several notions of…
Given a set of $n$ points $P$ in the plane, the first layer $L_1$ of $P$ is formed by the points that appear on $P$'s convex hull. In general, a point belongs to layer $L_i$, if it lies on the convex hull of the set $P \setminus…
In the point set embeddability problem, we are given a plane graph $G$ with $n$ vertices and a point set $S$ with $n$ points. Now the goal is to answer the question whether there exists a straight-line drawing of $G$ such that each vertex…
We introduce bindings that enable the convenient, efficient, and reliable use of software modules of CGAL (Computational Geometry Algorithm Library), which are written in C++, from within code written in Python. There are different tools…
Optimization on manifolds is a class of methods for optimization of an objective function, subject to constraints which are smooth, in the sense that the set of points which satisfy the constraints admits the structure of a differentiable…
We consider the construction of a polygon $P$ with $n$ vertices whose turning angles at the vertices are given by a sequence $A=(\alpha_0,\ldots, \alpha_{n-1})$, $\alpha_i\in (-\pi,\pi)$, for $i\in\{0,\ldots, n-1\}$. The problem of…
We provide a polynomial time cutting plane algorithm based on split cuts to solve integer programs in the plane. We also prove that the split closure of a polyhedron in the plane has polynomial size.
We present an algorithm to compute the geometric median of shapes which is based on the extension of median to high dimensions. The median finding problem is formulated as an optimization over distances and it is solved directly using the…
Polygonal building outlines are crucial for geographic and cartographic applications. The existing approaches for outline extraction from aerial or satellite imagery are typically decomposed into subtasks, e.g., building masking and…
Single-view point cloud completion aims to recover the full geometry of an object based on only limited observation, which is extremely hard due to the data sparsity and occlusion. The core challenge is to generate plausible geometries to…
In this paper, we study the problem of computing Euclidean geodesic centers of a polygonal domain $\mathcal{P}$ with a total of $n$ vertices. We discover many interesting observations. We give a necessary condition for a point being a…
Given a convex polygon $P$ with $n$ vertices, the two-center problem is to find two congruent closed disks of minimum radius such that they completely cover $P$. We propose an algorithm for this problem in the streaming setup, where the…
An arrangement of $n$ curves in the plane is given. The query is a point $q$ and the goal is to find the face of the arrangement that contains $q$. A data-structure for point-location, preprocesses the curves into a data structure of…
The theory of holographic algorithms, which are polynomial time algorithms for certain combinatorial counting problems, yields insight into the hierarchy of complexity classes. In particular, the theory produces algebraic tests for a…
We study the problem of planning paths for a team of robots for visually monitoring an environment. Our work is motivated by surveillance and persistent monitoring applications. We are given a set of target points in a polygonal environment…
Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is comparable to the role of linear programs in scalar optimization. Vector linear…
We present a short step interior point method for solving a class of nonlinear programming problems with quadratic objective function. Convex quadratic programming problems can be reformulated as problems in this class. The method is shown…
The quality evaluation of three deep learning-based coding solutions for point cloud geometry, notably ADLPCC, PCC GEO CNNv2, and PCGCv2, is presented. The MPEG G-PCC was used as an anchor. Furthermore, LUT SR, which uses multi-resolution…
This paper proposes a novel and simple algorithm of facet enumeration for convex polytopes. The complexity of the algorithm is discussed. The algorithm is implemented in Matlab. Some simple polytopes with known H-representations and…
Object reconstruction is an important task in many fields of application as it allows to generate digital representations of our physical world used as base for analysis, planning, construction, visualization or other aims. A reconstruction…