Computer-implemented methods and media bearing instructions for matching movements of objects are described. In one example, the method can include determining a position of a first point in a first coordinate system, converting the position of the first point from the first coordinate system to a second coordinate system, performing a transformation on a second point in the second coordinate system, wherein the second point is initialized to a starting position in the second coordinate system, determining an ending position of the second point in the second coordinate system based on the transformation, converting the ending position of the second point in the second coordinate system to the first coordinate system, and associating the ending position of the second point in the first coordinate system to the first point in the first coordinate system, wherein the associating causes a transformation of the first point to match the transformation performed on the second point.