c++ - Quaternion to EulerXYZ, how to differentiate the negative and positive quaternion -


i've been trying figure out difference between these, , why toeulerxyz not right rotation.

using mathgeolib:

axisx:

x   0.80878228  float y   -0.58810818 float z   0.00000000  float

axisy:

x   0.58811820  float y   0.80877501  float z   0.00000000  float

axisz:

x   0.00000000  float y   0.00000000  float z   1.0000000   float

code:

quat aq = quat::rotateaxisangle(axisx, degtorad(30)) * quat::rotateaxisangle(axisy, degtorad(60)) * quat::rotateaxisangle(axisz, degtorad(40)); float3 euleranglesa = aq.toeulerxyz();  quat bq = quat::rotateaxisangle(axisx, degtorad(-150)) * quat::rotateaxisangle(axisy, degtorad(120)) * quat::rotateaxisangle(axisz, degtorad(-140)); float3 euleranglesb = bq.toeulerxyz();

both toeulerxyz {x=58.675510 y=33.600880 z=38.327244 ...} (when converted degrees).

the difference can see, quaternions identical, 1 negative. toeulerxyz wrong though, 1 should negative ({x=-58.675510 y=-33.600880 z=-38.327244 ...}) (bq)

aq is:

 x  0.52576530  float  y  0.084034257 float  z  0.40772036  float  w  0.74180400  float

while bq is:

 x  -0.52576530 float  y  -0.084034257    float  z  -0.40772036 float  w  -0.74180400 float

is error mathgeolib, or weird nuance, or maybe can explain me going on logically.

there additional scenarios not negative

axisx:

-0.71492511 y=-0.69920099 z=0.00000000

axisy:

0.69920099 y=-0.71492511 z=0.00000000

axisz:

x=0.00000000 y=0.00000000 z=1.0000000

code:

quat aq = quat::rotateaxisangle(axisx, degtorad(0)) * quat::rotateaxisangle(axisy, degtorad(0)) * quat::rotateaxisangle(axisz, degtorad(-90)); float3 euleranglesa = aq.toeulerxyz();  quat bq = quat::rotateaxisangle(axisx, degtorad(-180)) * quat::rotateaxisangle(axisy, degtorad(180)) * quat::rotateaxisangle(axisz, degtorad(90)); float3 euleranglesb = bq.toeulerxyz();

these both yield same quaternion! 

x   0.00000000  float y   0.00000000  float z   -0.70710677 float w   0.70710677  float

the quaternions -q , q different; however, rotations represented 2 quaternions identical. phenomenon described saying quaternions provide double cover of rotation group so(3). algebra see simple: given vector represented quaternion p, , rotation represented represented quaternion q, rotation qpq^{-1}. on other hand, -qp(-q)^{-1} = -1qp(q)^{-1}(-1) = q(-1)p(-1)q^{-1} = qp(-1)^2q^{-1} = qpq^{-1}, same rotation. quaternions don't commute, pq != qp general quaternions, scalars -1 commute quaternions.

i believe toeulerxyz should same in both cases, appears be.


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