Constrained Surface Scaling
带约束的曲面放缩

A new method to scale a surface while holding the shape of specific features (trimming curves) unchanged is presented. The key of this method is using a new objective function to minimize the difference of the two surfaces before and after constrained scaling. The new objective function is defined as the integral of the square of the norm of the cross product of the two normal vectors on corresponding points of the two surfaces. Minimizing this objective function guarantees that the difference of the two normal vectors on every corresponding point of the two surfaces is as small as possible, which makes the shape and curvature distribution as close as possible. Compared with the Fix-and-Stretch method, the new method gives better results for several car parts with trimming curves. The high-light line models of the resulting surfaces produced by the two methods are also included.