The algebra and geometry of Steiner and other quadratically parametrizable surfaces

被引：36

作者：

Coffman, A ^{[1
]}

Schwartz, AJ ^{[1
]}

Stanton, C ^{[1
]}

机构：

[1] UNIV MICHIGAN,DEPT MATH,ANN ARBOR,MI 48109

来源：

COMPUTER AIDED GEOMETRIC DESIGN | 1996年 / 13卷 / 03期

关键词：

projective geometry; parametrized surfaces; linear algebra; analytic geometry;

D O I：

10.1016/0167-8396(95)00026-7

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

Quadratically parametrizable surfaces (x(1), x(2), x(3), x(4))=(phi(1)(u), phi(2)(u), phi(3)(u), phi(4)(u)) where phi(k) are homogeneous functions are studied in P-3(R). These correspond to rationally parametrizable surfaces in R(3). All such surfaces of order greater than two are completely catalogued and described. The geometry of the parametrizations as well as the geometry of the surfaces are revealed by the use of basic matrix algebra. The relationship of these two geometries is briefly discussed. The presentation is intended to be accessible to applied mathematicians and does not presume a knowledge of algebraic geometry.

引用

页码：257 / 286

页数：30