Image-to-3D models increasingly rely on hierarchical generation to disentangle geometry and texture. However, the design choices underlying these two-stage models--particularly the optimal choice of intermediate geometric representations--remain largely understudied. To investigate this, we introduce unPIC (undo-a-Picture), a modular framework for empirical analysis of image-to-3D pipelines. By factorizing the generation process into a multiview-geometry prior followed by an appearance decoder, unPIC enables a rigorous comparison of intermediate geometry representations. Through this framework, we identify that a specific representation, Camera-Relative Object Coordinates (CROCS), significantly outperforms alternatives such as depth maps, pretrained visual features, and other pointmap-based representations. We demonstrate that CROCS is not only easier for the first-stage geometry prior to predict, but also serves as an effective conditioning signal for ensuring 360-degree consistency during appearance decoding. Another advantage is that CROCS enables fully feedforward, direct 3D point cloud generation without requiring a separate post-hoc reconstruction step. Our unPIC formulation utilizing CROCS achieves superior novel-view quality, geometric accuracy, and multiview consistency; it outperforms leading baselines, including InstantMesh, Direct3D, CAT3D, Free3D, and EscherNet, on datasets of real-world 3D captures like Google Scanned Objects and the Digital Twin Catalog.