Example Based Repetitive Structure Synthesis

• Published in: Computer graphics forum 2015-08, Vol.34 (5), p.39-52
• Main Authors: Roveri, Riccardo, Öztireli, A. Cengiz, Martin, Sebastian, Solenthaler, Barbara, Gross, Markus
• Format: Article
• Language: English
• Subjects: Algorithms; Analysis; Computer graphics; Mathematical analysis; Mathematical models; Optimization; Repetitive structures; Representations; Studies; Subspaces; Synthesis; Topological manifolds
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.12695

We present an example based geometry synthesis approach for generating general repetitive structures. Our model is based on a meshless representation, unifying and extending previous synthesis methods. Structures in the example and output are converted into a functional representation, where the functions are defined by point locations and attributes. We then formulate synthesis as a minimization problem where patches from the output function are matched to those of the example. As compared to existing repetitive structure synthesis methods, the new algorithm offers several advantages. It handles general discrete and continuous structures, and their mixtures in the same framework. The smooth formulation leads to employing robust optimization procedures in the algorithm. Equipped with an accurate patch similarity measure and dedicated sampling control, the algorithm preserves local structures accurately, regardless of the initial distribution of output points. It can also progressively synthesize output structures in given subspaces, allowing users to interactively control and guide the synthesis in real‐time. We present various results for continuous/discrete structures and their mixtures, residing on curves, submanifolds, volumes, and general subspaces, some of which are generated interactively.