NURBS and Grid Generation

This paper provides a basic overview of NURBS and their application to numerical grid generation. Curve/surface smoothing, accelerated grid generation, and the use of NURBS in a practical grid generation system are discussed.

[1]  Gerald Farin,et al.  Triangular Bernstein-Bézier patches , 1986, Comput. Aided Geom. Des..

[2]  Bernd Hamann,et al.  Computational Geometry Tools in Grid Generation. , 1993 .

[3]  Joe F. Thompson,et al.  Numerical grid generation , 1985 .

[4]  Joe F. Thompson,et al.  Aspects of numerical grid generation - Current science and art , 1993 .

[5]  Fujio Yamaguchi,et al.  Curves and Surfaces in Computer Aided Geometric Design , 1988, Springer Berlin Heidelberg.

[6]  B. Barsky,et al.  An Introduction to Splines for Use in Computer Graphics and Geometric Modeling , 1987 .

[7]  G. Strang,et al.  An Analysis of the Finite Element Method , 1974 .

[8]  E. Andersson,et al.  The automatic generation of convex surfaces , 1987 .

[9]  B. Hamann.  Construction of B-spline approximations for use in numerical grid generation , 1994 .

[10]  Robert E. Barnhill,et al.  Representation and Approximation of Surfaces , 1977 .

[11]  G. Farin,et al.  Ann-dimensional Clough-Tocher interpolant , 1987 .

[12]  Bernd Hamann,et al.  Interactive surface correction based on a local approximation scheme , 1996, Comput. Aided Geom. Des..

[13]  Z. Warsi.  Numerical grid generation in arbitrary surfaces through a second-order differential-geometric model , 1986 .

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

[15]  J. Castillo.  Mathematical Aspects of Numerical Grid Generation , 1991, Frontiers in Applied Mathematics.

[16]  G. Farin.  NURBS for Curve and Surface Design , 1991 .

[17]  A. Robin Forrest,et al.  Interactive interpolation and approximation by Bezier polynomials , 1972, Comput. J..

[18]  Mamoru Hosaka,et al.  Modeling of Curves and Surfaces in CAD/CAM , 1992, Computer Graphics — Systems and Applications.

[19]  E. Kaufmann,et al.  Smoothing surfaces using reflection lines for families of splines , 1988 .

[20]  Gerald E. Farin,et al.  Fairing cubic B-spline curves , 1987, Comput. Aided Geom. Des..

[21]  A. J. Worsey,et al.  Degree reduction of Be´zier curves , 1988 .

[22]  Bernd Hamann,et al.  Grid generation, finite elements, and geometric design , 1995, Comput. Aided Geom. Des..

[23]  N. Weatherill.  Delaunay triangulation in computational fluid dynamics , 1992 .

[24]  Rae A. Earnshaw,et al.  State of the Art in Computer Graphics , 1994, Springer New York.

[25]  R. Klass.  Correction of local surface irregularities using reflection lines , 1980 .

[26]  Bernd Hamann,et al.  Elliptic grid generation using NURBS surfaces , 1996, Comput. Aided Geom. Des..

[27]  L. Piegl.  Rational B-spline Curves and Surfaces for CAD and Graphics , 1991 .

[28]  Gerald E. Farin,et al.  Curvature and the fairness of curves and surfaces , 1989, IEEE Computer Graphics and Applications.

[29]  Gerald E. Farin,et al.  Automatic fairing algorithm for B-spline curves , 1990, Comput. Aided Des..

[30]  J. Oden,et al.  The Mathematics of Surfaces II , 1988 .

[31]  R. Franke.  Scattered data interpolation: tests of some methods , 1982 .

[32]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .