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The rotation of the axes is a translation in the parallel coordinates and if the lines intersected outside the parallel axes it can be translated between them by rotations. The simplest example of this is rotating the axis by 180 degrees.<ref name="Gpc2" />
Scaling is necessary because the plot is based on interpolation (linear combination) of consecutive pairs of variables.<ref name="Gpc2">{{cite book |first1=Rida |last1=Moustafa |first2=Edward J. |last2=Wegman |chapter=Multivariate continuous data – Parallel Coordinates |
A smooth parallel coordinate plot is achieved with splines.<ref name="Gpc1">{{cite journal |first1=Rida |last1=Moustafa |first2=Edward J. |last2=Wegman |title=On Some Generalizations of Parallel Coordinate Plots |journal=Seeing a Million, A Data Visualization Workshop, Rain Am Lech (Nr.), Germany |year=2002 |url=http://herakles.zcu.cz/seminars/docs/infovis/papers/Moustafa_generalized_parallel_coordinates.pdf |archive-url=https://web.archive.org/web/20131224111246/http://herakles.zcu.cz/seminars/docs/infovis/papers/Moustafa_generalized_parallel_coordinates.pdf |url-status=dead |archive-date=2013-12-24 }}</ref> In the smooth plot, every observation is mapped into a parametric line (or curve), which is smooth, continuous on the axes, and orthogonal to each parallel axis. This design emphasizes the quantization level for each data attribute.<ref name="Gpc2" />
▲A smooth parallel coordinate plot is achieved with splines.<ref name="Gpc1">{{cite journal |first1=Rida |last1=Moustafa |first2=Edward J. |last2=Wegman |title=On Some Generalizations of Parallel Coordinate Plots |journal=Seeing a Million, A Data Visualization Workshop, Rain Am Lech (Nr.), Germany |year=2002 |url=http://herakles.zcu.cz/seminars/docs/infovis/papers/Moustafa_generalized_parallel_coordinates.pdf |archive-url=https://web.archive.org/web/20131224111246/http://herakles.zcu.cz/seminars/docs/infovis/papers/Moustafa_generalized_parallel_coordinates.pdf |url-status=dead |archive-date=2013-12-24 }}</ref> In the smooth plot, every observation is mapped into a parametric line (or curve), which is smooth, continuous on the axes, and orthogonal to each parallel axis. This design emphasizes the quantization level for each data attribute.<ref name="Gpc2" />
== Reading ==
Inselberg ({{harvnb|Inselberg|1997|p= }}) made a full review of how to visually read out parallel coords' relational patterns.<ref>{{citation|last1=Inselberg |first1=A.|year=1997 |chapter=Multidimensional detective |editor=|title=Information Visualization, 1997. Proceedings., IEEE Symposium on |series=|isbn=0-8186-8189-6|place=|pages=100–107|doi=10.1109/INFVIS.1997.636793}}</ref> When most lines between two parallel axis are somewhat parallel to each other, it suggests a positive relationship between these two dimensions. When lines cross in a kind of superposition of X-shapes, it's a negative relationship. When lines cross randomly or are parallel, it shows there is no particular relationship.
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* Heinrich, Julian and Weiskopf, Daniel (2013) ''[https://diglib.eg.org/handle/10.2312/conf.EG2013.stars.095-116 State of the Art of Parallel Coordinates]'', Eurographics 2013 - State of the Art Reports, pp. 95–116
* Moustafa, Rida (2011) '' Parallel coordinate and parallel coordinate density plots'', Wiley Interdisciplinary Reviews: Computational Statistics, Vol 3(2), pp. 134–148.
* Weidele, Daniel Karl I. (2019) ''[https://doi.org/10.1109/VISUAL.2019.8933632 Conditional Parallel Coordinates]'', IEEE Visualization Conference (VIS) 2019, pp.
==External links==
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