Systems and methods disclosed improve the speed of animating artwork by determining the handle affine transformations used to animate 2 Dimensional (2D) artwork in a computationally simpler manner than prior techniques. The improved technique represents vertex coordinates (e.g., x1, y1) in 2D artwork as the real and complex portions of complex numbers. Doing so allows minimizing a closed form expression to find handle affine transformations that provide a deformation of the object with minimal stretching and squashing in local areas. Determining handle affine transformation parameters in this way is more efficient computationally than prior techniques because it combines the local and global steps into a single formula. Moreover, the formulation can be quickly evaluated with only additions, multiplications, and square roots without any need for conditional branches. Furthermore, the form of the function allows it to be solved with a simple optimization method.
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