Related papers: Line-Torus Intersection for Ray Tracing: Alternati…
This work develops novel algorithms for high-performance networking in the presence of obstacles based on a method for communicating via ultrasonic rays reflected at the obstacles. The rays are curves determined by the variable speed of…
The development of complex component software systems can be made more manageable by first creating an abstract model and then incrementally adding details. Model transformation is an approach to add such details in a controlled way. In…
We consider the Vertex Cover problem in intersection graphs of axis-parallel rectangles on the plane. We present two algorithms: The first is an EPTAS for non-crossing rectangle families, rectangle families $\calR$ where $R_1 \setminus R_2$…
When a group acts on a set, it naturally partitions it into orbits, giving rise to orbit problems. These are natural algorithmic problems, as symmetries are central in numerous questions and structures in physics, mathematics, computer…
We study the design of robust subexponential algorithms for classical connectivity problems on intersection graphs of similarly sized fat objects in $\mathbb{R}^d$. In this setting, each vertex corresponds to a geometric object, and two…
The space complexity of functional programs is not well understood. In particular, traditional implementation techniques are tailored to time efficiency, and space efficiency induces time inefficiencies, as it prefers re-computing to…
This paper introduces a watertight technique to deal with the boundary representation of surface-surface intersection in CAD. Surfaces play an important role in today's geometric design. The mathematical model of non-uniform rational…
We investigate reading strategies for node-link diagrams that wrap around the boundaries in a flattened torus topology by examining eye tracking data recorded in a previous controlled study. Prior work showed that torus drawing affords…
Oriented object detection predicts orientation in addition to object location and bounding box. Precisely predicting orientation remains challenging due to angular periodicity, which introduces boundary discontinuity issues and symmetry…
This paper constructs (with challenging obstacles) on the three torus with its cubical decomposition: Firstly, a combinatorial graded intersection algebra (graded by the codimension) which is commutative and associative defined by…
We present efficient algorithms for detecting central and mirror symmetry for the case of algebraic curves defined by means of polynomial parametrizations. The algorithms are based on the existence of a linear relationship between two…
The aim of this paper is to present a new method of approximation of planar data set using only arcs or segments. The first problem we are trying to solve is the following: the CNC machines can work only with simple curves (arcs or…
A popular method for finding the projection onto the intersection of two closed convex subsets in Hilbert space is Dykstra's algorithm. In this paper, we provide sufficient conditions for Dykstra's algorithm to converge rapidly, in finitely…
Conical intersections are common in molecular physics and photochemistry, and are often invoked to explain observed reaction products. A conical intersection can occur when an excited electronic potential energy surface intersects with the…
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…
Finding a zero of a sum of maximally monotone operators is a fundamental problem in modern optimization and nonsmooth analysis. Assuming that resolvents of the operators are available, this problem can be tackled with the Douglas-Rachford…
We show that the detection of geometric intersection in an arbitrary representation of the mapping class group of surface implies the injectivity of that representation up to center, and vice versa. As an application, we discuss the…
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…
This paper focuses on designing a unified approach for computing the projection onto the intersection of an $\ell_1$ ball/sphere and an $\ell_2$ ball/sphere. We show that the major computational efforts of solving these problems all rely on…
By a numerical continuation method called a diagonal homotopy we can compute the intersection of two positive dimensional solution sets of polynomial systems. This paper proposes to use this diagonal homotopy as the key step in a procedure…