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Structure-Aware Geometry Processing

Final Report Summary - SMARTGEOMETRY (Structure-Aware Geometry Processing)

Geometric form is often dictated by a variety of factors including topological structure, object functions, force considerations, growth laws. Further, at suitable levels of abstractions, objects with similar functions tend to share similar forms. Discovering such connections are not only important to understand the workings of many natural processes, but essential to enable novel form-finding possibilities. Hence, in the history of science, we have long strived to build theories to explain empirical observations and common phenomenon. Notable examples include investigations of natural objects and processes that have led to the creation of velcro, porcelain, Kevlar-based fabric, structural layout of the Eiffel tower. In the absence of sufficient data such investigations, however, have been traditionally case-specific, tedious, done by experts, and difficult to generalize across many different objects. SmartGeometry investigated this classical question by developing data-driven methods.

Motivation: The relationship between form and function has long been discussed in art, architecture, mathematics, and natural science. The evolution of geometric form for organisms is believed to be strongly affected by environmental forces and functional considerations. Geometric and topological forms, however, are mostly recorded independent of object functions — 3D geometry, modeled or directly scanned, being represented at a low-level as a collection of points or triangles isolated from functional and physical considerations. The ability to jointly analyze large correlated 3D model collections reveals what remains unchanged and what are the main modes of changes that can help us connect back to the original function of objects.
Hence, in the SmartGeometry project, we developed algorithms to collectively analyze such model collections in order to gain a real understanding of the data specifically in terms of correlations and key differences.

Goals and novelty: Geometry processing has long investigated single objects in their low-level representations (points, polygons, feature curves, voxels), traditionally focusing on model repair, reconstruction, detail-preserving deformations. SmartGeometry revealed links between the extracted factored representations and associated object functions with application in next-generation smart design tools. Specifically, we
(i) developed both theoretical understanding and computational tools to decouple structure in the forms of relations among intra- and inter-model parts from low-dimensional variations, both structural and geometric, by analyzing unorganized model collections to generate factored representations, and
(ii) used the factored representations for structure-aware geometry processing to support exploration in high-dimensional design spaces, where extracted structures are automatically preserved, while computationally optimizing for fabrication cost, structural stability, and aesthetic considerations.
Note that the first item is along the long-standing goal in science to extract a data model as “a corrected, rectified, regimented, and in many instances idealized version of the data”. The extracted representations effectively parameterize the underlying shape manifolds (as algebraic constraints in the form of structures holding together simple geometric primitives) and used as in the second item to enable fundamentally new form-finding and globally coupled geometric optimization opportunities.

Outcome: As an effective factored representation, SmartGeometry developed graph-based storage of topological and geometric features. As a novel representation, we developed StructureNet to facilitate learning both topological and geometric variations. We developed novel design tools in the context of structure-aware manipulation, shape space exploration, novel 2D-3D synthesis tools. We demonstrated the power of the theoretical foundations on a variety of design scenarios including sketch-based modeling, static and dynamic garment design, curved folding patterns, architectural modeling, physics-guided simulation, and scanning setups, CAG modeling, and broadly in the context of generative modeling for indoor scenes and outdoor urbanscapes. Code and data developed during the project are publicly available for research use.