On Methods of Computer Graphics for Visualizing Densities

This article focuses on visualizing densities and density approximators. We develop the relationship between the isopleths, the gradient, and the surface normals for a density with two-dimensional support. We show that these form a trihedron. We also develop the algorithm for computing the surface n...

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Bibliographic Details
Published in:Journal of computational and graphical statistics 2002-03, Vol.11 (1), p.137-162
Main Authors: Wegman, Edward J, Luo, Qiang
Format: Article
Language:English
Subjects:
Density
Graphics
Lighting
Nomographs
Optical reflection
Point masses
Polygons
Rendering
Specular reflection
Stereo
Stereoscopy
Transparency
Visual design
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Summary:This article focuses on visualizing densities and density approximators. We develop the relationship between the isopleths, the gradient, and the surface normals for a density with two-dimensional support. We show that these form a trihedron. We also develop the algorithm for computing the surface normal for the isopleths of a density with three-dimensional support. With this information in hand, we discuss rendering and lighting models, contouring algorithms, stereoscopic display algorithms, and visual design considerations. We conclude with some examples and a discussion of our experiences in using rendering and lighting, transparency, stereoscopy, dynamic rotation, and dynamic thresholding techniques to visualize densities.
ISSN:1061-8600
1537-2715
DOI:10.1198/106186002317375659