#include <bullet/LinearMath/btVector3.h>
#include <bullet/LinearMath/btQuaternion.h>
#include <cstdio>
#define SQR2 0.707106781
int main(){
  btVector3 loc(1,0,0);
  btQuaternion rot(SQR2,0,0,SQR2);
  printf("R (%f,%f,%f,%f)\n",
    rot.getW(),
    rot.getX(),
    rot.getY(),
    rot.getZ()
  );
  btQuaternion arot(rot.getW(),-rot.getX(),-rot.getY(),rot.getZ());
  //The above screws it up..?
  //btQuaternion arot(SQR2,-0,-0,SQR2);//does it right
  printf("R^-1 (%f,%f,%f,%f)\n",
    arot.getW(),
    arot.getX(),
    arot.getY(),
    arot.getZ()
  );
  btQuaternion locq(0,loc.x(),loc.y(),loc.z());
  btQuaternion res = rot*locq*arot;
  printf("Now (%f,%f,%f,%f)\n",
    res.getW(),
    res.getX(),
    res.getY(),
    res.getZ()
  );
return 1;
}



OUTPUT:

$ ./a.out
R (0.707107,0.707107,0.000000,0.000000)
R^-1 (0.000000,0.707107,-0.707107,-0.000000)
Now (0.500000,0.500000,0.500000,-0.500000)