# Line Weaver: Importance-Driven Order Enhanced Rendering of Dense Line Charts

## Abstract

Line charts are an effective and widely used technique for visualizing series of ordered two-dimensional data points. The relationship between consecutive points is indicated by connecting line segments, revealing potential trends or clusters in the underlying data. However, when dealing with an increasing number of lines, the render order substantially influences the resulting visualization. Rendering transparent lines can help but unfortunately the blending order is currently either ignored or naively used, for example, assuming it is implicitly given by the order in which the data was saved in a file. Due to the noncommutativity of classic alpha blending, this results in contradicting visualizations of the same underlying data set, so-called "hallucinators". In this paper, we therefore present line weaver, a novel visualization technique for dense line charts. Using an importance function, we developed an approach that correctly considers the blending order independently of the render order and without any prior sorting of the data. We allow for importance functions which are either explicitly given or implicitly derived from the geometric properties of the data if no external data is available. The importance can then be applied globally to entire lines, or locally per pixel which simultaneously supports various types of user interaction. Finally, we discuss the potential of our contribution based on different synthetic and real-world data sets where classic or naive approaches would fail.

T. Trautner and S. Bruckner, "Line Weaver: Importance-Driven Order Enhanced Rendering of Dense Line Charts," Computer Graphics Forum, vol. 40, iss. 3, p. 399–410, 2021. doi:10.1111/cgf.14316

[BibTeX]

Line charts are an effective and widely used technique for visualizing series of ordered two-dimensional data points. The relationship between consecutive points is indicated by connecting line segments, revealing potential trends or clusters in the underlying data. However, when dealing with an increasing number of lines, the render order substantially influences the resulting visualization. Rendering transparent lines can help but unfortunately the blending order is currently either ignored or naively used, for example, assuming it is implicitly given by the order in which the data was saved in a file. Due to the noncommutativity of classic alpha blending, this results in contradicting visualizations of the same underlying data set, so-called "hallucinators". In this paper, we therefore present line weaver, a novel visualization technique for dense line charts. Using an importance function, we developed an approach that correctly considers the blending order independently of the render order and without any prior sorting of the data. We allow for importance functions which are either explicitly given or implicitly derived from the geometric properties of the data if no external data is available. The importance can then be applied globally to entire lines, or locally per pixel which simultaneously supports various types of user interaction. Finally, we discuss the potential of our contribution based on different synthetic and real-world data sets where classic or naive approaches would fail.

```
@article{Trautner-2021-LWI,
author = {Trautner, Thomas and Bruckner, Stefan},
title = {Line Weaver: Importance-Driven Order Enhanced Rendering of Dense Line Charts},
journal = {Computer Graphics Forum},
volume = {40},
number = {3},
pages = {399--410},
keywords = {information visualization, visualization techniques, line charts},
doi = {10.1111/cgf.14316},
abstract = {Line charts are an effective and widely used technique for visualizing series of ordered two-dimensional data points. The relationship between consecutive points is indicated by connecting line segments, revealing potential trends or clusters in the underlying data. However, when dealing with an increasing number of lines, the render order substantially influences the resulting visualization. Rendering transparent lines can help but unfortunately the blending order is currently either ignored or naively used, for example, assuming it is implicitly given by the order in which the data was saved in a file. Due to the noncommutativity of classic alpha blending, this results in contradicting visualizations of the same underlying data set, so-called "hallucinators". In this paper, we therefore present line weaver, a novel visualization technique for dense line charts. Using an importance function, we developed an approach that correctly considers the blending order independently of the render order and without any prior sorting of the data. We allow for importance functions which are either explicitly given or implicitly derived from the geometric properties of the data if no external data is available. The importance can then be applied globally to entire lines, or locally per pixel which simultaneously supports various types of user interaction. Finally, we discuss the potential of our contribution based on different synthetic and real-world data sets where classic or naive approaches would fail.},
year = {2021},
pdf = "pdfs/Trautner-2021-LWI.pdf",
thumbnails = "images/Trautner-2021-LWI-thumb.png",
images = "images/Trautner-2021-LWI-thumb.png",
vid = "vids/Trautner_2021_LineWeaver_video.mp4",
youtube = "https://youtu.be/-hLF5XSR_ws",
project = "MetaVis",
git = "https://github.com/TTrautner/LineWeaver"
}
```