Abstract: To generate developable strip models that closely approximate a given design surface while balancing approximation accuracy and developability, a construction method is proposed for approximate developable strip models whose boundaries interpolate the target surface and are optimizable. First, the B-spline target surface is extended along the parametric direction of greater curvature, and strip boundary curves are defined within the extended parametric domain to generate an initial region segmentation. Then, a monotonic mapping function between adjacent boundary curves is constructed to obtain a ruled strip model whose generators and boundaries lie strictly on the target surface. Furthermore, an energy function measuring surface quality is constructed, and a quasi-Newton method with boundary constraints is employed to optimize the shape parameters of the boundary curves, achieving coordinated optimization of region segmentation and strip developability. Experiments are conducted on freeform surfaces and typical industrial CAD models such as blades and gears, with comparisons against existing methods. In the freeform surface experiments, the proposed method reduces the average twist angle by more than 50% compared with the fixed-boundary method, and to around 20% compared with the improved developable surface approximation method. In the surface patch experiments on blades and gears, the average twist angles of the strip models reach 0.1° and 0.05°, respectively, meeting industrial application requirements.