Abstract: Aiming to meet the requirement of the non-linear dimension in the field of shoe last digital design, a surface deformation method according to feature size, which is based on differential coordinates, is proposed in this article. The non-linear dimension on shoe last is modified on the basis of the relationship between foot and last. Firstly, the change of the curve length is mapped to the deformation of the curve shape. Then, the altered curve is transformed into last surface through mesh deformation. The accuracy of the curve length constraint is ensured within a certain tolerance through iterative computations. Meanwhile, the location as well as the direction constraints are added according to rules of last design, enabling the surfaces after deformation to inherit the intrinsic shape characteristics of the original surface. The feature-preserving characteristic of Laplace deformation helps the deformed last maintain the original style. Moreover, the solving framework in the least-squares sense facilitates calculating errors uniformly, making the deformed surface more smooth and natural-looking. The results show that the proposed method is effective, practical and makes the surface deformation natural.

Key words: feature size, girth of last, Laplacian deformation, parametric design, shoe last