Abstract
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 hasC 1 continuity between its inner patches.
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References
Bardis L, Patrikalakis NM (1989) Approximate conversion of rational B-spline patches. Comput Aided Geom Design 6:189–204
Beeker E (1986) Smoothing of shapes designed with free-form surfaces. Comput Aided Design 18:224–232
Chiyokura H, Kimura F (1983) Design of solids with free-form surfaces. Comput. Graph. 17:289–298
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 15–34
Farin G (1993) Curves and surfaces for computer aided geometric design: a practical guide. Academic Press, San Diego
Hoschek J (1987) Approximate conversion of spline curves. Comput Aided Design 4:59–66
Hoschek J, Schneider F (1990) Spline conversion for trimmed rational Bézier and B-spline surfaces. Comput Aided Design 22:580–590
Patrikalakis NM (1989) Approximate conversion of rational splines. Comput Aided Geom Design 6:155–165
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 543–562
Tuohy ST, Bardis L (1993) Low-degree approximation of high degree B-spline surfaces. Eng Comput 9:198–209
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 597–606
Wolter FE, Tuohy ST (1992) Approximation of high degree and procedural curves. Eng Comput 8:61–80
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Tokuyama, Y., Konno, K. Approximate conversion of a rational boundary gregory patch to a nonuniform B-spline surface. The Visual Computer 11, 360–368 (1995). https://doi.org/10.1007/BF01909876
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DOI: https://doi.org/10.1007/BF01909876