Approximate merging of a pair of Bezier curves

Shi Min Hu, Rou Feng Tong, Tao Ju, Jia Guang Sun

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


This paper deals with the merging problem, i.e. to approximate two adjacent Bezier curves by a single Bezier curve. A novel approach for approximate merging is introduced in the paper by using the constrained optimization method. The basic idea of this method is to find conditions for the precise merging of Bezier curves first, and then compute the constrained optimization solution by moving the control points. `Discrete' coefficient norm in L2 sense and `squared difference integral' norm are used in our method. Continuity at the endpoints of curves are considered in the merging process, and approximate merging with points constraints are also discussed. Further, it is shown that the degree elevation of original Bezier curves will reduce the merging error.

Original languageEnglish
Pages (from-to)125-136
Number of pages12
JournalCAD Computer Aided Design
Issue number2
StatePublished - Feb 2001


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