Related papers: Clipping and Intersection Algorithms: Short Survey…

Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…

Most previous bounding-box-based segmentation methods assume the bounding box tightly covers the object of interest. However it is common that a rectangle input could be too large or too small. In this paper, we propose a novel segmentation…

We estimate from below the number of lines meeting each of given 4 disjoint smooth closed curves in a given cyclic order in the real projective 3-space and in a given linear order in the Euclidean 3-space. Similarly, we estimate the number…

The Euclidean shortest path problem (ESPP) is a well studied problem with many practical applications. Recently a new efficient online approach to this problem, RayScan, has been developed, based on ray shooting and polygon scanning. In…

Given two curves in $\PP^3$, either implicitly or by a parameterization, we want to check if they intersect. For that purpose, we present and further develop generalized resultant techniques. Our aim is to provide a closed formula in the…

This paper is devoted to presenting a new approach to determine the intersection of two quadrics based on the detailed analysis of its projection in the plane (the so called cutcurve) allowing to perform the corresponding lifting correctly.…

We study effective versions of unlikely intersections of images of torsion points of elliptic curves on the projective line.

We study the family of intersection graphs of low density objects in low dimensional Euclidean space. This family is quite general, and includes planar graphs. We prove that such graphs have small separators. Next, we present efficient…

We consider approximations for computing minimum weighted cuts in directed graphs. We consider both rooted and global minimum cuts, and both edge-cuts and vertex-cuts. For these problems we give randomized Monte Carlo algorithms that…

In this paper, we explore an open research problem concerning the reconstruction of 3D scenes from images. Recent methods have adopt 3D Gaussian Splatting (3DGS) to produce 3D scenes due to its efficient training process. However, these…

This paper describes the adaptation of a well-scaling parallel algorithm for computing Morse-Smale segmentations based on path compression to a distributed computational setting. Additionally, we extend the algorithm to efficiently compute…

We present robust algorithms for set operations and Euclidean transformations of curved shapes in the plane using approximate geometric primitives. We use a refinement algorithm to ensure consistency. Its computational complexity is…

This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three…

This paper considers an extension of origami geometry to the case of "folding" a three dimensional (3D) space along a plane. First, all possible incidence constraints between given points, lines and planes are analyzed by using the geometry…

Performing link prediction using knowledge graph embedding models has become a popular approach for knowledge graph completion. Such models employ a transformation function that maps nodes via edges into a vector space in order to measure…

Learning-based methods have become increasingly popular for solving vehicle routing problems due to their near-optimal performance and fast inference speed. Among them, the combination of deep reinforcement learning and graph representation…

A basic and an improved ear clipping based algorithm for triangulating simple polygons and polygons with holes are presented. In the basic version, the ear with smallest interior angle is always selected to be cut in order to create fewer…

Network embedding techniques aim at representing structural properties of graphs in geometric space. Those representations are considered useful in downstream tasks such as link prediction and clustering. However, the number of graph…

We study shortest paths and their distances on a subset of a Euclidean space, and their approximation by their equivalents in a neighborhood graph defined on a sample from that subset. In particular, we recover and extend the results of…

Motivated by hypergraph decomposition algorithms, we introduce the notion of edge-induced vertex-cuts and compare it with the well-known notions of edge-cuts and vertex-cuts. We investigate the complexity of computing minimum edge-induced…