SGP tutorial “Topology Optimization for Computational Fabrication” – Milan, 7 July 2019

Advances in 3D printing enable the fabrication of structures with unprecedented geometric complexity. In design engineering, the benefits of this manufacturing flexibility are probably best exploited in combination with the design of structures by topology optimization. Based on a volumetric element-wise parametrization of the design space, topology optimization aims at finding the optimal material distribution for a performance measure (e.g., maximum stiffness), under a given set of constraints. Besides their highly optimized physical properties, the resultant shapes typically exhibit good visual qualities, which are appreciated in industrial design and architecture.
In the first part of this course, we review the basics of topology optimization, and density-based approaches for stiffness maximization in particular. In the second part, we focus on some recent developments that control the resultant geometric features for 3D printing. MatLab code is provided for both parts.




Basic Matlab code


Bone-like infill


Subdivision infill


MMA solver

Eurographics Tutorial on “Topology Optimization for Computational Fabrication”


Additive manufacturing (AM) and topology optimization (TO) form a pair of complementary techniques in transforming digital models into physical replicas: AM enables a cost-effective fabrication of geometrically complex shapes, while TO provides a powerful design methodology for generating optimized models, which are typically complex from a geometric perspective. The potential of both techniques has recently been explored in graphics, resulting in fantastic applications especially regarding structural and aesthetic properties of fabricated models. In this tutorial, we start from the fundamentals of AM and TO, and proceed to advanced TO techniques which steer the optimization process, i.e., taking into account the manufacturing as well as aesthetic appearance.


Jun Wu, TU Delft
Niels Aage, TU Denmark
Sylvain Lefebvre, INRIA
Charlie Wang, TU Delft


Part1: Introduction – Jun Wu
Part2: Advanced Manufacturing – Charlie Wang
Part3: Topology optimization: Basics tools and methods – Niels Aage
Part4: Topology Optimization with Controllable Geometric Features – Jun Wu
Part5: Topology Optimization for Appearance and Structure Synthesis – Sylvain Lefebvre


Jun Wu, Niels Aage, Sylvain Lefebvre, Charlie Wang, “Topology Optimization for Computational Fabrication”, Eurographics 2017 – Tutorials