Mathematical Foundations of Arc Length-Based Aspect Ratio Selection
IEEE PacificVis 2016
Abstract:
The aspect ratio of a plot can strongly influence the perception of trends in the data. Arc length based aspect ratio selection (AL) has demonstrated many empirical advantages over previous methods. However, it is still not clear why and when this method works. In this paper, we attempt to unravel its mystery by exploring its mathematical foundation. First, we explain the rationale why this method is parameterization invariant and follow the same rationale to extend previous methods which are not parameterization invariant. As such, we propose maximizing weighted local curvature (MLC), a parameterization invariant form of local orientation resolution (LOR) and reveal the theoretical connection between average slope (AS) and resultant vector (RV). Furthermore, we establish a mathematical connection between AL and banking to 45 degrees and derive the upper and lower bounds of its average absolute slopes. Finally, we conduct a quantitative comparison that revises the understanding of aspect ratio selection methods in three aspects: (1) showing that AL, AWO and RV always perform very similarly while MS is not; (2) demonstrating the advantages in the robustness of RV over AL; (3) providing a counterexample where all previous methods produce poor results while MLC works well.Materials:
Paper: [PDF 2.5M].
Code: [ZIP 3.2M].
Data: [ZIP 4.8M].
PPT: [PPTX 1.4M].
Acknowledgement:
The authors wish to thank Fan Zhong for discussion. This work was supported in part by a grant from NSFC-Guangdong Joing Fund (U1501255), 973 program (2015CB352501), NSFC(11271350), and the Fundamental Research Funds of Shandong University.| Bibtex: | @article{Han_pacificVis:2016, author = {Fubo Han,Yunhai Wang,Jian Zhang, Oliver Deussen, Baoquan Chen}, title = {Rigorous Analysis of Arc Length-Based Aspect Ratio Selection}, conference = {IEEE Pacific Visualization 2016}, volume = {??}, number = {??}, year = {2016}, } |