ANALYSIS OF THE OFFSET TO A PARABOLA

被引：28

作者：

FAROUKI, RT ^{[1
]}

SEDERBERG, TW ^{[1
]}

机构：

[1] BRIGHAM YOUNG UNIV, DEPT CIVIL ENGN, PROVO, UT 84602 USA

来源：

COMPUTER AIDED GEOMETRIC DESIGN | 1995年 / 12卷 / 06期

基金：

美国国家科学基金会;

关键词：

PARABOLA; OFFSET; DOUBLE POINTS; QUADRATIC TRANSFORMATIONS; GENUS;

D O I：

10.1016/0167-8396(94)00038-T

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

Wei Lu has recently constructed a proper rational parameterization for the two-sided offset to a parabola-indicating that this locus, an irreducible curve of degree n = 6, is of genus 0. The theory of algebraic curves then requires that the parabola offset have 1/2(n - 1)(n - 2) = 10 double points. One affine node and six affine cusps are readily identified by geometric arguments; we show that the remaining three double points are accounted for by a non-ordinary double point at infinity, having double points in its first and second neighborhoods.

引用

页码：639 / 645

页数：7

共 10 条

[1]

Farouki R. T., 1990, Computer-Aided Geometric Design, V7, P83, DOI 10.1016/0167-8396(90)90023-K

[2] PYTHAGOREAN HODOGRAPHS [J].

FAROUKI, RT ;

SAKKALIS, T .

IBM JOURNAL OF RESEARCH AND DEVELOPMENT, 1990, 34 (05) :736-752

[3]

FAROUKI RT, 1990, COMPUT AIDED GEOM D, V7, P100

[4]

LU W, 1992, RATIONAL OFFSETS REP

[5]

PETERSON OJ, 1917, AM MATH MONTHLY, V24, P376

[6] RATIONAL CURVES AND SURFACES WITH RATIONAL OFFSETS [J].

POTTMANN, H .

COMPUTER AIDED GEOMETRIC DESIGN, 1995, 12 (02) :175-192

[7]

SALMON G, 1954, CONIC SECTIONS

[8]

Salmon G., 1960, HIGHER PLANE CURVES

[9]

SEDERBERG TW, 1986, COMPUT AIDED GEOM D, V6, P67

[10]

Walker RJ., 1962, ALGEBRAIC CURVES

← 1 →