3D Primitive Assembly from Generative Anchors

Many 3D objects can be approximated as assemblies of simple primitives, turning a surface into an editable structure of parts. Recovering that assembly from an observed 3D model requires both a global account of which parts exist and precise localization on the input. An image follows the same conversion after primitive-style abstraction and surface reconstruction. Directly generating primitive parameters must invent unobserved interiors, and overlapping solids often admit several valid programs. A detailed mesh defers the type choice, but spends many tokens on coordinates that still do not partition the observed surface. Point features preserve geometric detail, yet do not decide how many regions to keep; small exposed attachments are easily dropped. We recover primitive assemblies from 3D generative anchors. Conditioned on ShapeVAE, an autoregressive model generates a low-density proxy mesh disconnected along primitive contacts. These anchors are not the delivered geometry: connected components organize their hidden states into region queries, a point transformer predicts dense assignment and primitive type on the processed input surface, and analytic fitting restores editable bodies. Geometric precision is therefore carried by the dense surface, while expensive autoregression only produces token-efficient query summaries. The pipeline yields a variable-part assembly without a primitive-parameter language and without a prescribed part count.