Chebyshev Distance, also known as maximum metric or L-infinity distance, is a metric used in mathematics and computer science to determine the distance between two points in a multi-dimensional space. It is defined as the maximum absolute difference along any coordinate dimension.
Formally, if you have two points, P and Q, in an n-dimensional space represented as P = (p1, p2, …, pn) and Q = (q1, q2, …, qn), the Chebyshev Distance D between these two points is calculated using the following formula:
D(P, Q) = max(|pi – qi|) for i = 1 to n
This means that the distance is calculated by taking the maximum of the absolute differences of their respective coordinates. For example, in a 2D space, if two points are located at (3, 5) and (1, 2), the Chebyshev Distance would be:
D = max(|3 – 1|, |5 – 2|) = max(2, 3) = 3
Chebyshev Distance is particularly useful in various applications including robotics, game development, and data analysis, where determining the furthest distance in a grid-like layout is essential. Its simplicity and effectiveness make it a popular choice in scenarios that require quick distance measurements across multiple dimensions.