Tetrahedron mapping of points from n-space to three-space

We extend the triangulation method of Lee et al. (1977) and present a tetrahedron method for the sequential mapping of points in high-dimensional space into three-space. The three-space preserves distances among nodes of a tetrahedron. Whenever a new point is mapped, its distances to three points previously mapped are exactly preserved. Among these three points, one can be chosen as the point connected through a minimal spanning tree. Other two points can be chosen as the nearest neighbors among points previously mapped, or some fixed reference points. This method works well to display a moderate number of points where distances among points have to be maintained. It is also useful to display data clusters, and can be combined with linear mapping methods for visualizing large datasets. Various applications in pattern analysis are discussed.