A system and method of touchless interaction is provided for resolving a pivot point of an object where direct placement of a sensor at the pivot point is not practical. It applies to situations where the pivot point of a rigid object is inaccessible but remains stationary, while the other end is free to move and is accessible. The system maps the object's pivot point by way of an external sensor that detects constrained motion of the rigid object within a hemispherical banded boundary. It can also detect a geometric pattern and acceleration during the constrained motion to compensate for higher order rotations about the pivot point. Other embodiments are disclosed.