The importance of accurate geometric models of shapes, both naturally occurring and man-made, is rapidly growing with the maturing of novel manufacturing technologies and novel analysis technologies. The advent of big data challenges, and the rapid evolution of machine learning serve to confound the issue even more. In the past, Dagstuhl seminars on geometric modeling were focused on basic research. Starting with the 2017 seminar, the focus has been changed to focus on applications of geometric modeling. For this conference we have selected three core application areas that stretch the underlying mathematical underpinnings of the discipline to its limits and beyond:

• Geometric modeling and machine learning (including big data analysis)
• Geometric and physical challenges in additive manufacturing (3D Printing)
• Design optimization

This Dagstuhl Seminar will provide a forum for leading researchers to present new ideas, to exchange scientific insights, and to bring together practical applications and basic research. Except for the 2017 seminar previous seminar explored the theory of shape representations, shape transformations, and computational models for each. This seminar will explore application of this theory to the three above application challenge, strengthening the reliability and performance of applications in engineering, manufacturing, and scientific exploration. The goal of the seminar is to establish a common understanding between the Geometric Modeling research community and the above application fields:

• How to process and analyze huge 3D data sets that may be noisy and incomplete into clean, scalable, and easy to access 3D environments
• How to turn big, dispersed maybe noisy and incomplete geometric data into clean, scalable, and easy to access 3D information that can be used for change detection and decision making
• How to represent, simulate, control, and process complex, anisotropic, internal material enabled by additive manufacturing, and how to design for additive manufacturing
• How to perform topology optimization of internal structure of objects to enable additive manufacturing to reach its full potential
• How to introduce analysis-based design in CAD systems, with isogeometric analysis in mind

To address these questions, we will bring together participants from industry urgently in need of better solutions, researchers in the application areas represented by the three topics, and researchers in the geometric modeling community whose interests align with the three topic areas.

The scientific presentations will be 15 minutes. Senior researchers will give 3 overview talks on the 3 themes of the seminar. We will organize perspective working groups for each of the four topics and ask all participants to sign up for at least one working group. The length of the presentations has been shortened to allow more time for discussion and group dialog. Our goal is for each of the perspective groups to produce a "white paper" for the resulting publication.

Creative Commons BY 3.0 DE

Falai Chen, Tor Dokken, Géraldine Morin, and Timothy L. Strotman