Real solution formulas of cubic and quartic equations applied to generate dynamic diagrams with inequality constraints

Ting Zhao; Hoon Hong; Dongming Wang; Philippe Aubry

doi:10.1145/2245276.2245297

Real solution formulas of cubic and quartic equations applied to generate dynamic diagrams with inequality constraints

Ting Zhao^*
, Hoon Hong
, Dongming Wang
, Philippe Aubry

^*Corresponding author for this work

Beihang University
Laboratoire d'Informatique de Paris 6
North Carolina State University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

The approach of solving geometric constraints involving inequalities proposed by Hong and others uses triangular decomposition, solution formulas, and quantifier elimination. We show that for generating dynamic diagrams automatically the performance of this approach can be enhanced, in terms of stability of numeric computation and quality of generated diagrams, when the used solution formulas of cubic and quartic equations are replaced by newly introduced real solution formulas with inequality constraints. Several examples are presented to illustrate the enhanced approach and to demonstrate the advantages and effectiveness of the new solution formulas. An implementation of the enhanced approach in Java with interface to Epsilon and QEPCAD for automated generation of dynamic diagrams is outlined and some experimental data are provided.

Original language	English
Title of host publication	27th Annual ACM Symposium on Applied Computing, SAC 2012
Pages	94-101
Number of pages	8
DOIs	https://doi.org/10.1145/2245276.2245297
State	Published - 2012
Externally published	Yes
Event	27th Annual ACM Symposium on Applied Computing, SAC 2012 - Trento, Italy Duration: 26 Mar 2012 → 30 Mar 2012

Publication series

Name	Proceedings of the ACM Symposium on Applied Computing

Conference

Conference	27th Annual ACM Symposium on Applied Computing, SAC 2012
Country/Territory	Italy
City	Trento
Period	26/03/12 → 30/03/12

Keywords

dynamic diagram
geometric constraint solving
inequality constraint
quantifier elimination
real solution formula

Access to Document

10.1145/2245276.2245297

Cite this

@inproceedings{8ca93b5e1cb64befb794c4e64fea4367,

title = "Real solution formulas of cubic and quartic equations applied to generate dynamic diagrams with inequality constraints",

abstract = "The approach of solving geometric constraints involving inequalities proposed by Hong and others uses triangular decomposition, solution formulas, and quantifier elimination. We show that for generating dynamic diagrams automatically the performance of this approach can be enhanced, in terms of stability of numeric computation and quality of generated diagrams, when the used solution formulas of cubic and quartic equations are replaced by newly introduced real solution formulas with inequality constraints. Several examples are presented to illustrate the enhanced approach and to demonstrate the advantages and effectiveness of the new solution formulas. An implementation of the enhanced approach in Java with interface to Epsilon and QEPCAD for automated generation of dynamic diagrams is outlined and some experimental data are provided.",

keywords = "dynamic diagram, geometric constraint solving, inequality constraint, quantifier elimination, real solution formula",

author = "Ting Zhao and Hoon Hong and Dongming Wang and Philippe Aubry",

year = "2012",

doi = "10.1145/2245276.2245297",

language = "英语",

isbn = "9781450308571",

series = "Proceedings of the ACM Symposium on Applied Computing",

pages = "94--101",

booktitle = "27th Annual ACM Symposium on Applied Computing, SAC 2012",

note = "27th Annual ACM Symposium on Applied Computing, SAC 2012 ; Conference date: 26-03-2012 Through 30-03-2012",

}

Zhao, T, Hong, H, Wang, D & Aubry, P 2012, Real solution formulas of cubic and quartic equations applied to generate dynamic diagrams with inequality constraints. in 27th Annual ACM Symposium on Applied Computing, SAC 2012. Proceedings of the ACM Symposium on Applied Computing, pp. 94-101, 27th Annual ACM Symposium on Applied Computing, SAC 2012, Trento, Italy, 26/03/12. https://doi.org/10.1145/2245276.2245297

Real solution formulas of cubic and quartic equations applied to generate dynamic diagrams with inequality constraints. / Zhao, Ting; Hong, Hoon; Wang, Dongming et al.
27th Annual ACM Symposium on Applied Computing, SAC 2012. 2012. p. 94-101 (Proceedings of the ACM Symposium on Applied Computing).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Real solution formulas of cubic and quartic equations applied to generate dynamic diagrams with inequality constraints

AU - Zhao, Ting

AU - Hong, Hoon

AU - Wang, Dongming

AU - Aubry, Philippe

PY - 2012

Y1 - 2012

N2 - The approach of solving geometric constraints involving inequalities proposed by Hong and others uses triangular decomposition, solution formulas, and quantifier elimination. We show that for generating dynamic diagrams automatically the performance of this approach can be enhanced, in terms of stability of numeric computation and quality of generated diagrams, when the used solution formulas of cubic and quartic equations are replaced by newly introduced real solution formulas with inequality constraints. Several examples are presented to illustrate the enhanced approach and to demonstrate the advantages and effectiveness of the new solution formulas. An implementation of the enhanced approach in Java with interface to Epsilon and QEPCAD for automated generation of dynamic diagrams is outlined and some experimental data are provided.

AB - The approach of solving geometric constraints involving inequalities proposed by Hong and others uses triangular decomposition, solution formulas, and quantifier elimination. We show that for generating dynamic diagrams automatically the performance of this approach can be enhanced, in terms of stability of numeric computation and quality of generated diagrams, when the used solution formulas of cubic and quartic equations are replaced by newly introduced real solution formulas with inequality constraints. Several examples are presented to illustrate the enhanced approach and to demonstrate the advantages and effectiveness of the new solution formulas. An implementation of the enhanced approach in Java with interface to Epsilon and QEPCAD for automated generation of dynamic diagrams is outlined and some experimental data are provided.

KW - dynamic diagram

KW - geometric constraint solving

KW - inequality constraint

KW - quantifier elimination

KW - real solution formula

UR - https://www.scopus.com/pages/publications/84863565523

U2 - 10.1145/2245276.2245297

DO - 10.1145/2245276.2245297

M3 - 会议稿件

AN - SCOPUS:84863565523

SN - 9781450308571

T3 - Proceedings of the ACM Symposium on Applied Computing

SP - 94

EP - 101

BT - 27th Annual ACM Symposium on Applied Computing, SAC 2012

T2 - 27th Annual ACM Symposium on Applied Computing, SAC 2012

Y2 - 26 March 2012 through 30 March 2012

ER -

Real solution formulas of cubic and quartic equations applied to generate dynamic diagrams with inequality constraints

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Cite this