Related papers: A Simple and Correct Even-Odd Algorithm for the Po…
This paper proposed a method to judge whether the point is inside or outside of the simple convex polygon by the intersection of the vertical line. It determined the point to an area enclosed by two straight lines, then convert the problem…
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,…
Plotting solution sets for particular equations may be complicated by the existence of turning points. Here we describe an algorithm which not only overcomes such problematic points, but does so in the most general of settings. Applications…
Acceleration of algorithms is becoming a crucial problem, if larger data sets are to be processed. Evaluation of algorithms is mostly done by using computational geometry approach and evaluation of computational complexity. However in…
We consider a problem in computational origami. Given a piece of paper as a convex polygon $P$ and a point $f$ located within, fold every point on a boundary of $P$ to $f$ and compute a region that is safe from folding, i.e., the region…
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…
A hole in a graph G is an induced cycle of length at least four; an antihole is a hole in the complement of G. In 2005, Chudnovsky, Cornuejols, Liu, Seymour and Vuskovic showed that it is possible to test in polynomial time whether a graph…
In this work, we designed algorithms for the point in polygon problem based on the ray casting algorithm using equations from vector geometry. The algorithms were implemented using the python programming language. We tested the algorithm…
We investigate the problem of determining if a given graph corresponds to the dual of a triangulation of a simple polygon. This is a graph recognition problem, where in our particular case we wish to recognize a graph which corresponds to…
We describe a new algorithm to compute the geometric intersection number between two curves, given as edge vectors on an ideal triangulation. Most importantly, this algorithm runs in polynomial time in the bit-size of the two edge vectors.…
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…
An odd hole in a graph is a induced cycle with odd length greater than 3. In an earlier paper (with Sophie Spirkl), solving a longstanding open problem, we gave a polynomial-time algorithm to test if a graph has an odd hole. We subsequently…
A novel method has been introduced to solve a point inclusion in a polygon problem. The method is applicable to convex as well as non-convex polygons which are not self-intersecting. The introduced method is independent of rounding off…
Let $P$ be an orthogonal polygon of $n$ vertices, without holes. The Orthogonal Polygon Covering with Squares (OPCS) problem takes as input such an orthogonal polygon $P$ with integral vertex coordinates, and asks to find the minimum number…
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…
An even (respectively, odd) hole in a graph is an induced cycle with even (respectively, odd) length that is at least four. Bienstock [DM 1991 and 1992] proved that detecting an even (respectively, odd) hole containing a given vertex is…
Determining visibility in planar polygons and arrangements is an important subroutine for many algorithms in computational geometry. In this paper, we report on new implementations, and corresponding experimental evaluations, for two…
In this paper, we give an algorithm to infer the positions of the vertices of an unknown tetrahedron, given a sample of points which are uniformly distributed within the tetrahedron. The accuracy of the algorithm is demonstrated using some…
The odd-red bipartite perfect matching problem asks to find a perfect matching containing an odd number of red edges in a given red-blue edge-colored bipartite graph. While this problem lies in $\mathsf{P}$, its polyhedral structure remains…
The manuscript presents a theoretical proof in conglomeration with new definitions on Inaccessibility and Inside for a point S related to a simple or self intersecting polygon P. The proposed analytical solution depicts a novel way of…