perpVector.m

function v_perp=perpVector(point1,e_1,point2)
%finds the perpendicular vector v connecting the straight line defined by
%point1 and e_1 with point2
%
%SYNOPSIS v_perp=perpVector(point1,e_1,point2)
%
%INPUT point1, e_1 : point and UNIT vector defining the straight line
%      point2: point from which the new perpendicular vector should start
%      (all inputs can be lists of n-by-d, where d is the dimension)
%
%OUTPUT v_perp perpendicular vector from the straight line to the point
%           (norm(v_perp)=distance of the point from the line)
%
%c: 1/03 Jonas
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%============================
% TEST INPUT
%============================

[nRows1, nCols1] = size(point1);
[nRowsE, nColsE] = size(e_1);
[nRows2, nCols2] = size(point2);

if ~all([nCols1,nCols2]==nColsE)
    error('inconsistent dimensions!');
end

nEntries = max([nRows1,nRowsE,nRows2]);
if ~all([nRows1,nRowsE,nRows2]==nEntries | [nRows1,nRowsE,nRows2]==1)
    error('inconsistent number of entries')
end

if nRows1 == 1
    point1 = repmat(point1,nEntries,1);
end
if nRows2 == 1
    point2 = repmat(point2,nEntries,1);
end
if nRowsE == 1
    e_1 = repmat(e_1,nEntries,1);
end

%===============================



%===============================
% CALCULATE DISTANCE
%===============================

%vector between point1 and point2
v_temp=point2-point1;

%projection of v_temp on e_1
v_proj=(repmat(sum(v_temp.*e_1,2),1,nCols1)).*e_1;

%v_temp - the parallel projection = the perpendicular part
v_perp=v_temp-v_proj;