A customized shoe-last system is developed based on the deformation of characteristic NURBS curves for feet or shoe-lasts to enable customized shoes without a shoe-last database. Deformations of the feet or shoe-lasts characteristic curves are used to make new shoe-lasts with constraints of the arc-lengths. The system uses comfort matching rules between the feet and the shoe-lasts with the characteristic curves divided into four types according to their different deformation ways, orders, and constraints. Deformation roadmaps are then given with forward, reverse and bidirectional deformation roadmaps for the II-type curves with arc-length constraints. The bidirectional deformation uses an improved vertex substitution algorithm and a modified variable-parameter 4-point interpolatory subdivision scheme with a new arc-length loss actor and a rigid joint chain model. Customized shoe-last curves are produced from a mother shoe-last through sampling, grading, sectioning, simplifying, deforming, subdividing, and NURBS fitting. For the metatarsophalangeal contour curve, a bidirectional deformation test gives an arc length change of 1.0 mm. With this system, a man's shoe-last can be customized in less than 480 s to give accurate, practical customized shoes without a shoe-last database. This method greatly increases the redesign for customized shoe-lasts.
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