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Starting with MATLAB and Exploring Its Graphics Capabilities
Published in Jamal T. Manassah, Elementary Mathematical and Computational Tools For Electrical and Computer Engineers Using Matlab®, 2017
The non-Euclidean geometry that we will consider here is the so-called Taxicab geometry (the field of expertise of most taxi drivers in checkerboard laid-out cities). The Taxicab geometry is defined through its metric (i.e., the expression for measuring distance between two points). While the Euclidean distance between two points is determined as the crow flies; in Taxicab geometry the distance is determined as the taxi drives. While not invented here — Minkowski introduced this metric in the nineteenth century — it became the staple of urban planning in New York. (In Manhattan, north of Wall Street the city is criss-crossed by avenues that run south to north and by streets that run east to west, Broadway being the important exception.)
A static relocation strategy for electric car-sharing systems in a vehicle-to-grid framework
Published in Transportation Letters, 2021
Leonardo Caggiani, Luigi Pio Prencipe, Michele Ottomanelli
We applied the proposed model to the city center of Bari (Italy), considering ns = 15 stations, as shown in Figure 2. We have divided the service area into a number of zones equal to the number of stations. We assumed a CSS user’s willingness to walk to reach a station equal to 500 m (Herrmann, Schulte, and Voß 2014). For this reason, it must be ensured that, from any point of a zone, each related station is reachable on foot via a path no longer than 500 m. Since this area of the city shows a grid configuration of its road network, the distance between two points cannot be measured along the direct path (Euclidean distance) but along the grid. For these configurations, the distances between two points can be calculated according to the Taxicab geometry (Krause 1973). To assure a walking path up to 500 meters long, from a user’s origin to the nearest CSS station and vice versa, we have defined the borders of every district making sure that each one of them falls within a taxicab circle centered in its station and having a radius of 500 m. In particular, a taxicab circle with a radius of 500 m is equivalent to a square with semi-diagonals parallel to the grid and 500 m long (Çolakoğlu and Kaya 2007).
A manhattan metric based perturb and observe maximum power point tracking algorithm for photovoltaic systems
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2022
Manhattan distance metric, also known as Taxicab geometry or L1 norm, calculates the distance between two points in a grid-shaped search space (Penazzi, Accorsi, and Manzini 2019). The Manhattan distance dm(S1, S2) between operation points S1(V1, P1) and S2(V2, P2), which is shown in Figure 5, can be defined as: