/**
* 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);
}
}
/**
* Constructs and initializes a Quaternion from the specified rotation {@link #axis() axis} (non
* null) and {@link #angle() angle} (in radians).
*
* @param axis the PVector representing the axis
* @param angle the angle in radians
* @see #fromAxisAngle(PVector, float)
*/
public Quaternion(PVector axis, float angle) {
fromAxisAngle(axis, angle);
}