Two mathematical models in the context of boundary value problems are proposed for the geometric design of letters in Times Roman font.We adopt radial basis function meshless collocation method for numerically solving...Two mathematical models in the context of boundary value problems are proposed for the geometric design of letters in Times Roman font.We adopt radial basis function meshless collocation method for numerically solving the two proposed mathematical models in 2D and 3D.In this paper,B´ezier curves play an important role in the design of the letters.Three examples with simply and multiply-connected domains in 2D and 3D are presented to demonstrate the visual effect of the letters in Times Roman font.展开更多
In paper [1],it was shown that an explicit expression of the cardinal basis functions for two-point Hermite interpolation. This paper will show the explicit expression of Hermite interpolation under the Ball basis.
By using the blossom approach, we construct four new cubic rational Bernsteinlike basis functions with two shape parameters, which form a normalized B-basis and include the cubic Bernstein basis and the cubic Said-Bal...By using the blossom approach, we construct four new cubic rational Bernsteinlike basis functions with two shape parameters, which form a normalized B-basis and include the cubic Bernstein basis and the cubic Said-Ball basis as special cases. Based on the new basis, we propose a class of C2 continuous cubic rational B-spline-like basis functions with two local shape parameters, which includes the cubic non-uniform B-spline basis as a special case.Their totally positive property is proved. In addition, we extend the cubic rational Bernsteinlike basis to a triangular domain which has three shape parameters and includes the cubic triangular Bernstein-B′ezier basis and the cubic triangular Said-Ball basis as special cases. The G1 continuous conditions are deduced for the joining of two patches. The shape parameters in the bases serve as tension parameters and play a foreseeable adjusting role on generating curves and patches.展开更多
基金the financial support of the Ministry of Science and Technology(MOST),Taiwan,under the recruitment of visiting science and technology personnel with subsidies 110-2811-E-002-518the support of sabbatical leave provided by the University of Southern Mississippi.
文摘Two mathematical models in the context of boundary value problems are proposed for the geometric design of letters in Times Roman font.We adopt radial basis function meshless collocation method for numerically solving the two proposed mathematical models in 2D and 3D.In this paper,B´ezier curves play an important role in the design of the letters.Three examples with simply and multiply-connected domains in 2D and 3D are presented to demonstrate the visual effect of the letters in Times Roman font.
文摘In paper [1],it was shown that an explicit expression of the cardinal basis functions for two-point Hermite interpolation. This paper will show the explicit expression of Hermite interpolation under the Ball basis.
基金Supported by the National Natural Science Foundation of China(60970097 and 11271376)Postdoctoral Science Foundation of China(2015M571931)Graduate Students Scientific Research Innovation Project of Hunan Province(CX2012B111)
文摘By using the blossom approach, we construct four new cubic rational Bernsteinlike basis functions with two shape parameters, which form a normalized B-basis and include the cubic Bernstein basis and the cubic Said-Ball basis as special cases. Based on the new basis, we propose a class of C2 continuous cubic rational B-spline-like basis functions with two local shape parameters, which includes the cubic non-uniform B-spline basis as a special case.Their totally positive property is proved. In addition, we extend the cubic rational Bernsteinlike basis to a triangular domain which has three shape parameters and includes the cubic triangular Bernstein-B′ezier basis and the cubic triangular Said-Ball basis as special cases. The G1 continuous conditions are deduced for the joining of two patches. The shape parameters in the bases serve as tension parameters and play a foreseeable adjusting role on generating curves and patches.
基金supported by Natural Science Foundation of China(11271289,11502141)the Fundamental Research Funds for the Central Universitiesthe Key Program of NSFC-Guangdong Joint Fund of China(U1135003)
