Abstract : Digital representations of 3D objects allow people to create both digital artworks destined to be viewed through a screen, as well as physical manufactured objects through computer-aided design and manufacturing. Designing well-suited digital representations is thus central to let humans extend the range of what they can create through computer software and machines. In this talk, I will present four case studies, in which leveraging specific digital representations and associated algorithms allowed us to design software that supports complex authoring workflows: by decomposing animation authoring into 2D and 3D components, we support the insertion of animated doodles into captured footage ; by introducing a new primitive in VR painting, we can achieve more fine-grained color editing ; by parameterizing patterns for crochet granny square garments, we enable crocheters to re-use material across garments ; and by devising new primitives to represent machine motion, we allow for fine-grained control over fabrication machines. Throughout the presentation, I will emphasize high-level design decisions and practical research methods that guided us in developing adequate digital representations.