Assembler3 is a software tool that allows users to perform 3D parametric manipulations on 2D laser cutting plans. Assembler3 achieves this by semi-automatically converting 2D laser cutting plans to 3D, where users modify their models using available 3D tools (kyub), before converting them back to 2D. This workflow is 10x faster than using the traditional approach of editing 2D cutting plans directly. Assembler3 converts models to 3D in 5 steps: (1) plate detection, (2) joint detection, (3) material thickness detection, (4) joint matching based on hashed joint "signatures", and (5) interactive reconstruction. Once reconstructed, we expect users to store and share their models in 3D, which can simplify collaboration and thereby empower the laser cutting community to create models of higher complexity.