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
67
68
69
70
71
72
73
74
75
76
77
78
|
## 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 = intersectThreePlanes(plane1, plane2, plane3)
%INTERSECTTHREEPLANES Return intersection point between 3 planes in space.
%
% LINE = intersectThreePlanes(PLANE1, PLANE2, PLANE3)
% Returns the point or straight line belonging to three planes.
% PLANE: [x0 y0 z0 dx1 dy1 dz1 dx2 dy2 dz2]
% POINT: [x0 y0 z0]
% IF rank of the coefficient matrix r1 = 3 and
% Rank of the augmented matrix r2 = 3 return point
% Otherwise returns point with NaN values.
%
% See also
% planes3d, intersectPlanes, intersectLinePlane
% ------
% Author: Roozbeh Geraili Mikola
% E-mail: roozbehg@berkeley.edu or roozbehg@live.com
% Created: 2017-09-20
% Copyright 2017-2023
% plane normal
n1 = normalizeVector3d(cross(plane1(:,4:6), plane1(:, 7:9), 2));
n2 = normalizeVector3d(cross(plane2(:,4:6), plane2(:, 7:9), 2));
n3 = normalizeVector3d(cross(plane3(:,4:6), plane3(:, 7:9), 2));
% Uses Hessian form, ie : N.p = d
% I this case, d can be found as : -N.p0, when N is normalized
d1 = dot(n1, plane1(:,1:3), 2);
d2 = dot(n2, plane2(:,1:3), 2);
d3 = dot(n3, plane3(:,1:3), 2);
% create coefficient and augmented matrices
A = [n1;n2;n3];
D = [d1;d2;d3];
AD = [n1,d1;n2,d2;n3,d3];
% calculate rank of the coefficient and augmented matrices
r1 = rank(A);
r2 = rank(AD);
% if rank of the coefficient matrix r1 = 3 and
% rank of the augmented matrix r2 = 3 return point
% and if r1 = 2 and r2 = 2 return line,
% otherwise returns point with NaN values.
if r1 == 3 && r2 == 3
% Intersecting at a point
point = (A\D)';
else
point = [NaN NaN NaN];
end
|
