Geometric Kinematics for Urban Growth: A Theoretical Vector Field Framework

This paper presents a new approach and framework for the study of spatio-temporal geometric kinematics for urban growth built on deriving a vector field from the evolution of the shape as an inverse problem for the kinematics. Once we can compute the vector field, then the reason for the growth coming from socioeconomic and other factors can be related to the sources of the fields. This can make this concept very useful from a practical point of view. This paper presents the kinematic evolution of the shape that is derived by solving the inverse evolution problem using computational geometry. The solution of the problem allows for interpolation as well as extrapolation of the evolution. The paper developed the theory and algorithm for the evolution computational geometry and also shows how then various urban growth driving factors can be connected to the evolution parameters. We implemented the new algorithm and framework on a study area from Mumbai Metropolitan Region (MMR) in India where we had data available from three different years using remote sensing for the region growth as well as for urban growth factors from various sources. We solved the inverse computational geometry problem as well as built a relationship between the growth factors and growth rate using regression as demonstration of the concept.