linePosition

LINEPOSITION Position of a point on a line.

   POS = linePosition(POINT, LINE);
   Computes position of point POINT on the line LINE, relative to origin
   point and direction vector of the line.
   LINE has the form [x0 y0 dx dy],
   POINT has the form [x y], and is assumed to belong to line.

   POS = linePosition(POINT, LINES);
   If LINES is an array of NL lines, return NL positions, corresponding to
   each line.

   POS = linePosition(POINTS, LINE);
   If POINTS is an array of NP points, return NP positions, corresponding
   to each point.

   POS = linePosition(POINTS, LINES);
   If POINTS is an array of NP points and LINES is an array of NL lines,
   return an array of [NP NL] position, corresponding to each couple
   point-line.

   POS = linePosition(POINTS, LINES, 'diag');
   When POINTS and LINES have the same number of rows, computes positions
   only for couples POINTS(i,:) and LINES(i,:). The result POS is a column
   vector with as many rows as the number of points/lines.


   Example
   line = createLine([10 30], [30 90]);
   linePosition([20 60], line)
   ans =
       .5

   See also:
   lines2d, createLine, projPointOnLine, isPointOnLine

   ---------

   author : David Legland
   INRA - TPV URPOI - BIA IMASTE
   created the 25/05/2004.

0001 function pos = linePosition(point, line, varargin)
0002 %LINEPOSITION Position of a point on a line.
0003 %
0004 %   POS = linePosition(POINT, LINE);
0005 %   Computes position of point POINT on the line LINE, relative to origin
0006 %   point and direction vector of the line.
0007 %   LINE has the form [x0 y0 dx dy],
0008 %   POINT has the form [x y], and is assumed to belong to line.
0009 %
0010 %   POS = linePosition(POINT, LINES);
0011 %   If LINES is an array of NL lines, return NL positions, corresponding to
0012 %   each line.
0013 %
0014 %   POS = linePosition(POINTS, LINE);
0015 %   If POINTS is an array of NP points, return NP positions, corresponding
0016 %   to each point.
0017 %
0018 %   POS = linePosition(POINTS, LINES);
0019 %   If POINTS is an array of NP points and LINES is an array of NL lines,
0020 %   return an array of [NP NL] position, corresponding to each couple
0021 %   point-line.
0022 %
0023 %   POS = linePosition(POINTS, LINES, 'diag');
0024 %   When POINTS and LINES have the same number of rows, computes positions
0025 %   only for couples POINTS(i,:) and LINES(i,:). The result POS is a column
0026 %   vector with as many rows as the number of points/lines.
0027 %
0028 %
0029 %   Example
0030 %   line = createLine([10 30], [30 90]);
0031 %   linePosition([20 60], line)
0032 %   ans =
0033 %       .5
0034 %
0035 %   See also:
0036 %   lines2d, createLine, projPointOnLine, isPointOnLine
0037 %
0038 %   ---------
0039 %
0040 %   author : David Legland
0041 %   INRA - TPV URPOI - BIA IMASTE
0042 %   created the 25/05/2004.
0043 %
0044 
0045 %   HISTORY
0046 %   2005-07-07 manage multiple input
0047 %   2011-06-15 avoid the use of repmat when possible
0048 %   2012-10-24 rewrite using bsxfun
0049 %   2012-11-22 add support for the diag option
0050 
0051 % if diag is true, we need only to compute position of i-th point with i-th
0052 % line.
0053 diag = ~isempty(varargin) && ischar(varargin{1}) && strcmpi(varargin{1}, 'diag');
0054 
0055 if diag
0056     % In the case of 'diag' option, use direct correspondence between
0057     % points and lines
0058     
0059     % check input have same size
0060     np = size(point, 1);
0061     nl = size(line, 1);
0062     if np ~= nl
0063         error('matGeom:linePosition', ...
0064             'Using diag option, number of points and lines should be the same');
0065     end
0066     
0067     % direction vector of the lines
0068     vx = line(:, 3);
0069     vy = line(:, 4);
0070     
0071     % difference of coordinates between point and line origins
0072     dx = point(:, 1) - line(:, 1);
0073     dy = point(:, 2) - line(:, 2);
0074     
0075 else
0076     % General case -> return NP-by-NL array
0077     
0078     % direction vector of the lines
0079     vx = line(:, 3)';
0080     vy = line(:, 4)';
0081     
0082     % difference of coordinates between point and line origins
0083     dx = bsxfun(@minus, point(:, 1), line(:, 1)');
0084     dy = bsxfun(@minus, point(:, 2), line(:, 2)');
0085 
0086 end
0087 
0088 % squared norm of direction vector, with a check of validity
0089 delta = vx .* vx + vy .* vy;
0090 invalidLine = delta < eps;
0091 delta(invalidLine) = 1; 
0092 
0093 % compute position of points projected on the line, by using normalised dot
0094 % product (NP-by-NL array)
0095 pos = bsxfun(@rdivide, bsxfun(@times, dx, vx) + bsxfun(@times, dy, vy), delta);
0096 
0097 % ensure degenerated edges are correclty processed (consider the first
0098 % vertex is the closest one)
0099 if diag
0100     pos(invalidLine) = 0;
0101 else
0102     pos(:, invalidLine) = 0;
0103 end