Generative methods for 3D assets have recently achieved remarkable progress, yet providing intuitive and precise control over the object geometry remains a key challenge. Existing approaches predominantly rely on text or image prompts, which often fall short in geometric specificity: language can be ambiguous, and images are difficult to manipulate. In this work, we introduce SpaceControl, a training-free test-time method for explicit spatial control of 3D asset generation. Our approach accepts a wide range of geometric inputs, from coarse primitives to detailed meshes, and integrates seamlessly with modern generative models without requiring any additional training. A control parameter lets users trade off between geometric fidelity and output realism. Extensive quantitative evaluation and user studies demonstrate that SpaceControl outperforms both training-based and optimization-based baselines in geometric faithfulness while preserving high visual quality. Finally, we present an interactive interface for real-time superquadric editing and direct 3D asset generation, enabling seamless use in creative workflows. Project page: https://spacecontrol3d.github.io/.

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