Topology in CAO: Modern Symmetry

This lecture explores the birth of Topology through Euler's work on the Seven Bridges of Königsberg problem, leading to the study of continuous deformations, homeomorphisms, and topological equivalence, essential for Computer-Aided Design (CAO). It delves into the concept of homomorphisms, continuous mappings, and the importance of maintaining topological properties during transformations, focusing on the mapping of textures in graphic software. The lecture also discusses non-homomorphic deformations involving cuts and seams, emphasizing the preservation of neighborhood properties. Through examples and definitions, the instructor illustrates the fundamental principles of topological equivalence and the implications for geometric transformations in CAO.