On Methods of Computer Graphics for Visualizing Densities

Abstract

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.