Smoothing surfaces using reflection lines for families of splines
Computer-Aided Design - Special issue on the shape of surfaces
Energy, fairness, and a counterexample
Computer-Aided Design
The NURBS book (2nd ed.)
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Method to approximate the space curve of least energy and prescribed length
Computer-Aided Design
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This paper presents a new method for extending B-Spline curve. Cubic Bézier curve is used to construct the extending segment and G 2 continuity is used to describe the smoothness of joint point. Optimization objective functions are established based on the minimum precise exact energy and the minimum precise curvature variation of the extending curve, respectively. The degree of freedom of the extended curve is determined by minimizing the objective functions. The non-linear optimization can be transform to non-linear least-square problem which can be linearized by a Gauss-Newton iterative algorithm. New control points are computed by extending curve and original curve. The comparison of the curves with different objective functions is included.