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Shortest distance between a point and a line segment

i am looking for a way to calculate the minimum distance in all cases. the problems with solutions i found are:

  1. Solutions with graphical conceptual drawings show point always on perpendicular from line segment so it's "between line segment's end points". My geometry skills are horrible so i can't verify that these solutions work in all cases.

  2. Algorithm solutions are a: with fortran or some other language i don't fully understand, b: are flagged as incomplete by people, c: calling methods/functions that are not described in any way (considered trivial).

Good example of 2 a, b and c is

Shortest distance between a point and a line segment

i have the 2D line segment as double-type co-ordinate pair (x1, y1), (x2,y2) and point as double type co-ordinate (x3,y3). C#/Java/C solutions are all appreciated.

Thanks for your answers & BR: Matti

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    I counted implementations in 6 different languages here: stackoverflow.com/questions/849211/… Commented Dec 14, 2010 at 10:45
  • @oded: which part u refer? that it's asked and answered million times? or that there's no 'how to calculate' in the beginning? as i said apologies for bad search skills but if one can't imagine the 'how to calculate' to the beginning... well. ur link is 2 help people 2 understand each other. think u understood me perfectly. Commented Dec 14, 2010 at 10:55
  • You are a. Not describing your question properly. b. Not showing us what you have tried so far. c. Not explaining where you are having difficulties. Commented Dec 14, 2010 at 10:56
  • ok. missing 'how to...' seems 2 b a problem. didn't occur 2 me at all but i ask better questions in future. Commented Dec 14, 2010 at 10:57
  • @tim: this was the link i found earlier (php/fortran). actually most of the implemetations are flagged as faulty and C# missing so didn't help a lot. Commented Dec 14, 2010 at 11:08

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Answered also Shortest distance between a point and a line segment because that gathers solutions in all languages. Answer put also here because this questions asks specifically a C# solution. This is modified from http://www.topcoder.com/tc?d1=tutorials&d2=geometry1&module=Static :

//Compute the dot product AB . BC private double DotProduct(double[] pointA, double[] pointB, double[] pointC) { double[] AB = new double[2]; double[] BC = new double[2]; AB[0] = pointB[0] - pointA[0]; AB[1] = pointB[1] - pointA[1]; BC[0] = pointC[0] - pointB[0]; BC[1] = pointC[1] - pointB[1]; double dot = AB[0] * BC[0] + AB[1] * BC[1]; return dot; } //Compute the cross product AB x AC private double CrossProduct(double[] pointA, double[] pointB, double[] pointC) { double[] AB = new double[2]; double[] AC = new double[2]; AB[0] = pointB[0] - pointA[0]; AB[1] = pointB[1] - pointA[1]; AC[0] = pointC[0] - pointA[0]; AC[1] = pointC[1] - pointA[1]; double cross = AB[0] * AC[1] - AB[1] * AC[0]; return cross; } //Compute the distance from A to B double Distance(double[] pointA, double[] pointB) { double d1 = pointA[0] - pointB[0]; double d2 = pointA[1] - pointB[1]; return Math.Sqrt(d1 * d1 + d2 * d2); } //Compute the distance from AB to C //if isSegment is true, AB is a segment, not a line. double LineToPointDistance2D(double[] pointA, double[] pointB, double[] pointC, bool isSegment) { double dist = CrossProduct(pointA, pointB, pointC) / Distance(pointA, pointB); if (isSegment) { double dot1 = DotProduct(pointA, pointB, pointC); if (dot1 > 0) return Distance(pointB, pointC); double dot2 = DotProduct(pointB, pointA, pointC); if (dot2 > 0) return Distance(pointA, pointC); } return Math.Abs(dist); }
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7 Comments

Err, which points A,B,C are the line end points and which is the actual singular point ? You should really name the vars properly, tahts why we use names and not numbers.
It's in the comments. A and B are the vertices of the line or line segment, and C is the point in question. Once you've got that it's arguably more readable with single letter variables names.
The comment for the first function says //Compute the dot product AB . AC, but it appears as if it computes the dot AB • BC. Is this a typo, or is this me not fully understanding dot products?
This is giving NaN with vertical line and colinear point.
//Compute the dot product AB . AC... should not it be AB.BC ?
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If you have line

L: A * x + B * y + C = 0

Then distance from this line to point (x1, y1) is abs(A * x1 + B * y1 + C) / sqrt(A * A + B * B). in your case if you has interval, (xa, ya); (xb, yb) you should find min( distance(x1, y1, xa, ya), distance(x1, y1, xb, yb)) then see if perpendecular from (x1, y1) to line L is on the interval, then the answer is the distance is it. otherwise min of two distances.

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