CAREER: Partitive Solid Geometry for Computer-Aided Design: Principles, Algorithms, Workflows, & Applications

This Faculty Early Career Development Program (CAREER) grant will establish the foundations of a new geometric modeling framework – partitive solid geometry – for the design of complex two- and three-dimensional geometric patterns. Modeling complex patterns, such as cellular structures, is intrinsic to several areas of national interest, including consumer products, protective gear for sports and the military, and curved miniaturized electronics.

Making complex geometric modeling accessible to more designers and engineers is key to facilitating disruptive innovations in many engineering disciplines, including the automotive, aerospace, construction, additive manufacturing, mechanics, thermo-fluids, and acoustics fields. Current tools for generative design and modeling are highly automated, which makes it difficult for designers to explore new ideas and ask “what-if” questions.

A new representation of geometric solids is needed that will allow designers to apply their expertise, ideas, and creativity in designing cellular structures. Such a representation should also simultaneously support computationally efficient mechanical evaluation, such as finite element simulation. This research will make complex geometric modeling available to all, real-time and intuitive to interact with, useful for serious engineering design, and usable for recreational learning.

As a result, novice and expert designers will be able to creatively apply their knowledge in applications ranging from the design of new materials to new architectural forms and safe products. This grant will further enable a new type of learning mechanism, where younger audiences will be able to easily generate complex shapes, prototype them as puzzles through 3D printing, and play with the puzzles to discover basic principles of geometry.

This will fundamentally transform the way children develop their spatial reasoning ability through hands-on design and prototyping activities.

This research will introduce space-filling shapes as the underlying novel shape representation for partitive solid geometry, which will enable forward design workflows for the creation of complex shapes and structures for generative and procedural design. With this representation, the grant will integrate currently disparate methods such as implicit modeling, medial axis representations, and Voronoi tessellations into a single unified methodology for shape representation.

Efficient and robust algorithms will be developed and embedded within interactive software workflows that will allow users to directly and intuitively create shapes that were not possible before. Human subject studies will be conducted to investigate how these new workflows can promote creative thinking in engineering design. A hypothesis-driven approach will be taken to investigate partitive solid geometry for designing a wide variety of interlocking shapes, functionally graded cellular structures, and auxetic materials.

User-generated geometric models will be evaluated numerically and through mechanical tests to discover the relationship between the input geometry provided by the user and the behavior of the resulting shapes. A comprehensive education and outreach plan will include undergraduate internships and a new graduate course. The project will disseminate a free web-based modeling tool to researchers and the public.

The research will also create a large online encyclopedia of complex geometric models for the public to use. Through summer camps, the grant will introduce interactive generative design to K-12 students to promote spatial reasoning through play-based tangible learning.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.