Showing papers on "Delaunay triangulation published in 1982"

A precise method for determining contoured surfaces

Abstract: Although the petroleum geologist is concerned with analysing three-dimensional data, he relies entirely on two-dimensional portrayals - cross-sections and particularly contour maps of all types. With the advent of digital computers, machine contouring has become increasingly common, but little attention has been directed to the limitations of the various algorithms that can be employed to generate contour maps from a set of control points. For example, it is not widely appreciated that contouring procedures which faithfully honour the value of original control points produce poor predictions at locations where no control is available. Contouring a published set of topographic data shows how this and other limitations lead to approximations and errors in machine-generated contours. A new method based on triangulation interpolation using Delaunay tessellations (deltri analysis) is superior to existing methods. Not only does the method give the most accurate and objective measurement and display of the contoured surface, but it is also computationally efficient. Rapid calculation of volume of closure over contoured structures is possible. The method also allows estimation of the adequacy of the data on which the contouring is based by introducing a measure of 'roughness' of the surface. This is achieved by analysing the directions of normals to triangles surrounding each control point.

Computational Geometric Problems in Pattern Recognition

Abstract: This paper surveys recent results in the design and analysis of algorithms for solving geometric problems in pattern recognition. Among the problems considered are: the convex hull, the diameter, Voronoi diagrams, the relative neighborhood graph, polygon decomposition, and distance between sets. Some new results are presented; among them a new 0(n) algorithm for merging two convex polygons and a proof that a convex hull algorithm of Kim and Rosenfeld (35) works. Several open problems are also mentioned.

The perceptual graph: A new algorithm

Abstract: One of the major tools in the daily routine world of image processing is certainly... the lightpen. A contour which should be closed is broken. A moving particle has a continuous trajectory, but a camera will see only a dotted trail. Single cells overlap, and one wishes to separate them. The algorithm we propose here, which connects neighbouring points or particles, will bring a solution in such situations. Noteworthy is the fact that the execution time does not depend upon the number of points to be processed. Two particles are to be connected if in a given sense, the are neighbours. The neighborhood criterion used here goes back to Dirichlet and Delaunay. For its nice visual properties S. Sternberg called the result perceptual graph.

Yet another method for triangulation and contouring for automated cartography

Abstract: An algorithm is presented for hierarchical subdivision of a set of three-dimensional surface observations. The data structure used for obtaining the desired triangulation is also singularly appropriate for extracting contours. Some examples are presented, and the results obtained are compared with those given by Delaunay triangulation. The data points selected by the algorithm provide a better approximation to the desired surface than do randomly selected points.