/**
* Get the value of this quaternion as an axis-angle value.
*
* @param aa The axis angle object to put the converted values into
*/
public void get(AxisAngle4d aa) {
double d = x * x + y * y + z * z;
if (d > EPSILON) {
d = Math.sqrt(d);
double inv_d = 1 / d;
aa.x = x * inv_d;
aa.y = y * inv_d;
aa.z = z * inv_d;
aa.angle = 2 * Math.atan2(d, angle);
} else {
aa.x = 0.0f;
aa.y = 1.0f;
aa.z = 0.0f;
aa.angle = 0.0f;
}
}
/**
* Returns a transformation matrix that rotates refPoints to match coordPoints
*
* @param refPoints the points to be aligned
* @param referenceVectors
* @return
*/
private Matrix4d alignAxes(Vector3d[] axisVectors, Vector3d[] referenceVectors) {
Matrix4d m1 = new Matrix4d();
AxisAngle4d a = new AxisAngle4d();
Vector3d axis = new Vector3d();
// calculate rotation matrix to rotate refPoints[0] into coordPoints[0]
Vector3d v1 = new Vector3d(axisVectors[0]);
Vector3d v2 = new Vector3d(referenceVectors[0]);
double dot = v1.dot(v2);
if (Math.abs(dot) < 0.999) {
axis.cross(v1, v2);
axis.normalize();
a.set(axis, v1.angle(v2));
m1.set(a);
// make sure matrix element m33 is 1.0. It's 0 on Linux.
m1.setElement(3, 3, 1.0);
} else if (dot > 0) {
// parallel axis, nothing to do -> identity matrix
m1.setIdentity();
} else if (dot < 0) {
// anti-parallel axis, flip around x-axis
m1.set(flipX());
}
// apply transformation matrix to all refPoints
m1.transform(axisVectors[0]);
m1.transform(axisVectors[1]);
// calculate rotation matrix to rotate refPoints[1] into coordPoints[1]
v1 = new Vector3d(axisVectors[1]);
v2 = new Vector3d(referenceVectors[1]);
Matrix4d m2 = new Matrix4d();
dot = v1.dot(v2);
if (Math.abs(dot) < 0.999) {
axis.cross(v1, v2);
axis.normalize();
a.set(axis, v1.angle(v2));
m2.set(a);
// make sure matrix element m33 is 1.0. It's 0 on Linux.
m2.setElement(3, 3, 1.0);
} else if (dot > 0) {
// parallel axis, nothing to do -> identity matrix
m2.setIdentity();
} else if (dot < 0) {
// anti-parallel axis, flip around z-axis
m2.set(flipZ());
}
// apply transformation matrix to all refPoints
m2.transform(axisVectors[0]);
m2.transform(axisVectors[1]);
// combine the two rotation matrices
m2.mul(m1);
// the RMSD should be close to zero
Point3d[] axes = new Point3d[2];
axes[0] = new Point3d(axisVectors[0]);
axes[1] = new Point3d(axisVectors[1]);
Point3d[] ref = new Point3d[2];
ref[0] = new Point3d(referenceVectors[0]);
ref[1] = new Point3d(referenceVectors[1]);
if (SuperPosition.rmsd(axes, ref) > 0.1) {
System.out.println(
"Warning: AxisTransformation: axes alignment is off. RMSD: "
+ SuperPosition.rmsd(axes, ref));
}
return m2;
}