Heading, Pitch And Roll Angles

Heading, pitch and roll angles are Tait-Bryan angles, like thos used in aeroplanes. They have many (incorrect I assume) definitions across the Web.

Tait-Bryan angles: Imagine a human standing still while looking forward.

Heading or yaw is when you start rotating left and right (with your hands), so it's a rotation around VERTICAL axis.

Pitch is when you start rotating with your arms around the axis that goes from your left ear to your right ear. (Which did rotate along when you changed your "heading").

Roll is when you tilt your head left of right after applying heading and pitch. The correct roll is when center of the screen stays in center, no matter what roll angle is applied.

Calculation:

One of the ways to calculate heading-pitch-roll is to use quaternions like:

Quat(0,0,1, roll) * Quat(1,0,0, pitch) * Quat(0,1,0, heading)

The order IS IMPORTANT. Apply roll first, then pitch, then heading.

glRotate:

Using glRotate to calculate that kind of rotation will be tricky, since after you apply roll, your x and y axes are tilted and you need to apply pitch and heading to global x and y instead of new local ones. It might be possible to apply heading first (to 0,1,0), then pitch to (1,0,0) and then roll to (0,0,1), it probably should get correct result. Although this was not tested.

Maybe a good Fortran routine does the trick better than the stuff at 3Dengine.

Cheers,

Frank

Another clue is Wikipedia. But this only gives Yaw, Pitch and Roll, not the heading.

http://en.wikipedia.org/wiki/Yaw,_pitch_and_roll

Cheers,

Frank

I'll keep looking.

Frank

Thank you for your answer Frank,

I checked your idea to consider rotation of roll than pitch than heading. And it works as I wished.

I consider a reference frame linked to the gradiometer :

x is in the longitudinal direction, counted positively in the direction of the nose of the gradiometer.

y is in the transversal direction, counted positively in the port direction.

The relation \vec{e_x} x \vec{e_y} = \vec{e_z} defines the direction of the z axes.

In terms of quaternion, I consider the product

q' = qh . qp . qr . q . qr^(- 1) . qp^(-1). qh^(-1)

where

qr = [cos(r/2) -sin(r/2) 0 0]

qp = [cos(p/2) 0 -sin(p/2) 0]

qh = [cos(h/2) 0 0 -sin(h/2)]

q = [0 vx vy vz],

[vx vy vz] are the component of some vector in the frame linked to the gradiometer,

q' = [0 vx' vy' vz'],

[vx' vy' vz'] are the components of the considered vector in the UTM reference frame.

In order to take the magnetic declination d into account, I consider h = h'+d, where h' is the measured heading.

In terms of matrix,

I consider the relation

v' = Mh . Mp . Mr . v,

where

Mr=[1 0 0;

0 cos(r) sin(r);

0 -sin(r) cos(r)],

Mp=[cos(p) 0 -sin(p);

0 1 0;

sin(p) 0 cos(p)],

Mh=[cos(h) sin(h) 0;

-sin(h) cos(h) 0;

0 0 1]

It gives the same results.