A skeleton-based technique for modelling implicit surfaces

In this paper, we develop a skeleton-based technique to model implicit surfaces using 2-D piecewise algebraic splines, which allows the construction of generalized cylinders with arbitrary cross-sections. Our method is based on smooth blending of a set of locally constructed general cylinders corresponding to different cross-sections along a given skeleton. Firstly, freeform cross-sections are reconstructed implicitly using the 2-D piecewise algebraic splines, and then, different cross-section profiles are weighted and summed up along the skeleton using the Partial Shape Preserving (PSP) spline basis functions. In addition, the smooth piecewise polynomial blending operations is employed to blend the branches of implicitly constructed generalized cylinders together. The implicit generalized cylinders constructed using our method is model free, and can achieve extremely high smoothness and accuracy.