Structure and Appearance Optimization for Controllable Shape Design


The field of topology optimization seeks to optimize shapes under structural objectives, such as achieving the most rigid shape using a given quantity of material. Besides optimal shape design, these methods are increasingly popular as design tools, since they automatically produce structures having desirable physical properties, a task hard to perform by hand even for skilled designers. However, there is no simple way to control the appearance of the generated objects.

In this paper, we propose to optimize shapes for both their structural properties and their appearance, the latter being controlled by a user-provided pattern example. These two objectives are challenging to combine, as optimal structural properties fully define the shape, leaving no degrees of freedom for appearance. We propose a new formulation where appearance is optimized as an objective while structural properties serve as constraints. This produces shapes with sufficient rigidity while allowing enough freedom for the appearance of the final structure to resemble the input exemplar.

Our approach generates rigid shapes using a specified quantity of material while observing optional constraints such as voids, fills, attachment points, and external forces. The appearance is defined by examples, making our technique accessible to casual users. We demonstrate its use in the context of fabrication using a laser cutter to manufacture real objects from optimized shapes.

In ACM Transactions on Graphics (TOG) — Proceedings of ACM SIGGRAPH Asia



    author = {Mart\'{\i}nez, Jon\`{a}s and Dumas, J{\'e}r{\'e}mie and Lefebvre, Sylvain and Wei, Li-Yi},
    title = {Structure and Appearance Optimization for Controllable Shape Design},
    journal = {ACM Trans. Graph.},
    issue_date = {November 2015},
    volume = {34},
    number = {6},
    month = oct,
    year = {2015},
    issn = {0730-0301},
    pages = {229:1--229:11},
    articleno = {229},
    numpages = {11},
    url = {},
    doi = {10.1145/2816795.2818101},
    acmid = {2818101},
    publisher = {ACM},
    address = {New York, NY, USA},
    keywords = {manufacturing, modeling, texture synthesis, topology optimization},


This work was supported by ERC grant ShapeForge (StG-2012-307877) and general research fund Dynamic Element Textures (HKU 717112E).