A novel potential field based domain mapping method
Hari Kumar Voruganti, Bhaskar DasGupta, Günter Hommel · Annual Conference on Computers · 2006
A new approach is proposed for mapping a geometrically complicated domain to a simple well-shaped domain using the potential field theory. This bijective domain mapping gives a parameterization which is useful in handling many application problems like path planning, shape matching, morphing, etc. Harmonic function is chosen for establishing the potential field as it will never have local minima within the domain. This paper presents the domain mapping method and an application of the same to the robot motion planning problem. Potential field along with the streamlines provides two parameters required for representation of any point in the domain. Once the domain is mapped, any post-processing like path planning is easy as the domain of operation is convex. for example, path planning boils down to finding a straight line joining two points in a convex domain and mapping it back to the original domain. Results show that domain mapping is an effective method for shape transformation. For on-line applications, this method is extremely useful since after mapping computational effort required is very less in the query phase.