Budapesti Műszaki és Gazdaságtudományi Egyetem - Építészmérnöki Kar

DESCRIPTION OF THE COURSE

·        Topology in nutshell  

·        Tangent plane. Curves on surfaces. Geodesics. Spatial curves. 

·        Principal curvatures of surfaces, Gauss. and Minkowski curvature. Classification of surface points  

·        Hyperbolic, parabolic and elliptic surfaces. Geometry on the surface of a sphere.  

·        Quadratic surfaces (summary). Intersection, shadows and shades.  

·        Discretization of surfaces. Discrete curvature.

·        Triangulation of surfaces, convex hall, smoothing.

·        Platonic solids, symmetry.

·        Space filling, tessellations, tilings

·        Exotic surfaces (e.g.: Möbius strip) and sets (e.g.: fractals) 

The aim of this course is to introduce the knowledge of spatial geometry that is essential for the architect. The notion of curvature, the classification of surfaces based on curvature, the similarities and differences between discrete and continuous surfaces form the backbone of the course. Exercises include computer and manual editing. The course touches on currently open issues and research results in the topics. By completing the course, the student will be familiar with the geometric properties of surfaces encountered in future work and will be able to apply the knowledge gained here to solve complex geometric problems.