{"title":"Computing medial axis of a simple polygon in linear time based on R-L sequence","authors":"Hongyu Chen, Xiaodiao Chen, Yizhao Xue","doi":"10.1016/j.gmod.2025.101258","DOIUrl":null,"url":null,"abstract":"<div><div>Medial axis computation has wide applications in pattern recognition, image processing, finite element mesh generation, and CNC tool path extraction. Aiming to explore intrinsic geometric attributes of the medial axis of a simple polygon which can be accurately represented and faces its challenge of computational efficiency, an R-L sequence-based algorithm of linear computational complexity is proposed for achieving much higher efficiency; especially, it enables the complexity of Delaunay triangulation to be linear. The algorithm is done by reconstructing the Voronoi diagram tree of the given simple polygon, which can be easily performed in a breadth-first manner with a higher computational efficiency. The branches of the medial axis are naturally divided into several panels, such that the branches in the same panel cause no interference with each other and decrease a lot of computational costs. Based on our experiments, the efficiency of the proposed R-L algorithm can be 6 to 17 times greater than that of the state-of-the-art method in TVCG, and up to 419 times greater than the CGAL algorithm. In principle, it can be directly applied to compute the medial axis of curvilinear polygons, which expands the scope of application compared to Chin’s method.</div></div>","PeriodicalId":55083,"journal":{"name":"Graphical Models","volume":"139 ","pages":"Article 101258"},"PeriodicalIF":2.5000,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Graphical Models","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1524070325000050","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
引用次数: 0
Abstract
Medial axis computation has wide applications in pattern recognition, image processing, finite element mesh generation, and CNC tool path extraction. Aiming to explore intrinsic geometric attributes of the medial axis of a simple polygon which can be accurately represented and faces its challenge of computational efficiency, an R-L sequence-based algorithm of linear computational complexity is proposed for achieving much higher efficiency; especially, it enables the complexity of Delaunay triangulation to be linear. The algorithm is done by reconstructing the Voronoi diagram tree of the given simple polygon, which can be easily performed in a breadth-first manner with a higher computational efficiency. The branches of the medial axis are naturally divided into several panels, such that the branches in the same panel cause no interference with each other and decrease a lot of computational costs. Based on our experiments, the efficiency of the proposed R-L algorithm can be 6 to 17 times greater than that of the state-of-the-art method in TVCG, and up to 419 times greater than the CGAL algorithm. In principle, it can be directly applied to compute the medial axis of curvilinear polygons, which expands the scope of application compared to Chin’s method.
期刊介绍:
Graphical Models is recognized internationally as a highly rated, top tier journal and is focused on the creation, geometric processing, animation, and visualization of graphical models and on their applications in engineering, science, culture, and entertainment. GMOD provides its readers with thoroughly reviewed and carefully selected papers that disseminate exciting innovations, that teach rigorous theoretical foundations, that propose robust and efficient solutions, or that describe ambitious systems or applications in a variety of topics.
We invite papers in five categories: research (contributions of novel theoretical or practical approaches or solutions), survey (opinionated views of the state-of-the-art and challenges in a specific topic), system (the architecture and implementation details of an innovative architecture for a complete system that supports model/animation design, acquisition, analysis, visualization?), application (description of a novel application of know techniques and evaluation of its impact), or lecture (an elegant and inspiring perspective on previously published results that clarifies them and teaches them in a new way).
GMOD offers its authors an accelerated review, feedback from experts in the field, immediate online publication of accepted papers, no restriction on color and length (when justified by the content) in the online version, and a broad promotion of published papers. A prestigious group of editors selected from among the premier international researchers in their fields oversees the review process.