function [Ind,AlongDist,NormDist] = DistanceToLineSegment(p, A, B,tolerance)

Determines if a point p is close to a line segment defined by the end points A and B.

Also calculates normal and along distances from a point to a line segment.

There are two input formats:

[Ind,AlongDist,NormDist] = DistanceToLineSegment(p, A, B,tolerance)

where A and B define the end points of a line segment, and

[Ind,AlongDist,NormDist] = DistanceToLineSegment(p, coo , [],tolerance)

where coo is a vector defining the end points of individual connected line segments.

A point is considered to be on a line segment if:

Usefull to determine if point p is on or close to the line segment B-A and to find all nodal points along the boundary defined by the pairwise joining of points in A and B.

Inputs:

p : Nx2 matrix of points

A , B : Mx2 matrix defining start and end points of M line segments.

coo : Mx2 matrix defining the (x,y) coordinates of connected line segments.

Outputs:

Ind : all points in p that are within tolerance to any of the line segments.

The AlongDist and NormDist are min distances along and normal to the orientation of any of the line segments. (The AlongDist is normalized.)

Resonably fast if number of elements in p much greate than in A and B, i.e if many more points in the array p than there are number of line segments (points in A and B).

Example:

p=[3 0 ; 0 0 ] ; a=[1 0] ; b=[5 0]; tolerance=0.1;
[Ind,AlongDist,NormDist] = DistanceToLineSegment(p, a, b,tolerance)

Example: if xx and yy are vectors defining (x,y) locations, I can find all boundary nodes that are along the line segments joining (x,y) in the following manner:

[Ind,AlongDist,NormDist] = DistanceToLineSegment([x(Boundary.Nodes) y(Boundary.Nodes)],[xx(:) yy(:)],[],tolerance);

Boundary.Nodes(Ind) now gives me the nodal numbers of all nodes along the boundary defined by the line segments

Example:

p=[0 0 ; 0.5 0  ; 1 0 ; 1.5 0 ] ; coo=[0 0 ; 1 0 ] ; tolerance=0.1 ;
Ind = DistanceToLineSegment(p, coo, [],tolerance)

gives Ind=[1 ; 2 ; 3]

    if nargin<3 || isempty(B)
        B=[A(2:end,1) A(2:end,2)];
        A=[A(1:end-1,1) A(1:end-1,2)] ;
    end

    if nargin<4 ; tolerance=eps ; end;

    M=size(A,1);
    N=size(p,1);
    AlongDist=zeros(N,1)+Inf;
    NormDist=zeros(N,1)+Inf;


    Ind=[];
    for J=1:M
        a=A(J,:) ; b=B(J,:) ;

        d=b-a;
        l=norm(d);

        f(1)=d(2) ; f(2)=-d(1);
        e=p;
        e(:,1)=p(:,1)-a(1);
        e(:,2)=p(:,2)-a(2);

        dalong=e*d'/l^2      ;  % normalized distance, if point p within the `transverse' strip to b-a, then 0<AlongDist<1
        dnorm=abs(e*f'/l)   ;   % absolute distance normal to b-a

        Ind=[Ind;find(dalong>=-tolerance & dalong<=1+tolerance &  dnorm<=tolerance)];

        AlongDist=min(AlongDist,dalong);
        NormDist=min(NormDist,dnorm);


    end

    Ind=unique(Ind);

end

Published with MATLAB® R2016b