A new approach for surface fitting method of articular joint surfaces

The application of joint contact mechanics requires a precise configuration of the joint surfaces. B-Spline, and NURBS have been widely used to model joint surfaces, but because these formulations use a structured data set provided by a rectangular net first, then a grid, there is a limit to the accuracy of the models they can produce. However new imaging systems such as 3D laser scanners can provide more realistic unstructured data sets. What is needed is a method to manipulate the unstructured data. We created a parametric polynomial function and applied it to unstructured data sets obtained by scanning joint surfaces. We applied our polynomial model to unstructured data sets from an artificial joint, and confirmed that our polynomial produced a smoother and more accurate model than the conventional B-spline method. Next, we applied it to a diarthrodial joint surface containing many ripples, and found that our function's noise filtering characteristics smoothed out existing ripples. Since no formulation was found to be optimal for all applications, we used two formulations to model surfaces with ripples. First, we used our polynomial to describe the global shape of the objective surface. Minute undulations were then specifically approximated with a Fourier series function. Finally, both approximated surfaces were superimposed to reproduce the original surface in a complete fashion.