An iterative algorithm for multiwise merging of Bezier curves

This paper presents an iterative algorithm for multiwise merging of Bezier curves. By using the constraint, the distance is represented after simplification as a quartic polynomial in two parameters relating to the magnitudes of end tangents of the merged curve. These two parameters are restricted i...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2016-04, Vol.296, p.352-361
Main Authors: Lu, Lizheng, Jiang, Chengkai
Format: Article
Language:English
Subjects:
Curves (geometry)
Iterative algorithms
Mathematical analysis
Merging
Polynomials
Preserves
Simplification
Tangents
Online Access:Get full text
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Summary:This paper presents an iterative algorithm for multiwise merging of Bezier curves. By using the constraint, the distance is represented after simplification as a quartic polynomial in two parameters relating to the magnitudes of end tangents of the merged curve. These two parameters are restricted in a feasible region, in order for the merged curve to preserve the specified directions of end tangents. Then multiwise merging is formulated as a constrained minimization problem, and the classic projected Newton method is applied to find the minimizer. Some extensions of multiwise merging using constraints, other energy functionals and curve representations are also outlined. Several comparative examples are provided to demonstrate the effectiveness of the proposed method.
ISSN:0377-0427
DOI:10.1016/j.cam.2015.10.007