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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 [box3d, rotMat] = orientedBox3d(pts)
%ORIENTEDBOX3D Object-oriented bounding box of a set of 3D points.
%
% OOBB = orientedBox3d(PTS)
% REturns the oriented bounding box of the collection of points in the
% N-by-3 array PTS. The result is given as:
% [XC YC ZC L W H PHI THETA PSI]
% where (XC,YC,ZC) corresponds to the center of the box, (L,W,H)
% corresponds to the length, width, and depth of the box, and (PHI,
% THETA, PSI) is the orientation of the box as Euler angles.
%
% [OOBB, ROT] = orientedBox3d(PTS)
% Also returns the rotation matrix of the point cloud, as a 3-by-3
% numeric array.
%
% Example
% [v, f] = sphereMesh;
% phi=-360+720*rand; theta=-360+720*rand; psi=-360+720*rand;
% angles = [phi, theta, psi];
% rotMat = eulerAnglesToRotation3d(angles);
% rotMat(1:3,4) = randi([-100,100],3,1);
% scale = [randi([7,9],1,1), randi([4,6],1,1), randi([1,3],1,1)];
% pts = transformPoint3d(bsxfun(@times, v, scale), rotMat);
% box3d = orientedBox3d(pts);
% figure; drawPoint3d(pts, '.');
% axis equal; xlabel('x'); ylabel('y'); zlabel('z');
% drawCuboid(box3d, 'FaceColor', 'none');
%
% See also
% meshes3d, drawCuboid, rotation3dToEulerAngles
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2015-12-01, using Matlab 8.6.0.267246 (R2015b)
% Copyright 2015-2023 INRA - Cepia Software Platform
tri = convhulln(pts);
nFaces = size(tri, 1);
%% identify index of face with smallest width
indMinBreadth = 0;
minBreadth = Inf;
for iFace = 1:nFaces
faceInds = tri(iFace, :);
plane = createPlane(pts(faceInds, :));
breadth = max(abs(distancePointPlane(pts, plane)));
if breadth < minBreadth
minBreadth = breadth;
indMinBreadth = iFace;
end
end
% compute projection on reference plane
refPlane = createPlane(pts(tri(indMinBreadth, :), :));
pts2d = planePosition(projPointOnPlane(pts, refPlane), refPlane);
% compute 2D OOBB for projected points
box2d = orientedBox(pts2d);
% extract reference points from planar OOBB: the center, and two direction
% vectors
center2d = box2d(1:2);
L1 = box2d(3);
L2 = box2d(4);
markers2d = [0 0; L1/2 0; 0 L2/2];
% orient reference points to 2d basis
theta2d = box2d(5);
rot = createRotation(deg2rad(theta2d));
tra = createTranslation(center2d);
transfo = tra * rot;
markers2d = transformPoint(markers2d, transfo);
% backprojection to 3D space
markers3d = planePoint(refPlane, markers2d);
% compute 3D vectors and center
centerProj = markers3d(1,:);
v1n = normalizeVector3d(markers3d(2,:) - centerProj);
v2n = normalizeVector3d(markers3d(3,:) - centerProj);
% compute rotation matrix and convert to Euler Angles
v3n = crossProduct3d(v1n, v2n);
rotMat = [v1n' v2n' v3n'];
boxAngles = rotation3dToEulerAngles(rotMat);
% create 3D object-oriented bounding box
boxCenter3d = centerProj + v3n * minBreadth/2;
box3d = [boxCenter3d L1 L2 minBreadth boxAngles];
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