Circle Approximations on Spheroids

被引：3

作者：

Ahn, Young Joon ^{[1
]}

Cui, Jian ^{[2
]}

Hoffmann, Christoph ^{[2
]}

机构：

[1] Chosun Univ, Kwangju, South Korea

[2] Purdue Univ, W Lafayette, IN 47907 USA

来源：

JOURNAL OF NAVIGATION | 2011年 / 64卷 / 04期

关键词：

geodesic circle; spheroid; geodesic distance; geodesic path; VECTOR SOLUTION; INTERSECTION; NAVIGATION;

D O I：

10.1017/S0373463311000294

中图分类号：

U6 [水路运输]; P75 [海洋工程];

学科分类号：

0814 ; 081505 ; 0824 ; 082401 ;

摘要：

We present an approximation method for geodesic circles on a spheroid. Our approximation curve is the intersection of two spheroids whose axes are parallel, and it interpolates four points of the geodesic circle. Our approximation method has two merits. One is that the approximation curve can be obtained algebraically, and the other is that the approximation error is very small. For example, our approximation of a circle of radius 1000 km on the Earth has error 1.13 cm or less. We analyze the error of our approximation using the Hausdorff distance and confirm it by a geodesic distance computation.

引用

页码：739 / 749

页数：11

共 50 条

[1] Approximations for Multiple Scan Statistics on the Circle
Lin, Chien-Tai
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2014, 43 (10-12) : 2476 - 2488
[2] A totally positive basis for circle approximations
J. M. Carnicer
E. Mainar
J. M. Peña
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2019, 113 : 3383 - 3397
[3] Approximations for discrete scan statistics on the circle
Chen, J
Glaz, J
STATISTICS & PROBABILITY LETTERS, 1999, 44 (02) : 167 - 176
[4] A totally positive basis for circle approximations
Carnicer, J. M.
Mainar, E.
Pena, J. M.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2019, 113 (04) : 3383 - 3397
[5] DIOPHANTINE APPROXIMATIONS ON A CIRCLE AND HAUSDORFF DIMENSION
MELNICHUK, YV
MATHEMATICAL NOTES, 1979, 26 (3-4) : 666 - 670
[6] ON COMMUTING CIRCLE MAPPINGS AND SIMULTANEOUS DIOPHANTINE APPROXIMATIONS
MOSER, J
MATHEMATISCHE ZEITSCHRIFT, 1990, 205 (01) : 105 - 121
[7] RATIONAL-APPROXIMATIONS ON THE UNIT-CIRCLE
KOPETZKY, HG
MONATSHEFTE FUR MATHEMATIK, 1980, 89 (04): : 293 - 300
[8] Formulations of composite parametric cubic curves and circle approximations
Chen, DP
COMPUTER-AIDED DESIGN, 1996, 28 (6-7) : 567 - 573
[9] On the numerical approximations of stiff convection–diffusion equations in a circle
Youngjoon Hong
Chang-Yeol Jung
Roger Temam
Numerische Mathematik, 2014, 127 : 291 - 313
[10] Formulations of composite parametric cubic curves and circle approximations
Institute of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan
CAD Comput Aided Des, 6-7 (567-573):

← 1 2 3 4 5 →