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.
teacher profile teaching materials
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.
Programme
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.