Computational Symmetry for Geometry Data Analysis and Design ERC Starting Grant 2011 - 2016
The analysis and synthesis of complex 3D geometry is of crucial importance in many scientific disciplines (e.g. bio-medicine, material science, mechanical engineering, physics) and industrial applications (e.g. drug design, entertainment, architecture). We are currently witnessing a tremendous increase in the size and complexity of geometric data sets, largely fueled by significant advances in 3D acquisition and digital production technology. However, existing computational tools are often not suited to handle this complexity, leading to severe processing bottlenecks in many applications.
The goal of this project is to investigate a new generalized model of geometric symmetry as a unifying concept for studying spatial organization in geometric data. This model will allow exposing the inherent redundancies in digital 3D data and will enable scalable algorithms for analysis, processing, and design of large-scale geometric data sets. The proposed research addresses a number of fundamental questions: What is the information content of 3D geometric models? How can we represent, store, and transmit geometric data most efficiently? Can we we use symmetry to repair deficiencies and reduce noise in acquired data? What is the role of symmetry in the design process and how can it be used to reduce complexity? How can we transform randomness into order to obtain effective means of form finding?
We will investigate these questions with an integrated approach that combines theoretical studies with practical solutions for real-world applications. The proposed research has a strong interdisciplinary component and will consider the same fundamental questions from different perspectives, closely interacting with scientists of various disciplines, as well artists, architects, and designers. As application examples we will focus on architectural design and the reconstruction of digital 3D city models, yet the envisaged results will be relevant for other disciplines that are concerned with the analysis or synthesis of large-scale geometric data sets.