📄 rotationmat3d.mht
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Date: Mon, 25 May 2009 16:51:15 +0800
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<BODY><PRE>function R=3D rotationmat3D(r,Axis)
%function R=3D rotationmat3D(radians,Axis)
%
% creates a rotation matrix such that R * x=20
% operates on x by rotating x around the origin r radians around line
% connecting the origin to the point "Axis"
%
% example:
% rotate around a random direction a random amount and then back
% the result should be an Identity matrix
%
%r =3D rand(4,1);
%rotationmat3D(r(1),[r(2),r(3),r(4)]) * =
rotationmat3D(-r(1),[r(2),r(3),r(4)])
%
% example2:=20
% rotate around z axis 45 degrees
% Rtest =3D rotationmat3D(pi/4,[0 0 1])
%
%Bileschi 2009
if nargin =3D=3D 1
if(length(rotX) =3D=3D 3)
rotY =3D rotX(2);
rotZ =3D rotZ(3);
rotX =3D rotX(1);
end
end
% useful intermediates
L =3D norm(Axis);
if (L < eps)
error('axis direction must be non-zero vector');
end
Axis =3D Axis / L;
L =3D 1;
u =3D Axis(1);
v =3D Axis(2);
w =3D Axis(3);
u2 =3D u^2;
v2 =3D v^2;
w2 =3D w^2;
c =3D cos(r);
s =3D sin(r);
%storage
R =3D nan(3);
%fill
R(1,1) =3D u2 + (v2 + w2)*c;
R(1,2) =3D u*v*(1-c) - w*s;
R(1,3) =3D u*w*(1-c) + v*s;
R(2,1) =3D u*v*(1-c) + w*s;
R(2,2) =3D v2 + (u2+w2)*c;
R(2,3) =3D v*w*(1-c) - u*s;
R(3,1) =3D u*w*(1-c) - v*s;
R(3,2) =3D v*w*(1-c)+u*s;
R(3,3) =3D w2 + (u2+v2)*c;
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