INTEGRATION OF POLYNOMIALS OVER LINEAR POLYHEDRA IN EUCLIDEAN 3-DIMENSIONAL SPACE

被引：7

作者：

RATHOD, HT

RAO, HSG

机构：

来源：

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 1995年 / 126卷 / 3-4期

关键词：

D O I：

10.1016/0045-7825(95)00828-O

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

This paper is concerned with explicit formulas and algorithms for computing integrals of polynomials over a linear polyhedron in Euclidean three-dimensional space. Symbolic formulas for surface and volume integration are given. Two different approaches are discussed: The first algorithm is obtained by transforming a volume integral into a surface integral and then into a parametric line integral while the second algorithm is obtained by transforming a volume integral into a surface integral and then into a parametric double integral. These algorithms and formulas are followed by an application-example for which we have explained the detailed computational scheme. The symbolic results presented in this paper may lead to an easy incorporation of global geometric properties of solid objects, for example, the volume, centre of mass, moments of inertia, required in the engineering design process.

引用

页码：373 / 392

页数：20

共 50 条

[1] Integration of trivariate polynomials over linear polyhedra in Euclidean three-dimensional space
Rathod, HT
Rao, HSG
[J]. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES B-APPLIED MATHEMATICS, 1998, 39 : 355 - 385
[2] Integration of polynomials over N-dimensional linear polyhedra
Rathod, HT
Rao, HSG
[J]. COMPUTERS & STRUCTURES, 1997, 65 (06) : 829 - 847
[3] Boundary integration of polynomials over an arbitrary linear tetrahedron in Euclidean three-dimensional space
Rathod, HT
Hiremath, SV
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1998, 153 (1-2) : 81 - 106
[4] Integration of polynomials over an arbitrary tetrahedron in Euclidean three-dimensional space
Rathod, HT
Rao, HSG
[J]. COMPUTERS & STRUCTURES, 1996, 59 (01) : 55 - 65
[5] INTEGRATION OF POLYNOMIALS OVER N-DIMENSIONAL POLYHEDRA
BERNARDINI, F
[J]. COMPUTER-AIDED DESIGN, 1991, 23 (01) : 51 - 58
[6] Special Curves in 3-Dimensional Euclidean Space
[J]. Liu, Hui-Li (liuhl@mail.neu.edu.cn), 1669, Northeast University (38):
[7] DIFFERENTIATION OF SPINORS IN 3-DIMENSIONAL EUCLIDEAN SPACE
DODDS, B
[J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1973, 6 (MAY): : 473 - 480
[8] Software for exact integration of polynomials over polyhedra
De Loera, J. A.
Dutra, B.
Koeppe, M.
Moreinis, S.
Pinto, G.
Wu, J.
[J]. COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 2013, 46 (03): : 232 - 252
[9] Symbolic integration of polynomial functions over a linear polyhedron in Euclidean three-dimensional space
Rathod, HT
Rao, HSG
Hiremath, SV
[J]. COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING, 1996, 12 (08): : 461 - 470
[10] EMBEDDING OF RIEMANNIAN SURFACES IN 3-DIMENSIONAL EUCLIDEAN SPACE
RUEDY, R
[J]. COMMENTARII MATHEMATICI HELVETICI, 1968, 43 (04) : 417 - &

← 1 2 3 4 5 →