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Interesting Yaw, Pitch, Roll Problem

  • To: mathgroup at
  • Subject: [mg19142] Interesting Yaw, Pitch, Roll Problem
  • From: Robert Milharèiè <robert.m at>
  • Date: Thu, 5 Aug 1999 23:58:45 -0400
  • Organization: S-Net Ltd, Ljubljana, Slovenia
  • Sender: owner-wri-mathgroup at

The 3D rotations are made in following order:

1. Roll (Z axe rotation)
2. Yaw (Y axe rotation)
3. Pitch (X axe rotation)

A base koordinate system is specified by normalized vectors U (X
direction), V (Y direction), N (Z direction). Of course, the  U, V, N
vector are perpendicular to each oder. After applaying all rotations we
get new koordinate system Unew, Vnew, Nnew.
Does anyone know how to calculate all three angles (Roll, Yaw, Pitch) if
we know only base coordinate system vectors (U, V, N), new coordinate
system vectors (Unew, Vnew, Nnew) and order in which 3D rotations are
applied (Roll, Yaw, Pitch).

Here is what I allready have:

        Rp = Unew - (N*Unew)*N;
        Rpr = Rp/|Rp|
        P = Unew x N;
        Pn = P/|P|

        Yaw = -asin(N*Unew);
        Roll = acos(U*Rpr);
        Pitch = PI - acos(Vnew*Pn);

The problem is that this works only for angles between -90 and 90 but
not for angles between 90 and 270.

Lep pozdrav / Best regards

Robert Milharcic

ib-CADdy d.o.o. /
Dunajska 106
SI-1000 Ljubljana
Tel.: +386 61 168 44 30
Fax.: +386 61 168 22 25
e-mail: robert.m at

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