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UEC Int’l Mini-Conference No.53 13

Optimization of Point Set Visualization Based on LineSets and Bézier

Splines

Xianghan WEI ∗1 and Yoshio OKAMOTO 2

1 UEC Exchange Study Program (JUSST Program)
2 Department of Computer and Network Engineering
The University of Electro-Communications, Tokyo, Japan

Abstract

LineSets is an effective technique for set visualization, widely used in domains such as Geographic
Information Systems and Social Network Analytics. However, automatically generated LineSets face
challenges in visual clarity and aesthetics. This study focuses on optimizing LineSets to improve
visualization. It proposes an efficient algorithm based on Bézier splines to optimize curve smoothness
and multi-curve layout, enhancing the usability of LineSets.

Keywords: Set Visualization, LineSets, Bézier Splines, Optimization Methods

1 Introduction dle larger datasets with more sets and ele-
ments while maintaining clarity;
The visualization of sets and their relationships
is a fundamental task in data visualization, with • Enhanced Readability: The use of dis-
applications across various domains such as ge- tinct colors and well-placed curves allows
ographic information systems (GIS), social net- users to easily trace set memberships and
work analysis, and bioinformatics. The primary relationships.
goal of set visualization is to clearly represent These advantages make LineSets a suitable
the elements of each set and the relationships choice for applications requiring the visualiza-
between sets. Achieving this goal often requires tion of planar point sets, including map-based
reducing visual clutter and enabling users to ef- visualization, social network analysis, and other
ficiently retrieve information [1]. visual analytics scenarios [2].
LineSets is a novel method for visualizing 2D The problem of generating optimal LineSets
point sets. In LineSets, each set of points is for a given set of points remains a challenging
connected by a single curve with a unique color. task. Previous research [3, 4] has demonstrated
Points in a plane with different attributes or cat- that perceptually distinguishable colors, vary-
egories are distinguished by curves of different ing line widths, and different node diameters
colors. This approach offers significant advan- can improve task performance in automatically
tages over traditional methods: laid-out LineSets. However, the optimization of
curve drawing from a geometric perspective has
• Reduced Visual Clutter: By using been less explored. Curves generated by exist-
smooth curves instead of enclosed regions, ing algorithms often exhibit sharp turns, self-
LineSets minimize visual overlaps and pro- intersections, and overcrowded layouts, all of
vide a cleaner representation;
which negatively affect readability and aesthet-
ics. The goal of this study is to optimize the
• Improved Scalability: LineSets can han-
curves of LineSets for improved visualization.
∗ The author is supported by JASSO Scholarship. Specifically, we investigate how to optimize pa-