Structured shape completion recovers missing geometry as primitives rather than as unstructured points, which enables primitive-based surface reconstruction. Instead of following the prevailing cascade, we rethink how primitives and points should interact, and find it more effective to decode primitives in a dedicated pathway that attends to shared shape features. Following this principle, we present UniCo, which in a single feed-forward pass predicts a set of primitives with complete geometry, semantics, and inlier membership. To drive this unified representation, we introduce primitive proxies, learnable queries that are contextualized to produce assembly-ready outputs. To ensure consistent optimization, our training strategy couples primitives and points with online target updates. Across synthetic and real-world benchmarks with four independent assembly solvers, UniCo consistently outperforms recent baselines, lowering Chamfer distance by up to 50% and improving normal consistency by up to 7%. These results establish an attractive recipe for structured 3D understanding from incomplete data. Project page: https://unico-completion.github.io.

翻译：结构化形状补全将缺失几何恢复为基元而非非结构化点云，从而支持基于基元的表面重建。不同于主流级联方法，我们重新思考基元与点云应如何交互，发现通过专用通路解码基元并关注共享形状特征更为有效。基于此原则，我们提出UniCo模型，该模型通过单次前向传播即可预测具有完整几何、语义和内点归属的基元集合。为驱动这种统一表征，我们引入基元代理——可学习的查询向量，这些向量经过上下文适配后能直接生成可用于装配的输出结果。为确保优化一致性，我们的训练策略通过在线目标更新耦合基元与点云。在合成与真实场景基准测试中，使用四种独立装配求解器进行验证，UniCo始终优于近期基线方法，将倒角距离降低达50%，法向一致性提升达7%。这些结果为从不完整数据实现结构化三维理解提供了具有吸引力的解决方案。项目页面：https://unico-completion.github.io。