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Abstract In professional design workflows, designers often begin by creating sketch drawings before converting them into CAD programs. However, prior work on automatically interpreting these sketches has been limited to simplified inputs and fails to account for construction lines that are ubiquitous in real‐world drawings. We present CADrawer, a system that translates 3D sketches into CAD programs using an autoregressive approach, leveraging construction lines as a rich source of information for recovering intermediate CAD operations. At each step, CADrawer predicts the next modeling operation and its parameters based on a graph‐based representation of the sketch, which explicitly encodes spatial and temporal relationships between strokes. To improve generation quality, the system maintains multiple candidate programs in parallel, and a learned value function evaluates these partial programs to guide the search toward the most promising candidates. CADrawer is designed as a complement to 3D sketching interfaces, building on existing methods that creates 3D sketches. We evaluate our method across several datasets, including those containing dense construction lines and cases without ground‐truth B‐rep shapes. (see https://www.acm.org/publications/class‐2012 )