/**
* Sets the Quaternion as a rotation from the {@code from} direction to the {@code to} direction.
*
* <p><b>Attention:</b> this rotation is not uniquely defined. The selected axis is usually
* orthogonal to {@code from} and {@code to}, minimizing the rotation angle. This method is robust
* and can handle small or almost identical vectors.
*
* @see #fromAxisAngle(PVector, float)
*/
public void fromTo(PVector from, PVector to) {
float fromSqNorm = MathUtils.squaredNorm(from);
float toSqNorm = MathUtils.squaredNorm(to);
// Identity Quaternion when one vector is null
if ((fromSqNorm < 1E-10f) || (toSqNorm < 1E-10f)) {
this.x = this.y = this.z = 0.0f;
this.w = 1.0f;
} else {
PVector axis = from.cross(to);
float axisSqNorm = MathUtils.squaredNorm(axis);
// Aligned vectors, pick any axis, not aligned with from or to
if (axisSqNorm < 1E-10f) axis = MathUtils.orthogonalVector(from);
float angle = PApplet.asin(PApplet.sqrt(axisSqNorm / (fromSqNorm * toSqNorm)));
if (from.dot(to) < 0.0) angle = PI - angle;
fromAxisAngle(axis, angle);
}
}
/**
* Converts this Quaternion to Euler rotation angles {@code roll}, {@code pitch} and {@code yaw}
* in radians. {@link #fromEulerAngles(float, float, float)} performs the inverse operation. The
* code was adapted from: http://www.euclideanspace.com/maths/geometry
* /rotations/conversions/quaternionToEuler/index.htm.
*
* <p><b>Attention:</b> This method assumes that this Quaternion is normalized.
*
* @return the PVector holding the roll (x coordinate of the vector), pitch (y coordinate of the
* vector) and yaw angles (z coordinate of the vector). <b>Note:</b> The order of the
* rotations that would produce this Quaternion (i.e., as with {@code fromEulerAngles(roll,
* pitch, yaw)}) is: y->z->x.
* @see #fromEulerAngles(float, float, float)
*/
public PVector eulerAngles() {
float roll, pitch, yaw;
float test = x * y + z * w;
if (test > 0.499) { // singularity at north pole
pitch = 2 * PApplet.atan2(x, w);
yaw = PApplet.PI / 2;
roll = 0;
return new PVector(roll, pitch, yaw);
}
if (test < -0.499) { // singularity at south pole
pitch = -2 * PApplet.atan2(x, w);
yaw = -PApplet.PI / 2;
roll = 0;
return new PVector(roll, pitch, yaw);
}
float sqx = x * x;
float sqy = y * y;
float sqz = z * z;
pitch = PApplet.atan2(2 * y * w - 2 * x * z, 1 - 2 * sqy - 2 * sqz);
yaw = PApplet.asin(2 * test);
roll = PApplet.atan2(2 * x * w - 2 * y * z, 1 - 2 * sqx - 2 * sqz);
return new PVector(roll, pitch, yaw);
}
