Related papers: Efficient Computation of Visibility Polygons
Given a simple polygon P in the plane, we present new algorithms and data structures for computing the weak visibility polygon from any query line segment in P. We build a data structure in O(n) time and O(n) space that can compute the…
An efficient algorithm to enumerate the vertices of a two-dimensional (2D) projection of a polytope, is presented in this paper. The proposed algorithm uses the support function of the polytope to be projected and enumerated for vertices.…
The Integral Image algorithm is often applied in tasks that require efficient integration over images, such as object detection. In this paper we discuss theoretical aspects of the algorithm's continuous version. We suggest to define the…
This paper proposes a method for computing the visible occluding contours of subdivision surfaces. The paper first introduces new theory for contour visibility of smooth surfaces. Necessary and sufficient conditions are introduced for when…
We present an $O(n\log n)$-time algorithm that determines whether a given planar $n$-gon is weakly simple. This improves upon an $O(n^2\log n)$-time algorithm by Chang, Erickson, and Xu (2015). Weakly simple polygons are required as input…
We present a novel certified and complete algorithm to compute arrangements of real planar algebraic curves. It provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic curves in…
We introduce the \emph{visibility center} of a set of points inside a polygon -- a point $c_V$ such that the maximum geodesic distance from $c_V$ to see any point in the set is minimized. For a simple polygon of $n$ vertices and a set of…
Visibility plays an important role for decision making in cluttered, uncertain environments. This paper considers the problem of identifying optimal hiding spots for an agent against line-of-sight detection by an adversary whose location is…
In this paper, we study the following problem of reconstructing a simple polygon: Given a cyclically ordered vertex sequence of an unknown simple polygon P of n vertices and, for each vertex v of P, the sequence of angles defined by all the…
This thesis focuses on two concepts which are widely studied in the field of computational geometry. Namely, visibility and unit disk graphs. In the field of visibility, we have studied the conflict-free chromatic guarding of polygons, for…
With the advent of autonomous robots with two- and three-dimensional scanning capabilities, classical visibility-based exploration methods from computational geometry have gained in practical importance. However, real-life laser scanning of…
Determining if a point is in a polygon or not is used by a lot of applications in computer graphics, computer games and geoinformatics. Implementing this check is error-prone since there are many special cases to be considered. This holds…
We make use of the complex implicit representation in order to provide a deterministic algorithm for checking whether or not two implicit algebraic curves are related by a similarity, a central question in Pattern Recognition and Computer…
We present a generic C++ design to perform efficient and exact geometric computations using lazy evaluations. Exact geometric computations are critical for the robustness of geometric algorithms. Their efficiency is also critical for most…
We describe an efficient algorithm to compute a pseudotriangulation of a finite planar family of pairwise disjoint convex bodies presented by its chirotope. The design of the algorithm relies on a deepening of the theory of visibility…
Many algorithms used are based on geometrical computation. There are several criteria in selecting appropriate algorithm from already known. Recently, the fastest algorithms have been preferred. Nowadays, algorithms with a high stability…
Computing visibility on a geometric object requires heavy computations since it requires to identify pairs of points that are visible to each other, i.e. there is a straight segment joining them that stays in the close vicinity of the…
Planning is hard. The use of subgoals can make planning more tractable, but selecting these subgoals is computationally costly. What algorithms might enable us to reap the benefits of planning using subgoals while minimizing the…
This paper introduces a novel $k$-cell decomposition method for pursuit-evasion problems in polygonal environments, where a searcher is equipped with a $k$-modem: a device capable of seeing through up to $k$ walls. The proposed…
We present algorithms for computation and visualization of amoebas, their contours, compactified amoebas and sections of three-dimensional amoebas by two-dimensional planes. We also provide method and an algorithm for the computation…