# Line-Line Intersection (N lines, D space)

Version 1.0.0.0 (2.86 KB) by
Find intersection of N lines in D-dimensional space, in least squares sense.
Updated 29 Oct 2016

Find intersection of N lines in D-dimensional space, in least squares sense.
X = lineXline(A,B) -line starts & ends as N*D
X = lineXline({x y..}) -lines as D long cell of starts & ends as 2*N
[X,P,R] = lineXline(..) -extra outputs
[X,P,R,x,t,l] = lineXline(..) -plot outputs
X: Intersection point, in least squares sense, as 1*D
P: Nearest point to the intersection on each line, as N*D
R: Distance from intersection to each line, as N*1
x: Intersection point X as D-long cell of coordinates {x y..}
p: Nearest points P as D-long cell of coordinates {x y..} as N*1
l: Initial lines A-to-B as D-long cell of coordinates {x y..} as 2*N

Remarks:
-Lines are assumed to be infinite in both directions.
-Finds point nearest to all lines using minimum sum of squared distances.
-For parallel lines returns an arbitrary point and a warning.
-For lines of length zero returns NaNs.

Example: (3 lines, 2 dimensions)
[X,P,R,x,p,l] = lineXline([0 0;3 0;0 4],[5 5;0 5;5 2]);
plot(x{:},'*k',p{:},'.k',l{:})
X2 = lineXline(l) %alternate input form, same results

Example: (2 lines, 3 dimensions)
[X,P,R,x,p,l] = lineXline(rand(2,3),rand(2,3));
plot3(x{:},'*k',p{:},'.k',l{:})

Example: (4 lines, 5 dimensions)
[X,P,R] = lineXline(rand(4,5),rand(4,5))

### Cite As

Serge (2024). Line-Line Intersection (N lines, D space) (https://www.mathworks.com/matlabcentral/fileexchange/59805-line-line-intersection-n-lines-d-space), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2010b
Compatible with any release
##### Platform Compatibility
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Version Published Release Notes
1.0.0.0

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Changed 5th output, minor changes