Grand tour via geodesic interpolation of 2-frames

Daniel A. Asimov; Andreas Buja

doi:10.1117/12.172065

4 April 1994 Grand tour via geodesic interpolation of 2-frames

Daniel A. Asimov, Andreas Buja

Proceedings Volume 2178, Visual Data Exploration and Analysis; (1994) https://doi.org/10.1117/12.172065
Event: IS&T/SPIE 1994 International Symposium on Electronic Imaging: Science and Technology, 1994, San Jose, CA, United States

Abstract

Grand tours are a class of methods for visualizing multivariate data, or any finite set of points in n-space. The idea is to create an animation of data projections by moving a 2-dimensional projection plane through n-space. The path of planes used in the animation is chosen so that it becomes dense, that is, it comes arbitrarily close to any plane. One inspiration for the grand tour was the experience of trying to comprehend an abstract sculpture in a museum. One tends to walk around the sculpture, viewing it from many different angles. A useful class of grand tours is based on the idea of continuously interpolating an infinite sequence of randomly chosen planes. Visiting randomly (more precisely: uniformly) distributed planes guarantees denseness of the interpolating path. In computer implementations, 2-dimensional orthogonal projections are specified by two 1- dimensional projections which map to the horizontal and vertical screen dimensions, respectively. Hence, a grand tour is specified by a path of pairs of orthonormal projection vectors. This paper describes an interpolation scheme for smoothly connecting two pairs of orthonormal vectors, and thus for constructing interpolating grand tours. The scheme is optimal in the sense that connecting paths are geodesics in a natural Riemannian geometry.

Citation Download Citation

Daniel A. Asimov and Andreas Buja "Grand tour via geodesic interpolation of 2-frames", Proc. SPIE 2178, Visual Data Exploration and Analysis, (4 April 1994); https://doi.org/10.1117/12.172065

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