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Highway Safety of Smart Cities
Published in Ricardo Armentano, Robin Singh Bhadoria, Parag Chatterjee, Ganesh Chandra Deka, The Internet of Things, 2017
To find the convex shape with the minimal area containing all accidents (all of them have to be inside the shape or in the contour/edge of the shape). If this polygon is known, it is possible to calculate its area using the Shoelace formula (also known as the Gauss area formula) that requires only the appropriate sequence of the two-dimensional edges. The outer points of the polygon must be in a given order (e.g., in a clockwise direction).
Integrating building shape optimization into the architectural design process
Published in Architectural Science Review, 2020
Aram Yeretzian, Hmayag Partamian, Mayssa Dabaghi, Rabih Jabr
To ensure that the total usable interior area is kept constant, the total area of the floors is fixed. Since the floors can be treated as polygons, the area of each floor is defined by the Shoelace Formula given by where and .
Coupling of approximate convection diffusion wave method with ultrasonic sensor to estimate discharge in Himalayan Rivers
Published in ISH Journal of Hydraulic Engineering, 2023
Kirtan Adhikari, Chokey Yoezer, Jit Bahadur Mongar, Sangpo Tamang, Tenzin Phuentsh, Tshering Tashi
Natural river sections are highly irregular and thus complicates the computation of hydraulic properties. However, considering a river cross-section bounded by a water surface as a polygon and employing the shoelace algorithm eases the computation and it can potentially replace the earlier stated method elegantly. In this study, the channel cross-sectional data was obtained through a topographic survey using a total station. Let be the actual stations obtained through topographic survey and let be the corresponding elevations. The area of the polygon formed within the water surface is computed viz Shoelace formula Equation 13 and the wetted perimeter Equation 14 is computed employing coordinate geometry distance formula. Where the first and the last coordinates () and () in Figure 1(1) are obtained through linear interpolation of front and rear stations, respectively. Accordingly, the hydraulic properties are computed corresponding to different flow depths. Since the flow depth bears a unique relationship with the geometric properties of the channel section, it is convenient to associate the cross-sectional geometrical properties with the flow depth (). Flow depth and the stage is used interchangeably in this article. It represents the depth of water measured from an arbitrary datum at a particular instant.