Constructing continuous curves on point-cloud surfaces with Directed Projection Operator

With the development of 3D acquisition technology, the points based representation of complex objects and environment clouds has been widely applied in tool path generation, robot path planning and other fields. A new challenge is to construct continuous curves on point-cloud. We firstly proposed a new energy function to implement directed projection. Most importantly, we transformed the complex energy optimization relative to directed projection into simple numerical iteration named Directed Projection Operator(DPO). Then, by means of the DPO and its approximating surface, we provided two different approaches to construct G(2) continuous curves over the point-cloud surface. The constructed curve can not only be embedded into the point-cloud surface, but also be modified locally. A large number of experimental cases have verified the effectiveness and practicability of the proposed algorithms.