You are viewing a plain text version of this content. The canonical link for it is here.
Posted to user@commons.apache.org by Alexander Nozik <al...@gmail.com> on 2013/07/08 14:44:29 UTC
[math] Rotation around given direction
In order to solve some Monte-Carlo problem I need to implement the
following procedure: during interaction I know the difference between
the initial and the final angle "dTheta" (the direction is random) and
the initial polar angle "theta" (using notation like here
http://en.wikipedia.org/wiki/Spherical_coordinate_system#Cartesian_coordinates).
What i need to know is the final polar angle. Azimuthal angle does not
matter.
In order to do so I am creating two vectors with polar angles "theta"
and "theta + dTheta" and trying to rotate one around the other for a
random angle "phi" (phi could be fixed as well, it does not matter).
What i don't understand is why the angle between the final vector and
the initial one is not "dTheta"?
I use the following code:
double addTheta(double theta, double dTheta) {
double phi = generator.next() * 2 * Math.PI;
SphericalCoordinates init = new SphericalCoordinates(1, 0,
theta+dTheta);
SphericalCoordinates rotate = new SphericalCoordinates(1, 0,
theta);
Rotation rot = new Rotation(rotate.getCartesian(), phi);
Vector3D result = rot.applyTo(init.getCartesian());
assert Vector3D.angle(result, init.getCartesian()) == dTheta;
return Math.acos(result.getZ());
}
Thanks in advance.
---------------------------------------------------------------------
To unsubscribe, e-mail: user-unsubscribe@commons.apache.org
For additional commands, e-mail: user-help@commons.apache.org
Re: [math] Rotation around given direction
Posted by Luc Maisonobe <Lu...@free.fr>.
Hi Alexander,
Le 08/07/2013 14:44, Alexander Nozik a écrit :
> In order to solve some Monte-Carlo problem I need to implement the
> following procedure: during interaction I know the difference between
> the initial and the final angle "dTheta" (the direction is random) and
> the initial polar angle "theta" (using notation like here
> http://en.wikipedia.org/wiki/Spherical_coordinate_system#Cartesian_coordinates).
> What i need to know is the final polar angle. Azimuthal angle does not
> matter.
> In order to do so I am creating two vectors with polar angles "theta"
> and "theta + dTheta" and trying to rotate one around the other for a
> random angle "phi" (phi could be fixed as well, it does not matter).
> What i don't understand is why the angle between the final vector and
> the initial one is not "dTheta"?
>
> I use the following code:
>
> double addTheta(double theta, double dTheta) {
> double phi = generator.next() * 2 * Math.PI;
> SphericalCoordinates init = new SphericalCoordinates(1, 0,
> theta+dTheta);
> SphericalCoordinates rotate = new SphericalCoordinates(1, 0,
> theta);
> Rotation rot = new Rotation(rotate.getCartesian(), phi);
>
> Vector3D result = rot.applyTo(init.getCartesian());
>
> assert Vector3D.angle(result, init.getCartesian()) == dTheta;
The angle that should be equalt to dTheta is the angle between result
and rotate.getCartesian(), not the angle between result and
init.getCartesian(). The latter can take any value between 0 and 2 * dTheta.
best regards,
Luc
> return Math.acos(result.getZ());
>
> }
>
> Thanks in advance.
>
> ---------------------------------------------------------------------
> To unsubscribe, e-mail: user-unsubscribe@commons.apache.org
> For additional commands, e-mail: user-help@commons.apache.org
>
>
---------------------------------------------------------------------
To unsubscribe, e-mail: user-unsubscribe@commons.apache.org
For additional commands, e-mail: user-help@commons.apache.org