We present a method for detecting collisions between a system of spherical particles and an environment composed of triangles. The proposed algorithm takes into account the particles’ volume and is based on an intersection test between a triangle and a cylinder with spherical caps (the trajectory of a particle). The algorithm also efficiently calculates a close estimate of the point of intersec...

The triangle-to-triangle intersection test is a basic component of all collision detection data structures and algorithms. This paper presents a fast method for testing whether two triangles embedded in three dimensions intersect. Our technique solves the basic sets of linear equations associated with the problem and exploits the strong relations between these sets to speed up their solution. M...

In this article we present an algorithm to determine the intersection between rays and triangles based on the idea of the study of signs with respect to triangles. One of the advantages of this approach is its robustness due to its lack of trigonometric operations or complex divisions which might alter the result of the calculations. The algorithm is similar (or even better) in time to other ex...

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...

We present an efficient algorithm for triangle–triangle intersection test in oriented bounding box (OBB)-based collision detection. In testing two OBB leaf nodes (i.e., rectangles), many intermediate computation results can be reused for the intersection test of two triangles they contain. It is considerably easier to detect redundant operations when we work in the local coordinate of the bound...

abstract let ‎g=(v,e) ‎be a‎ ‎simple ‎connected ‎graph ‎with ‎vertex ‎set ‎v‎‎‎ ‎and ‎edge ‎set ‎‎‎e. ‎the szeged index ‎of ‎‎g is defined by ‎ where ‎ respectively ‎ ‎ is the number of vertices of ‎g ‎closer to ‎u‎ (‎‎respectively v)‎ ‎‎than ‎‎‎v (‎‎respectively u‎).‎ ‎‎if ‎‎‎‎s ‎is a‎ ‎set ‎of ‎size‎ ‎ ‎ ‎let ‎‎v ‎be ‎the ‎set ‎of ‎all ‎subsets ‎of ‎‎s ‎of ‎size ‎3. ‎then ‎we ‎define ‎three ‎...

At intersection, accidents often happen due to the complexity of traffic flow. The rapid development autonomous driving technology helps alleviate this problem. However, few test scenarios at intersection are involved in current standards and regulations. This paper analyzes typical conflict forms distribution laws flow proposes an regulation consisting 28 with their specific evaluation methods...

, for t ∈ R. (1) The line lab is the set of parameterizations of the rotations of R 2 that take a to b. We consider the set of n lines L = {lab : a, b ∈ P}. (2) To prove that P determines Ω(n/ log n) distinct distances, it suffices to prove that the number of pairs of intersecting lines in L is O(n logn). Let Nk denote the number of points in R that are incident to exactly k lines of L, and let...