A method is presented for shape transformation in the plane.
The primary strength of the proposed method over previous
approaches for shape transformation is that our method can 
achieve shape transformation in a domain that can contain 
obstacles which are possibly in motion. A smooth transformation
between  two given polygonal shapes is to be attained while 
ensuring that any part of the shape is free of collision with
the obstacles in the domain during the transformation process.
The problem is formulated as minimization of a cost function 
associated with each transformation path that controls length,
smoothness, and collision-freedom of the path. The problem is
solved in three steps. First, a population of tentative 
transformation paths is generated by combining path planning
for an anchor point in the shape and a randomization process.
Second, collision detection and shape deformation techniques 
are applied to keyframes along the paths to minimize the
occurrence of collision. Lastly, a genetic algorithm is used
to refine the population of transformation paths. Experimental
results are presented to demonstrate the feasibility of our
approach.