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Privacy-preserving geometric intersection (PGI) is an important issue in Secure multiparty computation (SMC). The existing quantum PGI protocols are mainly based on grid coding, which requires a lot of computational complexity. The…
As drones increasingly deliver packages in neighborhoods, concerns about collisions arise. One solution is to share flight paths within a specific zip code, but this compromises business privacy by revealing delivery routes. For example, it…
Cooperative robots can significantly assist people in their productive activities, improving the quality of their works. Collision detection is vital to ensure the safe and stable operation of cooperative robots in productive activities. As…
Online planning of collision-free trajectories is a fundamental task for robotics and self-driving car applications. This paper revisits collision avoidance between ellipsoidal objects using differentiable constraints. Two ellipsoids do not…
We obtain the bifurcation of some special curves on generic 1-parameter families of surfaces in the Minkowski 3-space. The curves treated here are the locus of points where the induced pseudo metric is degenerate, the discriminant of the…
The computation of collision probability ($\mathcal{P}_c$) is crucial for space environmentalism and sustainability by providing decision-making knowledge that can prevent collisions between anthropogenic space objects. However, the…
Quantum entangled states of light are essential for quantum technologies and fundamental tests of physics. While quantum information science has relied on systems with entanglement in 2D degrees of freedom, e.g. quantum bits with…
For multi-vehicle complex traffic scenarios in shared spaces such as intelligent intersections, safe coordination and trajectory planning is challenging due to computational complexity. To meet this challenge, we introduce a computationally…
A classical inequality which is due to Lickorish and Hempel says that the distance between two curves in the curve complex can be measured by their intersection number. In this paper, we show a converse version; the intersection number of…
We present a fully distributed collision avoidance algorithm based on convex optimization for a team of mobile robots. This method addresses the practical case in which agents sense each other via measurements from noisy on-board sensors…
A multi-cube method is developed for solving systems of elliptic and hyperbolic partial differential equations numerically on manifolds with arbitrary spatial topologies. It is shown that any three-dimensional manifold can be represented as…
We consider asymmetric convex intersection testing (ACIT). Let $P \subset \mathbb{R}^d$ be a set of $n$ points and $\mathcal{H}$ a set of $n$ halfspaces in $d$ dimensions. We denote by $\text{ch}(P)$ the polytope obtained by taking the…
Movie-Map, an interactive first-person-view map that engages the user in a simulated walking experience, comprises short 360{\deg} video segments separated by traffic intersections that are seamlessly connected according to the viewer's…
We are introducing two methods for revealing the true inflection point of data that contains or not error. The starting point is a set of geometrical properties that follow the existence of an inflection point p for a smooth function. These…
Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property…
This paper presents a very simple but efficient algorithm for 3D line segment detection from large scale unorganized point cloud. Unlike traditional methods which usually extract 3D edge points first and then link them to fit for 3D line…
A polygon C is an intersecting polygon for a set O of objects in the plane if C intersects each object in O, where the polygon includes its interior. We study the problem of computing the minimum-perimeter intersecting polygon and the…
This paper uses clustering algorithms to introduce a shape framework for deformable objects. Until now, the shape detection of the deformable objects has faced several challenges: 1) unable to form a unified framework for multiple shapes;…
The increasing wireless communication capabilities of vehicles creates opportunities for more efficient intersection management strategies. One promising approach is the replacement of traffic lights with a system wherein vehicles run…
The problem of finding a point in the intersection of closed sets can be solved by the method of alternating projections and its variants. It was shown in earlier papers that for convex sets, the strategy of using quadratic programming (QP)…