Template-Based Digital Surface Reconstruction of Shoe Lasts from Point Clouds

The shoe last is central to footwear design. Modern footwear CAD operates on parametric digital lasts, yet much last geometry—legacy collections and lasts that skilled last makers still sculpt by hand and copy by pantograph turning—exists only as physical models or as point-cloud scans lacking the structured parametric form that footwear CAD requires. This paper presents a complete template-based method for reconstructing a watertight parametric last from a segmented point cloud without intermediate triangulation. The only manual input is three landmark points—for which the system proposes standard positions—and the interactive confirmation of two boundary lines on the digitized last. From these, the method defines four feature points, a median plane, and a four-curve boundary network; all subsequent stages run without user interaction. A curvature-adaptive quadrilateral grid is constructed on the cloud by geodesic tracing and monitor-weighted area-orthogonality relaxation. A periodic Coons tube interpolates the grid and initializes the parameterization for a periodic tensor-product cubic B-spline surface fitted by penalized least squares with cyclic/open difference penalties, exact boundary interpolation, and toe-aware weighting. Cap surfaces close both collar and sole openings, and the model is exported as a watertight B-rep solid. Tests on sixteen industrial lasts using one fixed parameter set produced a mean one-sided deviation of 0.034 mm (RMS 0.058 mm) from the withheld industrial reference meshes in approximately 12 s per last. With synthetic noise at 50 dB SNR, the mean deviation increased by only 0.011 mm. A sampling-density study indicated near-second-order convergence before the control-net reaches an upper limit. The resulting solids import directly into CAD systems and support re-lasting, footwear design, and customization.