The mathematics of shape-geometry approach to the analysis of curveprofile

摘要

It has been previously shown that the visual approach to theanalysis of the behaviour of growth patterns can provide a viablesolution to the understanding of the physical behaviour of the subjectmatter. Also, it has been demonstrated that the shape of the profile canbe defined in terms of a number of characteristics some of which aregeneral for all profiles and others are specific to individualcircumstances. These characteristics, referred to as shape-parameters,are used for the analysis of the profile. Also, they are used forconstruction of the profile that the phenomenon is likely to assume. Themethod was validated by applying it to construction project expenditurepattern forecasting and further validation was undertaken by the use ofstatistical technique, namely, principal component analysis. In thispaper, the mathematics of the model is represented whereby, for a givenset of shape-parameters, the precise profile is mathematicallygenerated. Due to its complex nature, the problem is decomposed intoseparate modules each satisfying a number of requirements. The modulesoperate independently but when combined, the overall boundaryrequirements are also satisfied