Abstract
A combinatorial algorithm to construct Largest Area Parallelogram (LAPT) inside a digital object lying on a Triangular grid is proposed in this work. An inner triangular cover (ITC) is first constructed, where the sides of ITC lies on the grid line and within the object. After the ITC is constructed, the proposed algorithm maintain few lists and a set of rules to find the LAPT. It is observed that the algorithm runs in \(O(k\cdot \frac{n}{g}\lg \frac{n}{g})\) time where n number pixel on the boundary of the digital object, g is grid size, and k is the number of convexities.
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Al Aman, M.A.A., Paul, R., Sarkar, A., Biswas, A. (2023). Largest Area Parallelogram Inside a Digital Object in a Triangular Grid. In: Barneva, R.P., Brimkov, V.E., Nordo, G. (eds) Combinatorial Image Analysis. IWCIA 2022. Lecture Notes in Computer Science, vol 13348. Springer, Cham. https://doi.org/10.1007/978-3-031-23612-9_8
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