Reducing control points in lofted B-spline surface interpolation using common knot vector determination

A new algorithm for reducing control points in lofted surface interpolation to rows of data points is presented in this paper. The key step of surface lofting is to obtain a set of compatible B-spline curves interpolating each row. Given a set of points and their parameterization, a necessary and sufficient condition is proposed to determine the existence of interpolating B-spline curves defined on a given knot vector. Based on this condition, we first properly construct a common knot vector that guarantees the existence of interpolating B-spline curves to each row of points. Then we calculate a set of interpolating B-spline curves defined on the common knot vector by energy minimization. Using this method, fewer control points are employed while maintaining a visually pleasing shape of the lofted surface. Several experimental results demonstrate the usability and quality of the proposed method.

[1]  Hyungjun Park,et al.  Smooth surface approximation to serial cross-sections , 1996, Comput. Aided Des..

[2]  C. Woodward.  Skinning techniques for interactive B-spline surface interpolation , 1988 .

[3]  Ralph R. Martin,et al.  Reverse engineering of geometric models - an introduction , 1997, Comput. Aided Des..

[4]  Les A. Piegl,et al.  Surface skinning revisited , 2002, The Visual Computer.

[5]  Gerald Farin,et al.  Curves and surfaces for cagd , 1992 .

[6]  Hyungjun Park,et al.  A method for approximate NURBS curve compatibility based on multiple curve refitting , 2000, Comput. Aided Des..

[7]  G. Farin.  Curves and Surfaces for Cagd: A Practical Guide , 2001 .

[8]  Les A. Piegl,et al.  Reducing Control Points in Surface Interpolation , 2000, IEEE Computer Graphics and Applications.

[9]  Les A. Piegl,et al.  Surface approximation to scanned data , 2000, The Visual Computer.

[10]  D. Jupp.  Approximation to Data by Splines with Free Knots , 1978 .

[11]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[12]  Tzvetomir Ivanov Vassilev,et al.  Fair interpolation and approximation of B-splines by energy minimization and points insertion , 1996, Comput. Aided Des..

[13]  L. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communications.

[14]  C. D. Boor,et al.  Total Positivity of the Spline Collocation Matrix. , 1973 .

[15]  W. Kellaway,et al.  Linear Algebra and Matrix Theory , 1964 .

[16]  Hyungjun Park.  Lofted B-spline surface interpolation by linearly constrained energy minimization , 2003, Comput. Aided Des..