Shape analysis. Genetic Algorithms for generic curves interpretation and analytical curves restitution.

The main goal of this research activity is 3D data analysis and interpretation to study the geometric shaping of architectural elements belonging to Cultural Heritage moving from Point Cloud Semantic Segmentation to 3D modeling. We are testing Evolutionary Computing (EC) to study these shapes merging critical human-driven interpretation and Genetic Algorithms (GAs) driven interpretation. GAs allow to automate identification of open or closed polycentric curves (e.g. ovals) and of analytic curves (e.g. ellipse) starting from reality based planar sections (irregular polylines) extracted from point clouds. GAs, based on natural selection, are tools for solving both constrained and unconstrained optimization problems not well suited for standard algorithms. Moving from theoretical knowledge and treaties study, the research topic is the shape analysis and restitution of hemispherical domes profile (‘pointed arches’ or polycentric arches), i.e. ‘pointed domes’, and of ovoidal/ellipsoidal domes (generic and revolution surfaces). Starting from rules (from centers to points along profiles), our aim is to test a process to generate polycentric (closed or open) and elliptic profiles nearest to reality-based sections (from point along reality-based profiles to centers layout). The Evolutionary Solver (Galapagos component, GH, Rhino) starts from the identification of a given number of points (GENE POOL, i.e. variables) along the irregular reference polyline to select the best solutions (SELECTION) towards the optimal solutions (continuous semi-ideal profile) that best fit the reference curve by minimizing or maximizing different comparison conditions between the two curves (FITNESS)