Polhemus VIPER 4 - Page 72

USER MANUAL
Page 72 of 86 URM18PH392 Rev A. May 2020
operation, can produce only position or only orientation whereas others can produce both
P&O (although the user usually can opt for only those parameters desired).
PNO See P&O.
Position The (X, Y, Z) Cartesian coordinates of position tracking where normally +X is in the forward
direction; +Y is in the right hand direction; and +Z is downward.
Pitch See Elevation.
Quaternion Also called Orientation Quaternion or Attitude Quaternion. A four-parameter
mathematical notation for representing orientations and rotations of objects in three
dimensions. Compared to Euler angles they are simpler to compose and avoid the
problem of gimbal lock. Compared to rotation matrices they are more compact, more
numerically stable, and more efficient. Typically represented in the form q = q
0
+ iq
1
+
jq
2
+ kq
3
, a quaternion contains a vector and a scalar. In this form, q
0
is the scalar part
and (iq
1
+ jq
2
+ kq
3
) is the vector part. In Polhemus’ notation, quaternion parameters
(q
0-3
) are sometimes referred to as (w, x, y, z). The quaternion can be used to represent
the Sensor’s orientation without the need for trigonometric functions. Note that
Polhemus trackers output quaternion with the scaler value w first, followed by the
vector coords x, y, z.
The attitude matrix output from VIPER™ can be equivalently represented by the
following matrix using quaternions:
X Directional Cosines Y Directional Cosines Z Directional Cosines














q
+
q
-
q
-
q
)
qq
+
qq
2( )
qq
-
qq
2(
)
qq
-
qq
2(
q
-
q
+
q
-
q
)
qq
+
qq
2(
)
qq
+
qq
2( )
qq
-
qq
2(
q
-
q
-
q
+
q
2
3
2
2
2
1
2
0
23012031
1032
2
3
2
2
2
1
2
0
2103
20313021
2
3
2
2
2
1
2
0
Radian The SI (Système international) unit for measuring angles. An arc of a circle with the same
length as the radius of that circle subtends an angle of 1 radian. The circumference
subtends an angle of 2π radians. More generally, the magnitude in radians of the
subtended angle is expressed as θ = s/r, where s is the arc length and r is the radius. See
also Degree and Orientation Angles.
Reset Button System reset switch; does not cycle power but does a soft-reboot of VIPER™ SEU.
Response The interval of time between a request to the VIPER™ system to collect a data point and
when that data is available for input from the VIPER™ system.
Roll Coordinate of orientation tracking. Roll is a rotation around the X (horizontal
forward/aft) axis, where an increase in the angle is clockwise when viewed in the
positive direction along this axis. Note, in Polhemus’ default frame of reference, the +X
axis points forward, with +Y pointing to the right and +Z pointing down.