Deformation of surfaces along curves and their applications

The connections between parameter surfaces enable the development of various geometric designs. However, these surfaces are generally connected along their boundaries in a rectangular domain. This study investigated the methods for connecting surfaces along a curve. To this end, we introduced two-variable degenerate functions and utilized their algebraic properties to characterize the form of the parameter surfaces for practical surface construction. The results were used to deform the surfaces along the curve. For application, we presented the examples of deformations using Bézier surfaces and extended them to general surfaces.