针对鞋楦数字化设计中对非线性尺寸的约束要求，提出一种基于微分坐标变形的尺寸驱动曲面变形方法，实现围长驱动的楦型设计。基于足-楦尺寸的对应关系修改鞋楦上的非线性尺寸，将围长尺寸变化映射为围线形状的变化，再由变化后的围线形状通过网格变形技术转化为楦型曲面的形状修改。通过迭代计算，可以保证围度曲线长度的精确约束；同时，根据楦型设计规律增加的位置约束和方向约束使变形后的曲面能够继承原有楦型曲面内在的形状特征；拉普拉斯变形拥有的特征保持性特点使变形后的鞋楦仍然保持原有的楦型样式，且其最小二乘意义下的求解框架有利于均布计算误差，使变形更加光顺、自然。试验结果表明，所提方法变形自然，实用性强。
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.
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