Curve modeling is one of the basic work in computer aided geometric design and computer graphics. For the implicit conic fitting problem in this paper, the research methods that the objective function based on the min...Curve modeling is one of the basic work in computer aided geometric design and computer graphics. For the implicit conic fitting problem in this paper, the research methods that the objective function based on the minimal algebraic distance and geometric distance are summarized. The advantages and disadvantages of every method are analyzed simply, and the applications of the conic fitting are listed.展开更多
This paper discusses the problem that constructing a curve to satisfy the given endpoint constraints and chord-length parameters. Based on the research of Lu, the curve construction method for the entire tangent angle...This paper discusses the problem that constructing a curve to satisfy the given endpoint constraints and chord-length parameters. Based on the research of Lu, the curve construction method for the entire tangent angles region （α0, α1）∈（-r, r）×（-r, r） is given. Firstly, to ensure the weights are always positive, the three characteristics of cubic rational Bezier curve is proved, then the segment construction idea for the other tangent angles are presented in view of the three characteristics. The curve constructed with the new method satisfies the endpoint constraint and chord-length parameters, it＇s G1 continuous in every segment curve, and the shapes of the curve are well.展开更多
文摘Curve modeling is one of the basic work in computer aided geometric design and computer graphics. For the implicit conic fitting problem in this paper, the research methods that the objective function based on the minimal algebraic distance and geometric distance are summarized. The advantages and disadvantages of every method are analyzed simply, and the applications of the conic fitting are listed.
基金Supported by Shandong Province Higher Educational Science and Technology Program(No.J12LN34)Shandong Ji'nan College and Institute Independent Innovation Project(No.201303011,No.201303021,No.201303016)
文摘This paper discusses the problem that constructing a curve to satisfy the given endpoint constraints and chord-length parameters. Based on the research of Lu, the curve construction method for the entire tangent angles region （α0, α1）∈（-r, r）×（-r, r） is given. Firstly, to ensure the weights are always positive, the three characteristics of cubic rational Bezier curve is proved, then the segment construction idea for the other tangent angles are presented in view of the three characteristics. The curve constructed with the new method satisfies the endpoint constraint and chord-length parameters, it＇s G1 continuous in every segment curve, and the shapes of the curve are well.
