  Reverse engineering CAD models from raw geometry is a classic but challenging
research problem. In particular, reconstructing the CAD modeling sequence from
point clouds provides great interpretability and convenience for editing. To
improve upon this problem, we introduce geometric guidance into the
reconstruction network. Our proposed model, PS-CAD, reconstructs the CAD
modeling sequence one step at a time. At each step, we provide two forms of
geometric guidance. First, we provide the geometry of surfaces where the
current reconstruction differs from the complete model as a point cloud. This
helps the framework to focus on regions that still need work. Second, we use
geometric analysis to extract a set of planar prompts, that correspond to
candidate surfaces where a CAD extrusion step could be started. Our framework
has three major components. Geometric guidance computation extracts the two
types of geometric guidance. Single-step reconstruction computes a single
candidate CAD modeling step for each provided prompt. Single-step selection
selects among the candidate CAD modeling steps. The process continues until the
reconstruction is completed. Our quantitative results show a significant
improvement across all metrics. For example, on the dataset DeepCAD, PS-CAD
improves upon the best published SOTA method by reducing the geometry errors
(CD and HD) by 10%, and the structural error (ECD metric) by about 15%.
