Abstract: Measuring the girth of shoe last on polygonal mesh is an important problem in modern shoemaking CAD systems.In this paper we introduce a novel approach to measure the girth of digitized shoe last by extending the traditional geodesic with width.Firstly, it constructs a subsurface on shoe last based on a specified geodesic and its width.The energy of subsurface is defined in terms of a constrained mass-spring system.Secondly, an iterative optimization mechanism is employed to minimize the energy of this surface while it is moving on the shoe last.At last, the extended geodesic is extracted as the desired path of girth of the current shoe last after the convergence of aforementioned minimization.Furthermore, the time-consuming part of energy calculation is accelerated with a GPU implementation.Experimental results show that both precision and time performance of our approach can fulfill the requirements of shoe last measuring in the shoe-making industry.