Approximate conversion of a rational boundary gregory patch to a nonuniform B-spline surface
A rational boundary Gregory patch is characterized by the facts that anyn-sided loop can be smoothly interpolated and that it can be smoothly connected to an adjacent patch. Thus, it is well-suited to interpolate complicated wire frames in shape modeling. Although a rational boundary Gregory patch can be exactly converted to a rational Bézier patch to enable the exchange of data, problems of high degree and singularity tend to arise as a result of conversion. This paper presents an algorithm that can approximately convert a rational boundary Gregory patch to a bicubic nonuniform B-spline surface. The approximating surface hasC1 continuity between its inner patches.
Key wordsRational boundary Gregory patch Gregory patch Nonuniform B-spline surface Approximation Conversion C1 continuity Least squares
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- Bardis L, Patrikalakis NM (1989) Approximate conversion of rational B-spline patches. Comput Aided Geom Design 6:189–204Google Scholar
- Beeker E (1986) Smoothing of shapes designed with free-form surfaces. Comput Aided Design 18:224–232Google Scholar
- Chiyokura H, Kimura F (1983) Design of solids with free-form surfaces. Comput. Graph. 17:289–298Google Scholar
- Chiyokura H, Takamura T, Konno T, Harada T (1991)G 1 surface interprolation over irregular meshes with rational curves. In: Farin G (ed) NURBS for curve and surface designr. SIAM, Philadelphia, pp 15–34Google Scholar
- Farin G (1993) Curves and surfaces for computer aided geometric design: a practical guide. Academic Press, San DiegoGoogle Scholar
- Hoschek J (1987) Approximate conversion of spline curves. Comput Aided Design 4:59–66Google Scholar
- Hoschek J, Schneider F (1990) Spline conversion for trimmed rational Bézier and B-spline surfaces. Comput Aided Design 22:580–590Google Scholar
- Patrikalakis NM (1989) Approximate conversion of rational splines. Comput Aided Geom Design 6:155–165Google Scholar
- Takamura T, Ohta M, Toriya H, Chiyokura H (1990) A method to convert a Gregory patch and a rational boundary Gregory patch to a rational Bézier patch and its applications. In: Chua T, Kunii T (eds) CG International '90. Springer, Tokyo, pp 543–562Google Scholar
- Tuohy ST, Bardis L (1993) Low-degree approximation of high degree B-spline surfaces. Eng Comput 9:198–209Google Scholar
- Ueda K (1992) A method for removing the singularities from Gregory surfaces. In: Lyche T, Schumaker LL (eds) Mathematical Methods in computer aided geometric design II. Academic Press, San Diego, pp 597–606Google Scholar
- Wolter FE, Tuohy ST (1992) Approximation of high degree and procedural curves. Eng Comput 8:61–80Google Scholar