The mathematics of shape-geometry approach to the analysis of curve profile

Abstract

It has been previously shown that the visual approach to the analysis of the behaviour of growth patterns can provide a viable solution to the understanding of the physical behaviour of the subject matter. Also, it has been demonstrated that the shape of the profile can be defined in terms of a number of characteristics some of which are general for all profiles and others are specific to individual circumstances. These characteristics, referred to as shape-parameters, are used for the analysis of the profile. Also, they are used for construction of the profile that the phenomenon is likely to assume. The method was validated by applying it to construction project expenditure pattern forecasting and further validation was undertaken by the use of statistical technique, namely, principal component analysis. In this paper, the mathematics of the model is represented whereby, for a given set of shape-parameters, the precise profile is mathematically generated. Due to its complex nature, the problem is decomposed into separate modules each satisfying a number of requirements. The modules operate independently but when combined, the overall boundary requirements are also satisfied.