Journal of Engineering Mathematics & Statistics

Authors: Aniruddh Kulkarni, Sivnarayan Mishra, Deepender Rao, kamlesh Thakur

Abstract: Computational geometry is a fundamental area of theoretical computer science and applied mathematics that deals with the design and analysis of algorithms for solving geometric problems. These problems arise naturally in diverse fields such as computer graphics, robotics, geographic information systems, computer-aided design, wireless networks, and data analysis. Over the past few decades, computational geometry has evolved from a mainly theoretical discipline into a practical toolkit that supports modern computational systems. This paper presents a comprehensive review of computational geometry, focusing on its core concepts, classical and modern algorithms, data structures, and applications. Both exact and approximate geometric computations are discussed, along with algorithmic complexity issues. Some important problem classes such as convex hulls, nearest neighbor search, range searching, and geometric optimization are reviewed in detail. The paper also highlights recent trends and challenges in computational geometry, including high-dimensional problems and integration with machine learning. While the presentation is mostly survey-oriented, emphasis is given to intuitive explanations and practical relevance, making the paper useful for researchers and postgraduate students.

Keywords: Computational geometry, geometric algorithms, convex hull, range searching, spatial data structures