A surface modeling method based on the envelope template

Authors:
Lixin Cao;Wenlan Ba;Jian Liu
Affiliations:
School of Mechanical Engineering, Dalian University of Technology, Dalian, 116024, China;School of Mechanical Engineering, Dalian University of Technology, Dalian, 116024, China;School of Mechanical Engineering, Dalian University of Technology, Dalian, 116024, China
Venue:
Computer Aided Geometric Design
Year:
2011

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Abstract

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. G^2 or C^2 composite surfaces can be obtained utilizing the envelope template sweeping over the data points.