ABSTRACT
In this paper, the problem of particle spacing in geometric space is analyzed geometrically. Only for this problem, the "Grid theorem" is proposed in the geometric space. According to the theorem, the plane geometric graph is drawn on two adjacent particles in the geometric, and the two particles are planned in the graph. The diagonal bisector of each diagonal is drawn on the basis of the plane geometric diagram, and the diagonal center point is obtained. Furthermore, a direction of the same diagonal center point is taken as the secondary center point according to the subdivision line. Then, a feasible rule expression is obtained by summarizing and analyzing the results of the respective spacing, and the calculation and evaluation of this rule expression are extended.
- Tian Junqi, Han Banghe. Soft set advantage matrix of the diagonal properties and its induced reduction algorithm. Journal of Nanjing university (natural science), 2022, 58 (1): 49-59. DOI: 10.13232 / j. carol Carroll Nik juju. 2022. 01. 006.Google Scholar
- Zheng Qian, Liu Shan, Deng Lujuan, Corner detection algorithm based on parallelogram diagonal theory. Journal of zhengzhou university (engineering science), 2021, 42(4):19-25. (In Chinese) DOI: 10.13705/j.issn.1671-6833.2021.02.017.Google Scholar
- Yuan Lingyun, Yue Wenhong, Yang Ji. Exploration and Expansion of the teaching Content of "Diagonal Rule". Chemistry Teaching, 2020 (3): 80-85. (In Chinese) DOI: 10.3969/j.issn.1005-6629.2020.03.016.Google Scholar
- Cao Fangfang, Lv Quanyi. Parallel algorithm for solving asymmetric block tridiagonal linear equations. Journal of northwestern polytechnical university, 2011, 29 (2): 318-322. (In Chinese) DOI: 10.3969/j.issn.1000-2758.2011.02.030.Google Scholar
- Cui Xining, Lv Quanyi. Two-level parallel algorithm for solving block tridiagonal linear equations. Journal of northwestern polytechnical university, 2005, 23(6):817-820. (In Chinese) DOI: 10.3969/j.issn.1000-2758.2005.06.030.Google Scholar
- Sheng Yuebin, Song Xiaoqiu. A new distributed parallel algorithm for tridiagonal linear equations. Systems engineering and electronics, 2004, 26 (2): 258-260. DOI: 10.3321/j.issn: 1001-506x.2004.02.033.Google Scholar
- Li Lixin, Tan Jianrong. A Multi-diagonal Switching Algorithm for Forced Embedding Constrained Edges in Constrained Delaunay Triangulation. Chinese journal of computers, 1999, 22(10):1114-1118. (In Chinese) DOI: 10.3321/j.issn:0254-4164.1999.10.017.Google Scholar
- Pan Shuyuan. Correction and Communication: Presentation of Pythagorean Theorem in Elements of the Late Ming Dynasty (1607). Journal of Inner Mongolia normal university (natural science Chinese version), 2021, 50(5):396-405. (In Chinese) DOI: 10.3969/j.issn.1001-8735.2021.05.003.Google Scholar
- Sun Hui. All integer solutions of quadratic homogeneous Diophantine equation (n∑i =1) aix2i = by2. Journal of natural science of HEILONGJIANG university, 2003, 20(3):56-61. (In Chinese) DOI: 10.3969/j.issn.1001-7011.2003.03.014.Google Scholar
- Cai Yuejiang, Guo Yunting. Shang Gao did prove the Pythagorean Theorem – and also on the "moment" here should not be understood as a rectangle [J]. Mathematics practice and cognition, 2011, 41(12):1-5.Google Scholar
Index Terms
- Grid theorem: Expression Derived from Quadratic Division of Grid of Geometric Space by Diagonal Central Logic
Recommendations
Hierarchical grid conversion
Hierarchical grids appear in various applications in computer graphics such as subdivision and multiresolution surfaces, and terrain models. Since the different grid types perform better at different tasks, it is desired to switch between regular grids ...
Center stable matchings and centers of cover graphs of distributive lattices
ICALP'11: Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part ILet I be an instance of the stable marriage (SM) problem. In the late 1990s, Teo and Sethuraman discovered the existence of median stable matchings, which are stable matchings that match all participants to their (lower/upper) median stable partner. ...
Geometric modeling in shape space
SIGGRAPH '07: ACM SIGGRAPH 2007 papersWe present a novel framework to treat shapes in the setting of Riemannian geometry. Shapes -- triangular meshes or more generally straight line graphs in Euclidean space -- are treated as points in a shape space. We introduce useful Riemannian metrics ...
Comments