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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 [pos, zp] = planePosition(point, plane)
%PLANEPOSITION Compute position of a point on a plane.
%
% COORDS2D = planePosition(POINT, PLANE)
% POINT has format [X Y Z], and plane has format
% [X0 Y0 Z0 DX1 DY1 DZ1 DX2 DY2 DZ2], where :
% - (X0, Y0, Z0) is a point belonging to the plane
% - (DX1, DY1, DZ1) is a first direction vector
% - (DX2, DY2, DZ2) is a second direction vector
% Result COORDS2D has the form [XP YP], with XP and YP the coordinates of
% the point in the coordinate system of the plane.
%
% [COORDS2D, Z] = planePosition(POINT, PLANE)
% Also returns the coordinates along the normal of the plane. When the
% point is within the plane, this coordinate should be zero.
%
% Example
% plane = [10 20 30 1 0 0 0 1 0];
% point = [13 24 35];
% pos = planePosition(point, plane)
% pos =
% 3 4
%
% Example
% % plane with non unit direction vectors
% p0 = [30 20 10]; v1 = [2 1 0]; v2 = [-2 4 0];
% plane = [p0 v1 v2];
% pts = [p0 ; p0 + v1 ; p0 + v2 ; p0 + 3 * v1 + 2 * v2];
% pos = planePosition(pts, plane)
% pos =
% 0 0
% 1 0
% 0 1
% 3 2
%
%
% See also
% geom3d, planes3d, points3d, planePoint
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-02-21
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
% size of input arguments
npl = size(plane, 1);
npt = size(point, 1);
% check inputs have compatible sizes
if npl ~= npt && npl > 1 && npt > 1
error('geom3d:planePosition:inputSize', ...
'plane and point should have same size, or one of them must have 1 row');
end
% origin and direction vectors of the plane(s)
p0 = plane(:, 1:3);
v1 = plane(:, 4:6);
v2 = plane(:, 7:9);
% Principle
%
% for each (recentered) point, we need to solve the system:
% s * v1x + t * v2x + u * v3x = px
% s * v1y + t * v2y + u * v3y = py
% s * v1z + t * v2z + u * v3z = pz
% Assuming the point belong to the place, the value of u is 0. The last
% equation is kept only for homogeneity.
% We rewrite in matrix form:
% [ v1x v2x v3x ] [ s ] [ xp ]
% [ v1y v2y v3y ] * [ t ] = [ yp ]
% [ v1z v2z v3z ] [ u ] [ zp ]
% Or:
% A * X = B
% We need to solve X = inv(A) * B. In practice, we use the b/A notation,
% obtained after using transpositon on the A\b notation.
% X' = (inv(mat) * bsxfun(@minus, point, p0)')';
% X' = bsxfun(@minus, point, p0) * inv(mat');
% X' = bsxfun(@minus, point, p0) / mat';
% (and we compute the transpose of the basis transform)
% Compute dot products with direction vectors of the plane
if npl == 1
% we have npl == 1 and npt > 1
% build transpose of matrix that changes plane basis to global basis
mat = [v1 ; v2 ; cross(v1, v2, 2)];
tmp = bsxfun(@minus, point, p0) / mat;
pos = tmp(:, 1:2);
zp = tmp(:,3);
else
% NPL > 0 -> iterate over planes
% Number of points can be either 1, or the same number as planes
pos = zeros(npl, 2);
zp = zeros(npl, 1);
for ipl = 1:npl
mat = [v1(ipl,:) ; v2(ipl,:) ; cross(v1(ipl,:), v2(ipl,:), 2)];
% choose either point with same index, or the single point
ind = min(ipl, npt);
tmp = bsxfun(@minus, point(ind,:), p0(ipl,:)) / mat;
pos(ipl,:) = tmp(1,1:2);
zp(ipl) = tmp(1,3);
end
end
% % old version (:
% s = dot(point-p0, d1, 2) ./ vectorNorm3d(d1);
% t = dot(point-p0, d2, 2) ./ vectorNorm3d(d2);
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