Design: The goal of the course is to provide students with methods, tools and useful procedures to the knowledge and analysis of historic buildings, their physical characteristics, construction and conservation. Particular attention will be given to learning the methods of integrated survey, using traditional techniques of direct survey coordinated with 3D relief (image based and range based).
Mathematics: The course is aimed at studying and analysis of curves and surfaces in plane and in space as mathematical models of architectural elements. To learn, applying to different case studies, the differential properties of parametric curves and surfaces and their composition in a virtual model. By modelling you it is possible to process a thorough analysis of the architectural structure functional to several interventions in the field of restoration.
Mathematics: The course is aimed at studying and analysis of curves and surfaces in plane and in space as mathematical models of architectural elements. To learn, applying to different case studies, the differential properties of parametric curves and surfaces and their composition in a virtual model. By modelling you it is possible to process a thorough analysis of the architectural structure functional to several interventions in the field of restoration.
scheda docente
materiale didattico
Rigid movements and simmetries: translations, rotations and reflexions. Planar sections of a Point cloud. Optimal parametric curve from a set of points.
Parametric curves in R³. Torsion and binormal unit vector. Rigid movements in space. Parametric surfaces: exemples. Curves on surfaces.
Surfaces intersections. Domes and vaults. Wall bulging with respect to an optimal plane.
Parametric surface model out of an architectural example. Point-cloud/parametric-surface distance.
Programma
Parametric curves in R²: examples visualization and animations using Mathematica software. Curvature, tangent and normal unit vectors.Rigid movements and simmetries: translations, rotations and reflexions. Planar sections of a Point cloud. Optimal parametric curve from a set of points.
Parametric curves in R³. Torsion and binormal unit vector. Rigid movements in space. Parametric surfaces: exemples. Curves on surfaces.
Surfaces intersections. Domes and vaults. Wall bulging with respect to an optimal plane.
Parametric surface model out of an architectural example. Point-cloud/parametric-surface distance.