A surface modeling method based on the envelope template

In this paper, we present a novel surface modeling scheme based on an envelope template. A two-parameter family of interpolating surfaces is generated by repeated bicubic interpolation of the given data points, and then a solution to the envelope condition and the envelope of the family are constructed. The continuity conditions of two adjacent patches along the common boundary are derived by analyzing the geometric properties of the envelope patch. In order to facilitate surface modeling, an envelope template is constructed, which has many desirable advantages including simple structure, good local features and so on. G2G2 or C2C2 composite surfaces can be obtained utilizing the envelope template sweeping over the data points.

► A novel surface modeling scheme based on the envelope theory is proposed.
► The quadrilateral template and its degenerate cases are constructed.
► The composite surfaces with G2G2 or C2C2 continuity can be obtained by multiple templates.