Curve and curved surface approximation is a central topic in computational geometry with a large body of literature dealing with it. Increasingly demanding applications in realistic virtual environments, Geographic Information Systems, scientific visualisation and industrial design require constantly innovative approaches to handle special problems arising when computing with complex shapes. In particular, for manipulating shape representations, it is advantageous to reduce the complexity of the shape representation as much as possible, while staying geometrically close to the original data. For this purpose, researchers at the Freie Universität of Berlin designed novel algorithmic solutions for piecewise simplification of smooth curves with given error tolerance. High quality software was written in C++ programming language and was embedded in the Computational geometry algorithms library (CGAL), to demonstrate the feasibility of the new techniques in practice. The Freie Universität of Berlin pursued the effort in this direction further and gave computational geometry for surfaces' solid algorithmic foundations, to validate theoretical advances through the development of software packages. The three-dimensional mesher package provides advanced functionalities for approximating skin surfaces used for the visualisation of molecules in biological computing with a topologically correct mesh. In order to achieve transfer and diffusion of the software library components in industry, Geometryfactory has been charged with their commercial implementations.