AN ALGEBRAIC APPROACH TO CURVES AND SURFACES ON THE SPHERE AND ON OTHER QUADRICS

被引：111
作者：
DIETZ, R [1 ]
HOSCHEK, J [1 ]
JUTTLER, B [1 ]
机构：
[1] TH DARMSTADT,FACHBEREICH MATH,SCHLOSSGARTENSTR 7,W-6100 DARMSTADT,GERMANY
来源：
COMPUTER AIDED GEOMETRIC DESIGN | 1993年 / 10卷 / 3-4期
关键词：
RATIONAL CURVES AND SURFACES; UNIT SPHERE; PYTHAGOREAN QUADRUPLE; GENERALIZED STEREOGRAPHIC PROJECTION; NET PROJECTION; BIQUADRATIC BEZIER PATCH; INTERPOLATION; B-SPLINE REPRESENTATIONS; PRODUCT FORMULA;
D O I：
10.1016/0167-8396(93)90037-4
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
An explicit representation for any irreducible rational Bezier curve and Bezier surface patch on the unit sphere is given. The extension to general quadrics (ellipsoids, hyperboloids, paraboloids) is outlined. The construction is based on an algebraic result concerning Pythagorean quadruples in polynomial rings and can be additionally interpreted as a generalized stereographic projection onto the sphere. This projection is shown to be the composition of a hyperbolic projection (a special net projection) with a stereographic projection. The investigation of its properties leads to new results for the biquadratic Bezier patch on the sphere. Further attention is payed to the interpolation of a given point set with a spherical rational curve. The results are extended to rational B-spline curves and tensor product B-spline surfaces.
引用
收藏
页码：211 / 229
页数：19
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