Journal of Surveying Engineering

Simpson one‐third formula for calculating the area of an irregular region requires that the intervals between measurements be equal. In practice, however, taking measurements at equal intervals may be neither economical, especially if the region boundary exhibits varying fluctuations, nor physically possible. This paper develops a generalization of Simpson one‐third formula that allows the use of unequal intervals. The generalized Simpson (GS) formula is first derived for three ordinates based on Lagrange interpolating polynomial. A composite GS formula for calculating the area given any even number of intervals is then presented. An extended formula is developed for cases in which the number of intervals is odd. The extended formula gives the area for the last interval based on a quadratic polynomial which approximates the boundary shape. An algorithm for calculating the area (using even or odd unequal intervals) is presented. Application of the formulas is illustrated by a numerical example.

The shift in market emphasis from conventional to digital mapping is now approaching completion in Canada. However, while hardware and software are evolving rapidly, management preparation and practices are not keeping pace. In some private companies, the loosely planned implementation of digital mapping and geographic information systems are resulting in operational bottlenecks and, in some cases, significant financial losses. This paper draws on the industrial experience of the senior writer and examines the impact of digital mapping on the organization structure, systems management activities, and project management procedures in a private company. Some of the more significant issues of managing digital versus conventional mapping operations are discussed and some overal industry concerns are highlighted.

The formula used in surveying applications for estimating excavation volume for a rectangular pit assumes that the ground profile between the grid points is linear. In this paper, formulas that consider a nonlinear ground profile (NLP) between the grid points are presented. The NLP formulas are based on an extension of the known Simpson 1/3 and 3/8 formulas for calculating area of a region with irregular boundary. For an even number of intervals in each direction of the rectangular grid, the NLP formula is based on Simpson 1/3 formula. For an odd number of intervals in one or both directions of the rectangular grid, the NLP formula is based on a combination of Simpson 1/3 and 3/8 formulas. The NLP formulas are simple and amenable to computations by calculators or computers. The formulas should provide a better accuracy than the linear profile formula currently in use. Application of the NLP formulas is illustrated by a numerical example.

In order to properly apply transformations when using data derived from different space techniques, the corresponding frames should be clearly stated. Only then can a rigorous comparison of results be established. This review is an attempt to expound some of the basic definitions and concepts of reference frames to users from diverse backgrounds, who are not familiar with the geodetic terminology.