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Three‐dimensional stereoscopic plots

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Abstract Three‐dimensional (3‐d) stereoscopic plots allow human viewers to interpret printed plots, plots shown on a computer screen, or plots projected to a wall as realistic 3‐d images. Our human perception of depth, that is, the third dimension, works because of the fact that each of our eyes sees a slightly different image. When these images are combined in the human brain, we interpret the result as a third dimension that represents depth or distance. In 3‐d stereoscopic plots, two slightly different images are created and are presented to the two eyes of the viewer. When done well, a realistic 3‐d image is created in our brain. Various techniques exist to create and present the two different images to the human viewer. In this article, we will focus on techniques that have been used extensively in the field of statistics, that is, freeviewing of side‐by‐side images and anaglyphs. Additional techniques exist and will be presented in the context of Virtual Reality (VR) and CAVE environments. WIREs Comp Stat 2011 3 483–496 DOI: 10.1002/wics.189 This article is categorized under: Algorithms and Computational Methods > Computer Graphics Statistical Learning and Exploratory Methods of the Data Sciences > Exploratory Data Analysis Statistical and Graphical Methods of Data Analysis > Statistical Graphics and Visualization

Cube with inscribed octaeder, inspired by Abb. 295.1 in Ref 2: (a) Reconstructed for freeviewing of side‐by‐side images, and (b) red–cyan anaglyphs. (Reprinted with permission from Ref 3)

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Projection for two COPs. Subscripts l and ∗︁ relate to the left eye, subscripts r and × relate to the right eye, and no subscript and ○ relate to the imaginary central eye.

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Projection for a single COP.

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Model of two central projections.

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Four different projections of the 3‐d grand tour of the Iris data set, shown as red–cyan anaglyphs, were produced via the tourr package in R. The abbreviations SL (Sepal Length), SW (Sepal Width), PL (Petal Length), and PW (Petal Width) are used in these plots to denote the four variables of the Iris data set.

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Matrix of 3‐d scatterplots, showing each combination of three variables of the Iris data set as red–cyan anaglyphs. (Reprinted with permission from Ref 3.) The Anaglyphen 3D 2.0 software did not support the creation of any axis labels.

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Density of a bivariate beta distribution shown as red–cyan anaglyphs. (Reprinted with permission from Ref 3)

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Types of stereoscopic display systems, motivated by Figure 4 in Ref 9, and further extended with additional stereoscopic display systems.

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Viewing experience for anaglyphs where red and green filter glasses filter out what becomes invisible for each eye.

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Natural viewing of a point P that is located in front of a plane, compared to points A, B, and C that are located in a plane.

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Statistical Learning and Exploratory Methods of the Data Sciences > Exploratory Data Analysis
Algorithms and Computational Methods > Computer Graphics
Statistical and Graphical Methods of Data Analysis > Statistical Graphics and Visualization

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