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Summer Research Fellowship Programme of India's Science Academies

Comparative Analysis of the Conventional and Modified Triangular Prism Methods

Pooja A

Department of Civil Engineering, College of Engineering Guindy, Anna University, Chennai - 600 025

Prof Madhavi Latha G

Department of Civil Engineering, Indian Institute of Science, Bengaluru - 560 012

Abstract

The computation of the area of an irregular or undulated surface can be performed using the triangular prism method. Triangular prism method consists of discretising the surface into grid elements, calculating the grid surface area by dividing it into triangular prisms and adding up the areas to estimate the surface area of a grid element. The areas of all the grid elements are added together to get the entire surface area. Initially, the triangular prism had a number of limitations but now has been developed step by step over time. The modifications started from the two triangles concept that recommends the division of a grid element into two triangles instead of four triangles. The factor concept highlighted the basic logic behind the grid factors which would calculate the entire surface area without leaving out some rows and columns. The eight pixel algorithm used all real values of a grid rather than the calculated average used in the other methods. The fourcorner modified triangular prism method aids in calculating area for all grid sizes by adding up the cover contribution from each corner of the matrix. Due to the modifications, the limitations of the triangular prism method have reduced gradually, making it effective in its usage for applications that demand accuracy, precision and reliability. MATLAB code was developed for the different methods and a comparison of the results was performed.

‚ÄčKeywords: triangular prism method, MATLAB, modified triangular prism method

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