RE: [Algorithms] D3DXQuaternionRotationYawPitchRoll

[Oscar C. <osc...@cr...>]

Ignacio has already answered this question, but IMHO it deserves some =
more
attention.

>This heavily depends on the order that you apply the rotations.

IIRC, confusing factors also include handedness of matrices (left- or
right-hand rule), handedness of rotations (left- or right-hand grip =
rule),
where we measure an angle from and exactly what we mean by up :-)

As Ignacio says, it's trivial to build a quat from an axis+angle pair =
but
deciding which axis we want is the awkward part. Having decided what =
rules
to use, the code falls out of some basic trig - just like back in the =
day,
before all these new fangled matrices and quats.

By way of example...

Lets say I'm standing at the origin looking forward along the z axis, =
the y
axis is pointing up and the x axis to my right.

If I now move to look straight down at the xz plane (x pointing right, =
z
pointing up), my unrotated unit axis is pointing straight up with the =
global
vector [ 0 , 0 , 1 ].=20

I'm going to apply yaw about the local y axis using the right-hand grip
rule, so this vector will rotate counter-clockwise as I view it. My new =
unit
yaw vector is [ -sin(yaw) , 0 , cos(yaw) ].

Next I want to apply pitch about the local x axis, so I move to view =
the
plane formed by my yaw axis pointing right and the global y axis =
pointing
up. Moving counter-clockwise again, my yaw-pitch vector becomes [
-sin(yaw)cos(pitch) , sin(pitch) , cos(yaw)cos(pitch) ].

This vector can now be used as the axis, together with roll as the =
angle, to
a standard function that creates a quat from and angle+axis pair (using =
the
right-hand grip rule, of course :-)


-----Original Message-----
From: Ignacio Castano [mailto:cas...@ya...]
Sent: Friday, January 10, 2003 2:32 PM
To: gda...@li...
Subject: Re: [Algorithms] D3DXQuaternionRotationYawPitchRoll


Wolfgang Engel wrote:
> There is a Direct3D utility function, that creates a quaternion out =
from
yaw, pitch and roll to build up a quaternion as an axis-angle =
representation
of angular displacement.
> There are some open source implementations of this function in the
internet. I would like to understand how the quaternion is created in =
these
functions. I wasn't successful by looking into the source. Any hint =
would be
very much appreciated.

You can do this using the yaw and pitch to build an axis and using the =
roll
as the angle around that axis.
This heavily depends on the order that you apply the rotations.


Ignacio Casta=F1o
cas...@ya...