A New Approach to C2 Continuous Piecewise Bicubic Representation of the Articular Surfaces of Diarthrodial Joints

Abstract

Based on the force-deflection equation for a beam subjected to lateral point loads, a C2 continuous piecewise bicubic mathematical representation was proposed to model complicated geometrical surfaces, e.g. the articular surfaces of human joints. The method was then extended so that it could be used for mathematical modelling of incomplete nets of data points, as well as smoothing of noisy and/or filtering of erroneous data points. Mathematical techniques were also developed to calculate the required unknown parameters explicitly, with no need to solve the system of equations simultaneously. The performance of the proposed method was evaluated on a number of surface modelling problems, including two known analytical surfaces and the human femoral and patellar articular surfaces. The results indicate that the proposed method is precise, flexible, and easy to apply and has several advantages over the conventional smoothing methods, i.e. the B-spline approach.