1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
|
## 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 = projPointOnLine3d(point, line)
%PROJPOINTONLINE3D Project a 3D point orthogonally onto a 3D line.
%
% PT2 = projPointOnLine3d(PT, LINE).
% Computes the (orthogonal) projection of 3D point PT onto the 3D line
% LINE.
%
% Function works also for multiple points and lines. In this case, it
% returns multiple points.
% Point PT1 is a N-by-3 array, and LINE is a N-by-6 array.
% Result PT2 is a N-by-3 array, containing coordinates of orthogonal
% projections of PT1 onto lines LINE.
%
%
% See also
% projPointOnLine, distancePointLine3d
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2012-08-23
% Copyright 2012-2023 INRA - TPV URPOI - BIA IMASTE
% direction vector of the line
vx = line(:, 4);
vy = line(:, 5);
vz = line(:, 6);
% difference of point with line origin
dx = point(:,1) - line(:,1);
dy = point(:,2) - line(:,2);
dz = point(:,3) - line(:,3);
% Position of projection on line, using dot product
delta = vx .* vx + vy .* vy + vz .* vz;
tp = (dx .* vx + dy .* vy + dz .* vz) ./ delta;
% convert position on line to cartesian coordinates
point = [line(:,1) + tp .* vx, line(:,2) + tp .* vy, line(:,3) + tp .* vz];
|
