The haloed line effect is a technique where when a line in three-dimensional space passes in front of another line, a gap is produced in the projection of the more distant line. The gap is produced as if an opaque halo surrounded the closer line. This method for approximate hidden-line-elimination is advantageous because explicit surface equations are not necessary. The relative depth of lines, axes, curves and lettering is easily perceived. This technique is especially suitable for the display of finite element grids, three-dimensional contour maps and ruled surfaces. When the lines or curves on a surface are closer than the gap size, the gaps produced close up to produce a complete hidden-line-elimination. A simple but efficient implementation is described which can be used in the rendering of a variety of three-dimensional situations.

A new approach to the computation of Jardine and Sibson's (1968a) (fine) k-cluster method Bk is described. The algorithm makes use of the fact that the set of dissimilarities which are invariant under the Bk clustering transformation can be represented as an abstract graph. The proposed algorithms for computing this graph obtains both the (weak) k-ultrametric dissimilarity matrix and the k-clusters simultaneously.