Recovering an executable parametric CAD program from an observed object is fundamentally ambiguous, because the same final geometry can result from different construction procedures. We study this problem from four types of input: natural-language descriptions, rendered images, point clouds, and STEP/B-Rep geometry. MIRAGE-CAD maps each input to a shared construction representation and mediates program generation through an explicit construction-plan interface. The resulting Python CAD code is executed by an OpenCASCADE kernel to build the solid and export it as STEP. On 2,500 held-out queries per modality, the system achieves 55.4-70.0% build success and 52.3-66.2% STEP export success without retrieval at inference. Controlled comparisons show that strong reconstruction does not depend on expressing the construction representation as text: a decoder conditioned directly on the continuous representation also reconstructs strongly, while an exposure-matched plan-based decoder shows no detected material loss in per-part geometric fidelity. The explicit plan instead provides a readable and separately measurable intermediate representation whose agreement with the reference construction is informative about downstream execution success. Finally, we show that executable validity, geometric fidelity, and parametric responsiveness can diverge substantially and should therefore be evaluated separately.

翻译：暂无翻译