Publikation: Mathematical foundations of arc length-based aspect ratio selection
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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.
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HAN, Fubo, Yunhai WANG, Jian ZHANG, Oliver DEUSSEN, Baoquan CHEN, 2016. Mathematical foundations of arc length-based aspect ratio selection. 2016 IEEE Pacific Visualization Symposium (PacificVis). Taipei, Taiwan, 19. Apr. 2016 - 22. Apr. 2016. In: 2016 IEEE Pacific Visualization Symposium (PacificVis). Piscataway: IEEE, 2016, pp. 9-15. ISBN 978-1-5090-1451-4. Available under: doi: 10.1109/PACIFICVIS.2016.7465245BibTex
@inproceedings{Han2016Mathe-34968,
year={2016},
doi={10.1109/PACIFICVIS.2016.7465245},
title={Mathematical foundations of arc length-based aspect ratio selection},
isbn={978-1-5090-1451-4},
publisher={IEEE},
address={Piscataway},
booktitle={2016 IEEE Pacific Visualization Symposium (PacificVis)},
pages={9--15},
author={Han, Fubo and Wang, Yunhai and Zhang, Jian and Deussen, Oliver and Chen, Baoquan}
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