A Continuation Method for Visualizing Planar Real Algebraic Curves withÂ Singularities

doi:10.1007/978-3-319-99639-4_7

	A Continuation Method for Visualizing Planar Real Algebraic Curves withÂ Singularities
	Chen, Changbo; Wu, Wenyuan
	2018
会议日期	September 17, 2018 - September 21, 2018
会议地点	Lille, France
DOI	10.1007/978-3-319-99639-4_7
页码	99-115
英文摘要	We present a new method for visualizing planar real algebraic curves inside a bounding box based on numerical continuation and critical point methods. Since the topology of the curve near a singular point is not numerically stable, we trace the curve only outside neighborhoods of singular points and replace each neighborhood simply by a point, which produces a polygonal approximation that is -close to the curve. Such an approximation is more stable for defining the numerical connectedness of the complement of the curve, 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 circles centered at singular points, regular critical points of every connected component 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 and tracing the curve by a try-and-resume strategy. The effectiveness of the algorithm is illustrated by numerous examples. © 2018, Springer Nature Switzerland AG.
会议录	20th International Workshop on Computer Algebra in Scientific Computing, CASC 2018
语种	英语
电子版国际标准刊号	16113349
ISSN号	03029743
内容类型	会议论文
源URL	[http://119.78.100.138/handle/2HOD01W0/7981]
专题	中国科学院重庆绿色智能技术研究院
作者单位	Chongqing Key Laboratory of Automated Reasoning and Cognition, Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, University of Chinese Academy of Sciences, Beijing, China
推荐引用方式 GB/T 7714	Chen, Changbo,Wu, Wenyuan. A Continuation Method for Visualizing Planar Real Algebraic Curves withÂ Singularities[C]. 见:. Lille, France. September 17, 2018 - September 21, 2018.