Visualizing Planar and Space Implicit Real Algebraic Curves with Singularities
文献类型：期刊论文
| 作者 | Chen, Changbo1,2; Wu, Wenyuan1,2 ; Feng, Yong1,2
|
| 刊名 | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
 |
| 出版日期 | 2020-04-30 |
| 页码 | 23 |
| 关键词 | Continuation method critical point method real algebraic curve singularity |
| ISSN号 | 1009-6124 |
| DOI | 10.1007/s11424-020-8380-0 |
| 通讯作者 | Wu, Wenyuan(wuwenyuan@cigit.ac.cn) |
| 英文摘要 | This paper presents a new method for visualizing implicit real algebraic curves inside a bounding box in the 2-D or 3-D ambient space based on numerical continuation and critical point methods. The underlying techniques work also for tracing space curve in higher-dimensional space. Since the topology of a curve near a singular point of it is not numerically stable, the authors trace only the curve outside neighborhoods of singular points and replace each neighborhood simply by a point, which produces a polygonal approximation that is epsilon-close to the curve. Such an approximation is more stable for defining the numerical connectedness of the complement of the projection of the curve in Double-struck capital R-2, which is important for applications such as solving bi-parametric polynomial systems. The algorithm starts by computing three types of key points of the curve, namely the intersection of the curve with small spheres centered at singular points, regular critical points of every connected components of the curve, as well as intersection points of the curve with the given bounding box. It then traces the curve starting with and in the order of the above three types of points. This basic scheme is further enhanced by several optimizations, such as grouping singular points in natural clusters, tracing the curve by a try-and-resume strategy and handling "pseudo singular points". The effectiveness of the algorithm is illustrated by numerous examples. This manuscript extends the proposed preliminary results that appeared in CASC 2018. |
| 资助项目 | National Natural Science Foundation of China[11771421] ; National Natural Science Foundation of China[11671377] ; National Natural Science Foundation of China[61572024] ; CAS Light of West China Program of Chongqing[cstc2018jcyj-yszxX0002] ; Key Research Program of Frontier Sciences of CAS[QYZDB-SSW-SYS026] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000529846900002 |
| 出版者 | SPRINGER HEIDELBERG |
| 源URL | [http://119.78.100.138/handle/2HOD01W0/10933]  |
| 专题 | 中国科学院重庆绿色智能技术研究院 |
| 通讯作者 | Wu, Wenyuan |
| 作者单位 | 1.Univ Chinese Acad Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Chongqing Key Lab Automated Reasoning & Cognit, Chongqing Inst Green & Intelligent Technol, Chongqing 400714, Peoples R China |
| 推荐引用方式 GB/T 7714 | Chen, Changbo,Wu, Wenyuan,Feng, Yong. Visualizing Planar and Space Implicit Real Algebraic Curves with Singularities[J]. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,2020:23. |
| APA | Chen, Changbo,Wu, Wenyuan,&Feng, Yong.(2020).Visualizing Planar and Space Implicit Real Algebraic Curves with Singularities.JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,23. |
| MLA | Chen, Changbo,et al."Visualizing Planar and Space Implicit Real Algebraic Curves with Singularities".JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY (2020):23. |
入库方式： OAI收割
来源：重庆绿色智能技术研究院
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