TY - JOUR
T1 - Approximate merging of a pair of Bezier curves
AU - Hu, Shi Min
AU - Tong, Rou Feng
AU - Ju, Tao
AU - Sun, Jia Guang
N1 - Funding Information:
This work was supported by the Natural Science Foundation of China (project number 69902004). We thank Prof. Tong-Guang Jin and Prof. Guo-Zhao Wang for encouraging this work, and Dr Wen-Shen Xu for his useful suggestions. We especially thank the reviewers for their helpful comments.
PY - 2001/2
Y1 - 2001/2
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0035254239&partnerID=8YFLogxK
U2 - 10.1016/S0010-4485(00)00083-X
DO - 10.1016/S0010-4485(00)00083-X
M3 - Article
AN - SCOPUS:0035254239
SN - 0010-4485
VL - 33
SP - 125
EP - 136
JO - CAD Computer Aided Design
JF - CAD Computer Aided Design
IS - 2
ER -