An efficient algorithm to determine the intersection status between arbitrarily oriented ellipsoids and boxes (OBBs) is presented. By choosing a proper representation of the geometric objects and by utilizing an affine transformation of space, the problem is converted into a corresponding sphere-parallelepiped intersection test. Thereby, the evaluation of more costly mathematical operations oth...

This paper presents a method, along with some optimizations, for computing whether or not two triangles intersect. The code, which is shown to be fast, can be used in, for example, collision detection algorithms.

This paper proposes a new panel unit root test based on Simes’ [Biometrika 1986, “An Improved Bonferroni Procedure for Multiple Tests of Significance”] classical intersection test. The test is robust to general patterns of cross-sectional dependence and yet straightforward to implement, only requiring p-values of time series unit root tests of the series in the panel, and no resampling. Monte C...

This paper addresses the problem of obtaining a consistent estimate (or upper bound) of the covariance matrix when combining two quantities with unknown correlation. The combination is defined linearly with two gains. When the gains are chosen a priori, a family of consistent estimates is presented in the paper. The member in this family having minimal trace is said to be “family-optimal”. When...

We explore the geometry linking the shape of a curved mirror surface to the distortions it produces on a scene it reflects. Our analysis is local and differential. We assume a simple calibrated scene composed of lines passing through a point. We demonstrate that local information about the geometry of the surface may be recovered up to the second order from either the orientation and curvature ...

‎let $r$ be a commutative ring with non-zero identity. ‎we describe all $c_3$‎- ‎and $c_4$-free intersection graph of non-trivial ideals of $r$ as well as $c_n$-free intersection graph when $r$ is a reduced ring. ‎also, ‎we shall describe all complete, ‎regular and $n$-claw-free intersection graphs. ‎finally, ‎we shall prove that almost all artin rings $r$ have hamiltonian intersection graphs. ...

A proper non-empty subset C of the points of a linear space S = (P; L) is called line-closed if any two intersecting lines of S , each meeting C at least twice, have their intersection in C. We show that when every line has k points and every point lies on r lines the maximum size for such sets is r + k ? 2. In addition it is shown that this cannot happen for projective spaces PG(n; q) unless q...

Abstract A local ring R is regular if and only every finitely generated -module has finite projective dimension. Moreover, the residue field k a test module: This characterization can be extended to bounded derived category $\mathsf {D}^{\mathsf f}(R)$ , which contains small objects regular. Recent results of Pollitz, completing work initiated by Dwyer–Greenlees–Iyengar, yield an analogous for ...

The station location problem consists of placing new stations along the railway tracks of an existing network in order to increase the number of users. In this paper we consider the problem for a railway network consisting of two intersecting lines forming an angle α. An approach for solving the problem in polynomial time for sufficiently large angles α is presented.