Method for Processing Graph Degeneracy in Dynamic Geometry Based on Domain Design

A dynamic geometry system, as an important application in the field of geometric constraint solving, is widely used in elementary mathematics education; moreover, the dynamic geometry system is also a fundamental environment for automated theorem proving in geometry. In a geometric constraint solvin...

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Published in:Journal of computer science and technology Vol. 36; no. 4; pp. 910 - 921
Main Authors: Guan, Hao, Rao, Yong-Sheng, Zhang, Jing-Zhong, Cao, Sheng, Qin, Xiao-Lin
Format: Journal Article
Language:English
Published: Singapore Springer Singapore 01.07.2021
Springer
Springer Nature B.V
Institute of Computing Science and Technology,Guangzhou University,Guangzhou 510006,China
University of Chinese Academy of Sciences,Beijing 100049,China%Institute of Computing Science and Technology,Guangzhou University,Guangzhou 510006,China%School of Computer Science and Engineering,University of Electronic Science and Technology of China Chengdu 61173,China%Chengdu Institute of Computer Applications,Chinese Academy of Sciences,Chengdu 610041,China
University of Chinese Academy of Sciences,Beijing 100049,China
Chengdu Institute of Computer Applications,Chinese Academy of Sciences,Chengdu 610041,China
Subjects:
Algorithms
Artificial Intelligence
Computer Science
Critical point
Data structures
Data Structures and Information Theory
Design optimization
Euclidean geometry
Geometric constraints
Geometry
Information Systems Applications (incl.Internet)
Methods
Regular Paper
Software Engineering
Theory of Computation
critical point
degeneracy
domain model
dynamic geometry
ISSN:1000-9000, 1860-4749
Online Access:Get full text
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Summary:A dynamic geometry system, as an important application in the field of geometric constraint solving, is widely used in elementary mathematics education; moreover, the dynamic geometry system is also a fundamental environment for automated theorem proving in geometry. In a geometric constraint solving process, a situation involving a critical point is often encountered, and geometric element degeneracy may occur at this point. Usually, the degeneracy situation must be substantively focused on during the learning and exploration process. However, many degeneracy situations cannot be completely presented even by the well-known dynamic geometry software. In this paper, the mechanisms causing the degeneracy of a geometric element are analyzed, and relevant definitions and formalized descriptions for the problem are provided according to the relevant modern Euclidean geometry theories. To solve the problem, the data structure is optimized, and a domain model design for the geometric element and the constraint relationships thereof in the dynamic geometry system are formed; furthermore, an update algorithm for the element is proposed based on the novel domain model. In addition, instances show that the proposed domain model and the update algorithm can effectively cope with the geometric element degeneracy situations in the geometric constraint solving process, thereby achieving unification of the dynamic geometry drawing and the geometric intuition of the user.
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ISSN:1000-9000
1860-4749
DOI:10.1007/s11390-021-0095-8