If the tool works as demoed, it will change how artists work with 2D vector shapes, allowing them to manipulate and rotate ...

How about some transformations? If a shape is transformed, its appearance is changed. This can be done in a number of ways, including translation, reflection and rotation. So firstly, translation.

Homogeneous vector and plane, homogeneous transformation, position and orientation transformations, kinematics and inverse kinematic solutions of robot manipulators and mobile robots, Jacobian and ...