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
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
|
## 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 poly = clipPlane(plane, box)
%CLIPPLANE Compute the 3D polygon representing a clipped plane.
%
% POLY = clipPlane(PLANE, BOUNDS)
% Computes the vertices of the 3D polygon that represents the result of
% the clipping of the plane by the given BOUNDS.
% PLANE is given as [X0 Y0 Z0 DX1 DY1 DZ1 DX2 DY2 DZ2],
% BOUNDS is given as [XMIN XMAX YMIN YMAX ZMIN ZMAX].
% The result POLY is given as N-by-3 numeric array representing the
% coordinates of the polygon, or an emptyarray if the plane lies totally
% outside of the bounds.
%
%
% Example
% plane = [5 5 5 1 0 0 0 1 0];
% bounds = [0 10 0 10 0 10];
% poly = clipPlane(plane, bounds)
% poly =
% 0 0 5
% 10 0 5
% 10 10 5
% 0 10 5
%
% See also
% planes3d, createPlane, drawPlane3d
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2021-11-09, using Matlab 9.10.0.1684407 (R2021a) Update 3
% Copyright 2021-2023 INRAE - BIA Research Unit - BIBS Platform (Nantes)
% retrieve min/max coords
xmin = box(1);
xmax = box(2);
ymin = box(3);
ymax = box(4);
zmin = box(5);
zmax = box(6);
% create lines corresponding to the edges of the bounding box
lineX00 = [xmin ymin zmin 1 0 0];
lineX01 = [xmin ymin zmax 1 0 0];
lineX10 = [xmin ymax zmin 1 0 0];
lineX11 = [xmin ymax zmax 1 0 0];
lineY00 = [xmin ymin zmin 0 1 0];
lineY01 = [xmin ymin zmax 0 1 0];
lineY10 = [xmax ymin zmin 0 1 0];
lineY11 = [xmax ymin zmax 0 1 0];
lineZ00 = [xmin ymin zmin 0 0 1];
lineZ01 = [xmin ymax zmin 0 0 1];
lineZ10 = [xmax ymin zmin 0 0 1];
lineZ11 = [xmax ymax zmin 0 0 1];
% compute intersection point with each line
piX00 = intersectLinePlane(lineX00, plane);
piX01 = intersectLinePlane(lineX01, plane);
piX10 = intersectLinePlane(lineX10, plane);
piX11 = intersectLinePlane(lineX11, plane);
piY00 = intersectLinePlane(lineY00, plane);
piY01 = intersectLinePlane(lineY01, plane);
piY10 = intersectLinePlane(lineY10, plane);
piY11 = intersectLinePlane(lineY11, plane);
piZ00 = intersectLinePlane(lineZ00, plane);
piZ01 = intersectLinePlane(lineZ01, plane);
piZ10 = intersectLinePlane(lineZ10, plane);
piZ11 = intersectLinePlane(lineZ11, plane);
% concatenate points into one array
points = [...
piX00;piX01;piX10;piX11; ...
piY00;piY01;piY10;piY11; ...
piZ00;piZ01;piZ10;piZ11;];
% check validity: keep only points inside window (with tolerance)
ac = sqrt (eps);
ivx = points(:,1) >= xmin-ac & points(:,1) <= xmax+ac;
ivy = points(:,2) >= ymin-ac & points(:,2) <= ymax+ac;
ivz = points(:,3) >= zmin-ac & points(:,3) <= zmax+ac;
valid = ivx & ivy & ivz;
points = unique(points(valid, :), 'rows');
% If there is no intersection point, escape.
if size(points, 1) < 3
poly = [];
return;
end
% the two spanning lines of the plane
d1 = plane(:, [1:3 4:6]);
d2 = plane(:, [1:3 7:9]);
% position of intersection points in plane coordinates
u1 = linePosition3d(points, d1);
u2 = linePosition3d(points, d2);
% reorder vertices in the correct order
inds = convhull(u1, u2);
inds = inds(1:end-1);
% return the set of points that compose the polygon
poly = points(inds, :);
|
