On NURBS: A Survey

Nonuniform rational B-spline (NURBS) curves and surfaces, which are based on rational and B-splines, are defined. The important characteristics of NURBS that have contributed to their wide acceptance as standard tools for geometry representation and design are summarized. Their application to representing conic sections and commonly used surfaces, designing curves and surfaces, and modifying shapes is examined.<<ETX>>

[1]  B. Barsky,et al.  Determining a set of B-spline control vertices to generate an interpolating surface , 1980 .

[2]  L. Piegl.  Modifying the shape of rational B-splines. part2: surfaces , 1989 .

[3]  Les A. Piegl,et al.  Infinite Control Points-A Method for Representing Surfaces of Revolution Using Boundary Data , 1987, IEEE Computer Graphics and Applications.

[4]  A. L. Klosterman.  A geometric modeler based on a dual-geometry representation polyhedra and rational b-splines , 1984 .

[5]  Hartmut Prautzsch,et al.  Degree elevation of B-spline curves , 1984, Comput. Aided Geom. Des..

[6]  G. Alexits.  Approximation theory , 1983 .

[7]  A. R. Forrest,et al.  The twisted cubic curve: a computer-aided geometric design approach , 1980 .

[8]  S. A. Coons.  SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS , 1967 .

[9]  Richard E. Parent.  A system for sculpting 3-D data , 1977, SIGGRAPH.

[10]  Les A. Piegl,et al.  Algorithms for Computing Conic Splines , 1990 .

[11]  Les A. Piegl,et al.  A technique for smoothing scattered data with conic sections , 1987 .

[12]  Tom Lyche,et al.  Discrete B-splines and subdivision techniques in computer-aided geometric design and computer graphics , 1980 .

[13]  L. Piegl,et al.  Curve and surface constructions using rational B-splines , 1987 .

[14]  Richard Franklin Riesenfeld,et al.  Applications of b-spline approximation to geometric problems of computer-aided design. , 1973 .

[15]  David F. Rogers,et al.  Mathematical elements for computer graphics , 1976 .

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

[17]  Kenneth James Versprille.  Computer-aided design applications of the rational b-spline approximation form. , 1975 .

[18]  Les A. Piegl,et al.  Interactive Data Interpolation by Rational Bezier Curves , 1987, IEEE Computer Graphics and Applications.

[19]  Hiroshi Akima,et al.  A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures , 1970, JACM.

[20]  Tom Lyche,et al.  Algorithms for degree-raising of splines , 1985, TOGS.

[21]  Les A. Piegl,et al.  A menagerie of rational B-spline circles , 1989, IEEE Computer Graphics and Applications.

[22]  G. W. Vickers,et al.  Simplified method for interactive adjustment of surfaces , 1980 .

[23]  Richard F. Riesenfeld,et al.  Aspects of modelling in computer aided geometric design , 1975, AFIPS '75.

[24]  Gábor Renner,et al.  Method of shape description for mechanical engineering practice , 1982 .

[25]  Michael A. Penna,et al.  Projective geometry and its applications to computer graphics , 1986 .

[26]  Wayne E. Carlson.  Techniques for the generation of three-dimensional data for use in complex image synthesis , 1982 .

[27]  D. F. Rogers.  Constrained B-spline curve and surface fitting , 1989 .

[28]  Andries van Dam.  PHIGS+ functional description revision , 1988, SIGGRAPH 1988.

[29]  C. R. Deboor,et al.  A practical guide to splines , 1978 .

[30]  Alan H. Barr,et al.  Global and local deformations of solid primitives , 1984, SIGGRAPH.

[31]  M. Cox.  The Numerical Evaluation of B-Splines , 1972 .

[32]  Charles D. Woodward,et al.  Cross-sectional design of B-spline surfaces , 1987, Comput. Graph..

[33]  I. Faux,et al.  Computational Geometry for Design and Manufacture , 1979 .

[34]  C. D. Boor,et al.  On Calculating B-splines , 1972 .

[35]  W. Boehm.  Inserting New Knots into B-spline Curves , 1980 .

[36]  Riesenfeld,et al.  Homogeneous Coordinates and Projective Planes in Computer Graphics , 1981, IEEE Computer Graphics and Applications.

[37]  R. Daniel Bergeron,et al.  SUDS - SUrface Description System , 1984, Eurographics.

[38]  David F. Rogers,et al.  B-Spline Curves and Surfaces for Ship Hull Definition , 1977 .

[39]  E. S. Cobb.  Design of sculptured surfaces using the b-spline representation , 1984 .

[40]  E. T. Y. Lee,et al.  Choosing nodes in parametric curve interpolation , 1989 .

[41]  Les A. Piegl,et al.  A geometric investigation of the rational bezier scheme of computer aided design , 1986 .

[42]  Gerald E. Farin,et al.  The octant of a sphere as a non-degenerate triangular Bézier patch , 1987, Comput. Aided Geom. Des..

[43]  Wayne Tiller,et al.  Rational B-Splines for Curve and Surface Representation , 1983, IEEE Computer Graphics and Applications.

[44]  C. D. Boor.  B(asic)-Spline Basics. , 1986 .