(i) Shape Understanding: Algorithmically understand important relations between objects and object parts in 3D objects, e.g., identify symmetries, detect regular structures, create shape abstractions, or understand invariants and variabilties across model collections.

(ii) Smart Manipulation: Abstract input geometry into structure and variations to explicitly encode non-local constraints. Beyond immediate application to denoising and smart reconstruction, such abstractions immediately allows intuitive and powerful shape manipulation, image-based editing, and constrained shape space exploration.

(iii) Computational Design: The ability to characterize design spaces using collection of (non-linear) constraints opens the possibility to directly optimize on design manifolds leading to fabrication-aware design, guided shape exploration, and in general computational design.