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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 mat = createRotation3dLineAngle(line, theta)
%CREATEROTATION3DLINEANGLE Create rotation around a line by an angle theta.
%
% MAT = createRotation3dLineAngle(LINE, ANGLE)
%
% Example
% origin = [1 2 3];
% direction = [4 5 6];
% line = [origin direction];
% angle = pi/3;
% rot = createRotation3dLineAngle(line, angle);
% [axis angle2] = rotation3dAxisAndAngle(rot);
% angle2
% angle2 =
% 1.0472
%
% See also
% transforms3d, rotation3dAxisAndAngle, rotation3dToEulerAngles,
% eulerAnglesToRotation3d
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2010-08-11, using Matlab 7.9.0.529 (R2009b)
% Copyright 2010-2023 INRA - Cepia Software Platform
% determine rotation center and direction
center = [0 0 0];
if size(line, 2)==6
center = line(1:3);
vector = line(4:6);
else
vector = line;
end
% normalize vector
v = normalizeVector3d(vector);
% compute projection matrix P and anti-projection matrix
P = v'*v;
Q = [0 -v(3) v(2) ; v(3) 0 -v(1) ; -v(2) v(1) 0];
I = eye(3);
% compute vectorial part of the transform
mat = eye(4);
mat(1:3, 1:3) = P + (I - P)*cos(theta) + Q*sin(theta);
% add translation coefficient
mat = recenterTransform3d(mat, center);
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