问题
Object rotate in 3D. I have rotation center and coordinate of 2 point in rotate and not rotate position. Calculate quaternion that rotate object from first position to two position.
回答1:
We have to vector OA' and OB' in first position of object
OA and OB in second position
Q vector part quaternion Q0 scalar part
fig.1
COMMENT
OAOB - dot vector product
OAxOB - cross vector product
Quaternion of rotation object from first positon to second was:
1 case
If OA
where Q0-2=([(OA-OA')x(OB-OB')]/[OAOB'-OA'OB])2+1
If OA
OB'-OBOA'=0, then2 case
if [OA'+OA]x[OB'+OB] not equal zero and OB-OB' not equal zero,
then exist m that OA-OA'=m(OB-OB'). Search it.
Q=n*(mOB'+OA'),
where n=Q0(OB-OB')2/(2*OB*[OA'xOB'])
Q0-2=(OB-OB')4*(OB'+OA')2/(2*OB*[OA'xOB'])2+1
If OAOB'-OBOA'=0 and [OA+OA']x[OB+OB']=0
3 case
If OB+OB'not equal zero, then
Q=(OB+OB')/|OB+OB'|, Q0=0
else
4 case
OB+OB'=0
Q=([OB']x[OA'])/|[OB']x[OA']|, Q0=0
From quaternion we can calculate rotation matrix or Euler angles
回答2:
Look at answer to similar question How to find correct rotation from one vector to another?
Your difference that second vector "up" is not perpendicular to first "dir". Just make it and problem solved
来源:https://stackoverflow.com/questions/21771676/calculate-quaternion-by-coordinate-2-points-of-object-in-two-positions