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## Copyright (C) 2024 David Legland
## 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.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function point = projPointOnPlane(point, plane)
%PROJPOINTONPLANE Return the orthogonal projection of a point on a plane.
%
% PT2 = projPointOnPlane(PT1, PLANE);
% Compute the (orthogonal) projection of point PT1 onto the plane PLANE,
% given as [X0 Y0 Z0 VX1 VY1 VZ1 VX2 VY2 VZ2] (origin point, first
% direction vector, second directionvector).
%
% The function is fully vectorized, in that multiple points may be
% projected onto multiple planes in a single call, returning multiple
% points. With the exception of the second dimension (where
% SIZE(PT1,2)==3, and SIZE(PLANE,2)==9), each dimension of PT1 and PLANE
% must either be equal or one, similar to the requirements of BSXFUN. In
% basic usage, point PT1 is a [N*3] array, and PLANE is a [N*9] array
% (see createPlane for details). Result PT2 is a [N*3] array, containing
% coordinates of orthogonal projections of PT1 onto planes PLANE. In
% vectorised usage, PT1 is an [N*3*M*P...] matrix, and PLANE is an
% [X*9*Y...] matrix, where (N,X), (M,Y), etc, are either equal pairs, or
% one of the two is one.
%
% See also
% planes3d, points3d, planePosition, intersectLinePlane
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-02-18
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
% Unpack the planes into origins and normals, keeping original shape
plSize = size(plane);
plSize(2) = 3;
[origins, normals] = deal(zeros(plSize));
origins(:) = plane(:,1:3,:);
normals(:) = crossProduct3d(plane(:,4:6,:), plane(:, 7:9,:));
% difference between origins of plane and point
dp = bsxfun(@minus, origins, point);
% relative position of point on normal's line
t = bsxfun(@rdivide, sum(bsxfun(@times,normals,dp),2), sum(normals.^2,2));
% add relative difference to project point back to plane
point = bsxfun(@plus, point, bsxfun(@times, t, normals));
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