Distance between a point and a triangle in 3D

pointTriangleDistance calculates the distance between a point and a triangle in 3D.

Description

Calculate the distance of a given point P from a triangle TRI.
Point P is a row vector of the form 1x3. The triangle is a matrix
 formed by three rows of points TRI = [P1;P2;P3] each of size 1x3.
 dist = pointTriangleDistance(TRI,P) returns the distance of the point P to the triangle TRI.
 [dist,PP0] = pointTriangleDistance(TRI,P) additionally returns the closest point PP0 to P on the triangle TRI.

• MATLAB release: MATLAB 7.0.4 (R14SP2)

[creek]

Good work.

[Thomas O'Shea]

 

[jixian]

good job,thank you, i learn a lot.

[Gordon]

Very nice, and faster than my implementation. However, there's an error somewhere in there. Try plugging the following triangle and point in:

tri=[-0.351987256452018,-2.20321765626083,2.02537449847930;-1.63376366769586,1.51438594345573,0.862041724660671;-0.688413485634898,-1.58953522933881,-1.14541245917166];
p=[1.38048000996529,3.61393939643154,3.46074586955261];

[tridist,tripoint]=pointTriangleDistance(tri,p);
tridist
norm(p-tripoint)

output:
tridist =
    6.1630
ans =
    4.4997

But tridist should be the same as the norm from the initial point to the closest point (output from the function as PP0). Plotting it, it looks like PP0 is getting to the right spot, so there must be an issue with that particular path through the code. Notice that if you truncate the values I gave above, the correct answer is reached (i.e. if you only use 4 places past the decimal).

Using R2010a