/**
* 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);
}
}
/**
* Returns the 3x3 inverse rotation matrix associated with the Quaternion.
*
* <p><b>Attention:</b> This is the classical mathematical rotation matrix.
*/
public final float[][] inverseRotationMatrix() {
return MathUtils.get3x3UpperLeftMatrixFromPMatrix3D(inverseMatrix());
}
/**
* Returns the 3x3 rotation matrix associated with the Quaternion.
*
* <p><b>Attention:</b> The method returns the European mathematical representation of the
* rotation matrix.
*
* @see #inverseRotationMatrix()
*/
public final float[][] rotationMatrix() {
return MathUtils.get3x3UpperLeftMatrixFromPMatrix3D(matrix());
}
/**
* Set the Quaternion from a (supposedly correct) 3x3 rotation matrix given in the upper left 3x3
* sub-matrix of the PMatrix3D.
*
* @see #fromRotationMatrix(float[][])
*/
public final void fromMatrix(PMatrix3D pM) {
fromRotationMatrix(MathUtils.get3x3UpperLeftMatrixFromPMatrix3D(pM));
}