This article provides an introduction to some recent results in billiard dynamics. We present results that follow from a study of compact Riemann surfaces (equipped with a holomorphic 1-form) and an SL2R action on the moduli spaces of these surfaces. We concentrate on the progress toward classification of “optimal” billiard tables, those with the simplest trajectory structure.

this paper aims to discuss the requirements of safe and smooth trajectory planning of transporter mobile robots to perform non-prehensile object manipulation task. in non-prehensile approach, the robot and the object must keep their grasp-less contact during manipulation task. to this end, dynamic grasp concept is employed for a box manipulation task and corresponding conditions are obtained an...

background:growth is one of the most important indices in child health. the best and most effective way to investigate child health is measuring the physical growth indices such as weight, height and head circumference. among these measures, weight growth is the simplest and the most effective way to determine child growth status. weight trend at a given age is the result of cumulative growth e...

Motivated by the increasing availability of vehicle trajectory data, we propose learn-to-route, a comprehensive trajectory-based routing solution. Specifically, we first construct a graph-like structure from trajectories as the routing infrastructure. Second, we enable trajectory-based routing given an arbitrary (source, destination) pair. In the first step, given a road network and a collectio...

This paper presents an easy and efficient method to estimate the pen trajectory based on minimizing the pen movement. Given start and end vertices, the complexity of the proposed algorithm is linear. In addition, the algorithm clearly identifies alternatives that do not affect the overall length of the pen trajectory, making enough room for other criteria, e.g. vision rules, to be applied.

Excellent physical performance of soccer players is inevitable for the success of a team. Despite of this, a large-scale, quantitative analysis of the maximal speed of the players is missing due to the sensitive nature of trajectory datasets. We propose a novel method to derive the in-game speed profile of soccer players from event-based datasets, which are widely accessible. We show that eight...

This paper presents an alternative formulation for the cone-beam projections given an arbitrary source trajectory and detector orientation. This formulation leads to a new inversion formula. As a special case, the inversion formula for the spiral source trajectory is derived.

The paper describes trajectory generation algorithms based on nonlinear smoothing filters, which can be applied to kinodynamic motion planning for mobile robots in a two-dimensional or three-dimensional space. The trajectory generators operate fully online to reach a given target point according to a pursuit-based logic. The logic sets reference inputs and dynamic constraints for a set of nonli...

The need to query spatiotemporal databases that store trajectories of moving objects arises in a broad range of application domains. In this work, we focus on in-memory distance threshold queries which return all moving objects that are found within a given distance d of a fixed or moving object over a time interval. We propose algorithms to solve such queries efficiently, using an R-tree index...

In this paper, we propose a method for locating 3D position of a soccer ball from monocular image sequence of soccer games. Toward this goal, we adopted ground-model-to-image transformation together with physics-based approach that a ball follows the parabolic trajectory in the air. By using the transformation the heights of a ball can be easily calculated using simple triangular geometric rela...