TY - GEN

T1 - Visual signature of high-dimensional geometry in parallel coordinates

AU - Yan, Xiaoqi

AU - Lai, Chi Fu

AU - Fu, Chi Wing

PY - 2014

Y1 - 2014

N2 - Although we can interactively rotate a 3D projected high-dimensional geometry and observe its dynamic changes, this traditional visualization method is limited and highly sensitive to the choice of viewing direction. Parallel-coordinates plots supplement this visualization scenario by providing statistical analysis of the geometry for distinct pairs of co-dimensions. Such analysis results in visual signatures that embed geometric structures such as symmetry, and thus allows us to overview the status of the missing dimensions while exploring the projected geometry. This paper presents a blue-noise sampling approach for efficient construction of continuous parallel-coordinates plots of high-dimensional geometric surfaces defined by mathematical equations. We employ the parallel-coordinates plots with the embedded visual signatures to assist the interactive exploration of high-dimensional geometries, typically for 2-manifold embedded in 4-space. While we interactively explore the 3D projected geometry, we can observe dynamic changes on its visual signature. Various geometric properties can also be identified and visualized. Moreover, we can interactively brush the plots, and see their counterparts in the 3D projection. Assorted geometric properties such as curvature can further be used to enhance the visual signature.

AB - Although we can interactively rotate a 3D projected high-dimensional geometry and observe its dynamic changes, this traditional visualization method is limited and highly sensitive to the choice of viewing direction. Parallel-coordinates plots supplement this visualization scenario by providing statistical analysis of the geometry for distinct pairs of co-dimensions. Such analysis results in visual signatures that embed geometric structures such as symmetry, and thus allows us to overview the status of the missing dimensions while exploring the projected geometry. This paper presents a blue-noise sampling approach for efficient construction of continuous parallel-coordinates plots of high-dimensional geometric surfaces defined by mathematical equations. We employ the parallel-coordinates plots with the embedded visual signatures to assist the interactive exploration of high-dimensional geometries, typically for 2-manifold embedded in 4-space. While we interactively explore the 3D projected geometry, we can observe dynamic changes on its visual signature. Various geometric properties can also be identified and visualized. Moreover, we can interactively brush the plots, and see their counterparts in the 3D projection. Assorted geometric properties such as curvature can further be used to enhance the visual signature.

KW - Computer Graphics-Applications

KW - Mathematical Software

KW - Parallel coordinates

KW - coordinated and multiple views

KW - geometry-based Techniques

KW - visualization in mathematics

UR - http://www.scopus.com/inward/record.url?scp=84899561647&partnerID=8YFLogxK

U2 - 10.1109/PacificVis.2014.41

DO - 10.1109/PacificVis.2014.41

M3 - Conference contribution

AN - SCOPUS:84899561647

SN - 9781479928736

T3 - IEEE Pacific Visualization Symposium

SP - 65

EP - 72

BT - Proceedings - 2014 IEEE Pacific Visualization Symposium, PacificVis 2014

T2 - 2014 7th IEEE Pacific Visualization Symposium, PacificVis 2014

Y2 - 4 March 2014 through 7 March 2014

ER -