Problems, methods and techniques for conversion of numerical representation into mathematical representation. R. M. for Design.

Reverse Modelling (RM) is the process that makes it possible to deduce the representation of the of physical model’s shape by digital acquisition. The aim of the process can be various, in design it can be used both for restyling operations and for more strictly design operations. Today, methodologies and techniques used don’t follow standard procedures, in some cases craft operations are prevailing, in other cases actions aim to the highest strictness to reach extreme accuracy in the result. In the design process of the object, RM has a further task: working out the existing detachment between prototype and projected model, taking an active role in the ideational path of the object. Only an experimental applicative research allows analyzing problems, methods and techniques of commutation from a numerical model (cloud of points, survey) to a mathematical model (digital project). The study’s goal is to solve problems in the RM process applied to the design project. The experience was carried out making use of new potentialities given by digital devices, used to integrate the typical tools of design and descriptive geometry in their most contemporary acceptation. The research has led also to alternative results compared to today’s computational techniques used in the resolving procedures of the problem. The research was dealt with a systematic methodology, which is structured in a first step of cognitive investigation phase, a second step of analysis, then the survey, afterwards an experimental application. The cognitive phase has examined the tools of digital survey, the software of analysis and editing of numerical data and the software of mathematical modelling. The analysis phase was addressed to the problems of mathematical representation in design object. The following phase of survey was characterized by the searching of geometric entities of the object, deduced from the acquired numerical data, therefore the experimentation solved the relationships between prototype, acquired data and ideational mental model. The results come through the tools of our field of study, which express in this research their potential as means of comprehension and solution of the Reverse Modelling process.