Orthographic Star Coordinates

• Published in: IEEE transactions on visualization and computer graphics Vol. 19; no. 12; pp. 2615 - 2624
• Main Authors: Lehmann, Dirk J., Theisel, Holger
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.12.2013; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Computer Graphics; Data visualization; Distortion; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Information Storage and Retrieval - methods; Mathematical models; Minimization; multivariate visualization; Nonlinear distortion; Orthographic; Principal component analysis; Projection; Start plot; Studies; Three dimensional; Three-dimensional displays; Tours; Two dimensional; User-Computer Interface; visual analytics; Visualization
• ISSN: 1077-2626; 1941-0506
• DOI: 10.1109/TVCG.2013.182

Star coordinates is a popular projection technique from an nD data space to a 2D/3D visualization domain. It is defined by setting n coordinate axes in the visualization domain. Since it generally defines an affine projection, strong distortions can occur: an nD sphere can be mapped to an ellipse of arbitrary size and aspect ratio. We propose to restrict star coordinates to orthographic projections which map an nD sphere of radius r to a 2D circle of radius r. We achieve this by formulating conditions for the coordinate axes to define orthographic projections, and by running a repeated non-linear optimization in the background of every modification of the coordinate axes. This way, we define a number of orthographic interaction concepts as well as orthographic data tour sequences: a scatterplot tour, a principle component tour, and a grand tour. All concepts are illustrated and evaluated with synthetic and real data.