A curve modeling method based on the envelope template

This paper proposes a novel curve modeling method based on an envelope curve template. As the theoretical basis for the envelope template, a family of interpolating curves is generated by repeated interpolation of the given data points. On this basis, a family of one-parameter interpolating cylindrical surfaces is introduced, and then the envelope condition and its envelope surface are given, and the directrix of which serves as the prototype for curve modeling. After analyzing the geometric properties of the directrix of the envelope, the continuity conditions of two adjacent curve segments at the common point are derived. At a technical level, an envelope curve template is constructed, and the expected G2G2 or C2C2 composite curves can be obtained utilizing the envelope template sweeping over the data points.