Some properties of n-dimensional triangulations

A number of mathematical results relevant to the problem of constructing a triangulation, i.e., a simplicial tessellation, of the convex hull of an arbitrary finite set of points in n-space are described. The principal results achieved are: (1) a set of n+2 points in n-space may be triangulated in at most 2 different ways; (2) the sphere test defined in this report selects a preferred one of these two triangulations; (3) a set of parameters is defined that permits the characterization and enumeration of all sets of n+2 points in n-space that are significantly different from the point of view of their possible triangulation; (4) the local sphere test induces a global sphere test property for a triangulation; and (5) a triangulation satisfying the global sphere property is dual to the n-dimensional Dirichlet tesselation, i.e., it is a Delaunay triangulation

The covariance matrix for the solution vector of an equality-constrained least-squares problem

Methods are given for computing the covariance matrix for the solution vector of an equality-constrained least squares problem. The methods are matched to the solution algorithms given in the book, 'Solving Least Squares Problems.

Integrals of a C-1-compatible triangular surface element

Definite integrals are evaluated for the cardinal functions of an interpolation method which provides C sup 1 continuity over a triangular grid

Study of the accuracy of the double-precision arithmetic operations on the IBM 7094 computer

Accuracy of double-precision arithmetic operations on IBM 7094 compute

Cockpit resource management training

The 6th General Flight Crew Training Meeting held in Montreal in May, 1984 was for most IATA member airlines the first time they had been exposed to what was then a relatively new aspect of flight crew training-resource management training. In reviewing the results of this meeting the IATA Flight Crew Training SubCommittee (FCTSC), which had been responsible for the agenda and the meeting itself, concluded that because very few airlines had implemented a program or even appeared to understand the term resource management, a member airline survey should be conducted and the results analyzed. This presentation shows the results of that survey in a form which can be related to the topics of the workshop

Sparse matrix methods based on orthogonality and conjugacy

A matrix having a high percentage of zero elements is called spares. In the solution of systems of linear equations or linear least squares problems involving large sparse matrices, significant saving of computer cost can be achieved by taking advantage of the sparsity. The conjugate gradient algorithm and a set of related algorithms are described

C super 1: Compatible interpolation over a triangle

An elementary derivation and a complete description is given of an algorithm for interpolation over a plane triangle when function values and first partial derivatives are given at the vertices. The method gives C1 continuity with neighboring triangles. The interpolation method is mathematically equivalent to one that has been discussed previously in the literature; however, the algorithmic form given here is more efficient than has previously been described

Tracking decision-making during architectural design

There is a powerful cocktail of circumstances governing the way decisions are made during the architectural design process of a building project. There is considerable potential for misunderstandings, inappropriate changes, change which give rise to unforeseen difficulties, decisions which are not notified to all interested parties, and many other similar problems. The paper presents research conducted within the frame of the EPSRC funded ADS project aiming at addressing the problems linked with the evolution and changing environment of project information to support better decision-making. The paper presents the conceptual framework as well as the software environment that has been developed to support decision-making during building projects, and reports on work carried out on the application of the approach to the architectural design stage. This decision-tracking environment has been evaluated and validated by professionals and practitioners from industry using several instruments as described in the paper