Abstract
A new method for determining knots to construct polynomial curves is presented. At each data point, a quadric curve which passes three consecutive points is constructed. The knots for constructing the quadric curve are determined by minimizing the internal strain energy, which can be regarded as a function of the angle. The function of the angle is expanded as a Taylor series with two terms, then the two knot intervals between the three consecutive points are defined by linear expression. Between the two consecutive points, there are two knot intervals, and the combination of the two knot intervals is used to define the final knot interval. A comparison of the new method with several existing methods is included.
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A preliminary version of this paper appeared in Proc. the 1st Korea-China Joint Conference on Geometric and Visual Computing.
Supported by the National Natural Science Foundation of China (Grant Nos. 60403036, 60573114).
Cai-Ming Zhang is a professor and Ph.D. supervisor in the School of Computer Science and Technology at Shandong University. He is now also the dean and professor of the School of Computer Science and Technology at the Shandong Economic University. He received the B.S. and M.E. degrees in computer science from Shandong University in 1982 and 1984, respectively, and the Dr. Eng. degree in computer science from the Tokyo Institute of Technology, Japan, in 1994. From 1997 to 2000, Dr. Zhang has held visiting position at the University of Kentucky, USA. His research interests include CAGD, CG, information visualization and medical image processing.
Hui-Jian Han is an associate professor in the Computer School of Shandong Economic University. He received the M.E. degree in computer science from Shandong University in 2003. His current research interests include computer graphics, information visualization and CAGD.
Fuhua Frank Cheng is a professor of computer science and supervisor of the Graphics and Geometric Modeling Lab at the University of Kentucky where he joined the faculty in 1986. He received the B.S. and M.S. degrees in mathematics from the “National Tsing Hua University” in 1973 and 1975, respectively, the M.S. degree in mathematics, the M.S. degree in computer science, and the Ph.D. degeree in applied mathematics and computer science from the Ohio State Unversity, in 1978, 1980 and 1982, repectively. Dr. Cheng has held visiting positions at the University of Tokyo and the Unversity of Aizu, Japan. His research interests include computer aided geometric modeling, computer graphics, and parallel computing in geometric modeling and computer graphics.
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Zhang, CM., Han, HJ. & Cheng, F.F. Determining Knots by Minimizing Energy. J Comput Sci Technol 21, 261–264 (2006). https://doi.org/10.1007/s11390-006-0261-z
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DOI: https://doi.org/10.1007/s11390-006-0261-z