Author(s): Dr. João Rafael Costa

Abstract: The efficient computation of circular curve elements that pass through multiple points is essential in various applications, including civil engineering, computer graphics, and robotics. This paper explores the utilization of the Cosine Theorem as a mathematical tool for accurately determining the geometric properties of circular curves. By applying the Cosine Theorem, we can efficiently calculate the radius and central angles of a circle that passes through three non-collinear points. This approach simplifies the computation process, reduces the need for iterative methods, and enhances both accuracy and computational efficiency. The method is particularly valuable in real-time applications and is applicable across a wide range of fields, from infrastructure design to path planning in robotics. The results demonstrate that the Cosine Theorem provides a reliable and practical solution for generating circular curves that meet specific design criteria, ensuring the integrity and safety of various systems. As technology advances, the integration of such mathematical techniques will continue to play a critical role in precision engineering and other disciplines.

Pages: 24-26 | Views: 25 | Downloads: 12

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