Nearest approaches to multiple lines in n-dimensional space

Leija Han and John C. Bancroft


An efficient matrix approach is described to obtain the nearest approach to nonintersecting lines in 3-dimensional or any n-dimensional spaces. By the nearest approach, we mean the nearest point(s) or vector(s) to all lines and also each on-line point or vector with respective to that nearest-to-all point(s) or vector(s) as well. The point of nearest approach on each line is also evaluated giving the nearest vector to all lines. The entire solution set can be provided by the matrix approach simultaneously, ensuring efficiency and accuracy at the same time.

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