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## Copyright (C) 2004-2011 David Legland <david.legland@grignon.inra.fr>
## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in the
## documentation and/or other materials provided with the distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
## -*- texinfo -*-
## @deftypefn {Function File} {@var{pt} =} intersectLinePlane (@var{line}, @var{plane})
## @deftypefnx {Function File} {@var{pt} =} intersectLinePlane (@dots{}, @var{tol})
## Intersection point between a 3D line and a plane
##
## PT = intersectLinePlane(LINE, PLANE)
## Returns the intersection point of the given line and the given plane.
## LINE: [x0 y0 z0 dx dy dz]
## PLANE: [x0 y0 z0 dx1 dy1 dz1 dx2 dy2 dz2]
## PT: [xi yi zi]
## If LINE and PLANE are parallel, return [NaN NaN NaN].
## If LINE (or PLANE) is a matrix with 6 (or 9) columns and N rows, result
## is an array of points with N rows and 3 columns.
##
## PT = intersectLinePlane(LINE, PLANE, TOL)
## Specifies the tolerance factor to test if a line is parallel to a
## plane. Default is 1e-14.
##
## Example
## @example
## # define horizontal plane through origin
## plane = [0 0 0 1 0 0 0 1 0];
## # intersection with a vertical line
## line = [2 3 4 0 0 1];
## intersectLinePlane(line, plane)
## ans =
## 2 3 0
## # intersection with a line "parallel" to plane
## line = [2 3 4 1 2 0];
## intersectLinePlane(line, plane)
## ans =
## NaN NaN NaN
## @end example
##
## @seealso{lines3d, planes3d, points3d, clipLine3d}
## @end deftypefn
function point = intersectLinePlane (line, plane, tol = sqrt(eps))
# unify sizes of data
nLines = size (line, 1);
nPlanes = size (plane, 1);
# N planes and M lines not allowed
if nLines ~= nPlanes && min (nLines, nPlanes) > 1
error ('Octave:invalid-input-arg', ...
'Input must have same number of rows, or one must be 1');
end
# plane normal
n = cross (plane(:,4:6), plane(:,7:9), 2);
# difference between origins of plane and line
dp = bsxfun (@minus, plane(:, 1:3), line(:, 1:3));
# dot product of line direction with plane normal
denom = sum (bsxfun (@times, n, line(:,4:6)), 2);
# relative position of intersection point on line (can be inf in case of a
# line parallel to the plane)
t = zeros (size (denom));
tf = denom != 0;
t(tf) = sum (bsxfun (@times, n, dp),2)(tf) ./ denom(tf);
# compute coord of intersection point
point = bsxfun (@plus, line(:,1:3), bsxfun (@times, [t t t], line(:,4:6)));
# set indices of line and plane which are parallel to NaN
par = abs (denom) < tol;
point(par,:) = NaN;
endfunction
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