Is there a function in MATLAB that calculates the shortest distance from a point to a line?

Is there a function in MATLAB that calculates the shortest distance from a point to a line?

Answer 1

[MathWorks Support Team]

The ability to automatically calculate the shortest distance from a point to a line is not available in MATLAB. To work around this, see the following function:

function d = point_to_line(pt, v1, v2)

      a = v1 - v2;

      b = pt - v2;

      d = norm(cross(a,b)) / norm(a);

In this function, pt, v1, and v2 are the three-dimensional coordinates of the point, one vertex on the line, and a second vertex on the line, respectively. The following example illustrates how this function would be called:

v1 = [0,0,0];

v2 = [3,0,0];

pt = [0,5,0];

distance = point_to_line(pt,v1,v2)

[Rik]

There is a difference between a line and a line segment. What you need to do is calculate the distance to the end points as well, and only use the distance to the line if the max of the end point distances is smaller than the length of the line segment.

Answer 2

[Rik]

You can modify the staff answer with the code below to make it support a point cloud. I added input checks to this and uploaded it to the FEX.

function d = point_to_line(pt, v1, v2)
% pt should be nx3
% v1 and v2 are vertices on the line (each 1x3)
% d is a nx1 vector with the orthogonal distances
v1 = repmat(v1,size(pt,1),1);
v2 = repmat(v2,size(pt,1),1);
a = v1 - v2;
b = pt - v2;
d = sqrt(sum(cross(a,b,2).^2,2)) ./ sqrt(sum(a.^2,2));

[Rik]

Sure. What is the exact code you used? I also uploaded this (with some input checking) to the File Exchange, so that should give you an understandable error.