论文信息 - Exact and approximate computation of B-spline curves on surfaces

Exact and approximate computation of B-spline curves on surfaces

Abstract Curves on surfaces are important elements in computer aided geometric design. After presenting a method to explicitly compute these curves in three-dimensions, practical algorithmic issues are discussed concerning the efficiency of the implementation. Good approximations are important because of the quite high degree of exact curves on surfaces. We present two approximate solutions to the problem. The first is derived from the exact representation, while the second extends conventional least-squares approximation by incorporating the geometry of the surface as well. The efficiency and behaviour of the algorithms are evaluated by means of examples.

Gábor Renner | Volker Weiss | G. Renner | V. Weiss

[1] Knut Mørken,et al. Knot removal for parametric B-spline curves and surfaces , 1987, Comput. Aided Geom. Des..

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

[3] Hartmut Prautzsch,et al. A fast algorithm to raise the degree of spline curves , 1991, Comput. Aided Geom. Des..

[4] Ron Goldman,et al. Functional composition algorithms via blossoming , 1993, TOGS.

[5] Rida T. Farouki,et al. On the numerical condition of polynomials in Bernstein form , 1987, Comput. Aided Geom. Des..

[6] Stephen Mann,et al. An optimal algorithm for expanding the composition of polynomials , 1997, TOGS.

[7] Tony DeRose,et al. Composing Bézier simplexes , 1988, TOGS.

[8] Les A. Piegl,et al. The NURBS Book , 1995, Monographs in Visual Communication.

[9] T. Lyche,et al. A Data-Reduction Strategy for Splines with Applications to the Approximation of Functions and Data , 1988 .

[10] Donald E. Knuth,et al. The Art of Computer Programming, Volume I: Fundamental Algorithms, 2nd Edition , 1997 .

[11] Rida T. Farouki,et al. On the stability of transformations between power and Bernstein polynomial forms , 1991, Comput. Aided Geom. Des..

[12] E. T. Y. Lee,et al. Computing a chain of blossoms, with application to products of splines , 1994, Comput. Aided Geom. Des..

[13] Yuan-Ping Hu,et al. Moving a B-spline surface to a curve--a trimmed surface matching algorithm , 1997, Comput. Aided Des..