Surface-dependent growth kinematics in euclidean 3-space

摘要

In this paper, we investigate the surface-dependent growth model in Euclidean 3-space. The surface-dependent model is developed for modeling the kinematics of surface growth for objects that can be generated by the curves on the surface, such as parasites and plants. This paper includes two main purposes for this model. The first is to parameterize this model using quaternions and homothetic motions, while expressing matrix representations of the surface-dependent growth model. The second one is to construct the surface-dependent growth model by using the growth velocity components related to the Darboux frame at each point of the generating curve. Moreover, to support the theory studied in the paper, various examples are illustrated.