Tesi di LAUREA SPECIALISTICA Titolo Ricostruzione di superfici a partire da una nuvola di punti Data 2009-12-23 Autore/i Cargnelutti, Renata Relatore Mussio, L. Full text non disponibile Abstract Data processing is the principal technique of analysis in many fields of earth sciences and planning, like Survey and Mapping. Classical techniques are nowadays supported by information technology, artificial intelligence and robotics too. The union between usual and modern issues leads to improvement and invention of instruments able to acquire, treat and analyse spatially referenced data. This work has its main focus in reconstructing objects in a 3D space. Objects are intended with complex morphology (concave and not-stellar), since objects with opposite characteristics (stellar, convex) are already being studied and analysed. Algorithms of triangulation (in two and three dimensions) are the baseline of this work: by evaluating cases with difficult usability of these algorithms, the problem will be refined with other criteria or functions (splines, or curves under particular conditions). Chapter one introduces the fields, which are considered central in this thesis. In the following three chapters, there are theoretical approaches to the methods used in the last chapter of the thesis itself: in particular, there is an exposition of approximation theory, a presentation of Delaunay triangulation and elements for a direct reconstruction of an external surface. In chapter five, there are some examples of applications, in order to present instruments used so far, with their limitations (for instance, 2D representations considerably restrict optimal visualization of an area). Furthermore, there are some examples of surface reconstruction, provided with data from different sources. An important aspect that this work tries to develop is the study of data capture. In some fields, such as frameworks, there are two different problems. The first appears when there is little information about an object, therefore it is quite difficult to make an analysis and get reliable results: the problem has a rank defect. The second problem that I have studied canbe noticed when there is too much information about an object or an area, then it is necessary to reduce data in order to handle them and begin aninvestigation: the problem suffers from correlation effect, which can mineesteems reliability. In the last chapter, there is the simulation that I have realized through a manual reconstruction. Procedure develops as follows: given a set of data, the matter starts with cluster analysis. The problem is evaluating every point assignment, to chains or sowed: the difference consists in density of points, since a chain is a closed line, while a sowed also has internal points. In the latter situation, least squares or classical interpolation are not suitable. The discriminating idea is then applying Delaunay triangulation: in particular, there are rules that must be respected (for example, circle’s criterion in two dimensions or sphere’s criterion in three dimensions), but that give useful indications about the way to proceed. Through implementation of software, it is possible to reconstruct surfaces and realize solid modeling of concave and non-stellar objects.