CURDIS:A template for incremental curve discretization algorithms and its application to conics

We introduce CURDIS,a template for algorithms to discretize arcs of regular curves by incrementally producing a list of support pixels covering the arc.In this template,algorithms proceed by finding the tangent quadrant at each point of the arc and determining which side the curve exits the pixel according to a tailored criterion.These two elements can be adapted for any type of curve,leading to algorithms dedicated to the shape of specific curves.While the calculation of the tangent quadrant for various curves,such as lines,conics,or cubics,is simple,it is more complex to analyze how pixels are traversed by the curve.In the case of conic arcs,we found a criterion for determining the pixel exit side.This leads us to present a new algorithm,called CURDIS-C,specific to the discretization of conics,for which we provide all the details.Surprisingly,the criterion for conics requires between one and three sign tests and four additions per pixel,making the algorithm efficient for resource-constrained systems and feasible for fixed-point or integer arithmetic implementations.Our algorithm also perfectly handles the pathological cases in which the conic intersects a pixel twice or changes quadrants multiple times within this pixel,achieving this generality at the cost of potentially computing up to two square roots per arc.We illustrate the use of CURDIS for the discretization of different curves,such as ellipses,hyperbolas,and parabolas,even when they degenerate into lines or corners.

Gym-ANM: Reinforcement learning environments for active network management tasks in electricity distribution systems

Active network management(ANM)of electricity distribution networks include many complex stochastic sequential optimization problems.These problems need to be solved for integrating renewable energies and distributed storage into future electrical grids.In this work,we introduce Gym-ANM,a framework for designing reinforcement learning(RL)environments that model ANM tasks in electricity distribution networks.These environments provide new playgrounds for RL research in the management of electricity networks that do not require an extensive knowledge of the underlying dynamics of such systems.Along with this work,we are releasing an implementation of an introductory toy-environment,ANM6-Easy,designed to emphasize common challenges in ANM.We also show that state-of-the-art RL algorithms can already achieve good performance on ANM6-Easy when compared against a model predictive control(MPC)approach.Finally,we provide guidelines to create new Gym-ANM environments differing in terms of(a)the distribution network topology and param-eters,(b)the observation space,(c)the modeling of the stochastic processes present in the system,and(d)a set of hyperparameters influencing the reward signal.Gym-ANM can be downloaded at https://github.com/robinhenr y/gym-anm.