3D visualisations in simulations of future land use: exploring the possibilities of new,standard visualisation tools

Abstract

Three-dimensional (3D) visualisations are an interesting method for representing model outcomes. Most visualisation techniques require expensive software and a lot of time to create them. When the visualisations need to be adapted frequently, a faster and more flexible method is needed. The first step of the proposed model is to create the 3D elements. These elements are combined with the base map, and distributed to the public using Google Earth. Both freely available and commercial software are used in this process.     

LEAST-SQUARE SOLUTIONS WITH WEIGHTS

Abstract

The modern abridged method of solution as applied to observation equations was given in an earlier number of this Review. The present article, applying the same abridged method to the solution of conditioned equations, shows how the weights of any functions of the adjusted values can be obtained as well as the corrections themselves. The case where the weights of adjusted functions are most frequently required in practice is that of a triangulation base extension figure. It is well known that the error generated in reaching the first side of the main triangulation proper from the measured base may be considerably greater than thereafter when sides are long and grazing shots rare. For this reason it is good practice to compute rigorously the probable error of the first main side from the base. It is usually found that the p.e. of the base itself is only a small fraction of the total. If the total p.e. of this first main side is too large, it may then be considered whether the extension figure should not be either completely reobserved or even redesigned to give a better result. Even if the observations themselves are all considered to be of equal weight (as is common practice nowadays with good instruments and good methods of observing), the weights of the adjusted functions will still differ from the mean, depending on the condition equations set up by the extension figure adopted.     

THE APPLICATION OF THE GAUSS METHOD OF COLLIMATION TO THE ADJUSTMENT OF SURVEY INSTRUMENTS

Abstract

Gauss's method of collimation is usually given scant attention in survey text-books. The following notes are based on experiments carried out at Accra in making a collimation base, the collimator being a Watts 2I-inch self-adjusting level fitted with a parallelplate micrometer.     

SOME SUGGESTIONS FOR SPEEDING UP WORK ON TOPOGRAPHICAL SURVEYS

Abstract

A Few notes will now be given on the subject of triangulation on which practically all the methods already outlined depend. If we have a triangulation ready for us on which to base our work, so much the better; but, if not, we must make every effort to carry one through either from our own measured base or from any existing points on the edge of our work. For reconnaissance survey, such a triangulation must be carried out with the greatest expedition; even if all refinements are sacrificed to speed, it is extraordinary how small the errors will be found to be when a more rigid triangulation is made. Any unorthodox method such as carrying through with a resected point or with an astronomical azimuth may be adopted. A bush will often make a good point to observe to, also piles of bushes with a flag on a reed or stick.     

THE PROJECTIVE TRANSFORMATION IN AERIAL SURVEYING

Abstract

4.3. Having found s we may proceed to obtain the coordinates of the air station. This is the vertex of a pyramid, the base edges being of lengths a, b, c and the opposite edges measuring u, v, w respectively. Let h be the distance of the vertex from the plane of the base, and suppose d, e₁ e₂, e₃ are respectively twice the areas of the base and of the oblique faces in order.     

DUALITY IN BI-PROJECTIVE CORRESPONDENCE

Abstract

Bi-projection connotes the method of constructing plastic models of an object by projecting two photographs taken from different stations. The variables representing the relative orientation of the two plates and others representing the direction of the base are shown to satisfy symmetrical bi-linear equations, from which it follows that solutions always occur in pairs, and when one solution of a pair is known the other can be written down immediately. It is unlikely that any doubt will ever arise in practice on which solution should be taken. The equations are well suited for the numerical solution of the biprojective problem using the cartesian coordinates of corresponding points on the plates.     

NOTES ON TRAVERSING WITH SUBTENSE BAR

Abstract

The advantages of subtense measurements with a horizontal base are well known, but this method has not yet gained much popularity witH the ordinary surveyor and an acknowledgment of, its usefulness in cadastral and engineering surveys has not yet found a proper place. Everyone knows the difficulties of direct chaining in hilly and rough country or in industrial and mining districts where numerous obstructions are usually encountered and where reliable accuracy throughout the area under survey would be difficult to maintain. Adoption of the subtense bar in such circumstances is the best answer to the problem, and the establishment of control points by this method assures economy and reliability. The subtense bar is easy and direct in use and the precision of the results obtained are comparable with precise chaining. The use of an invar bar or a steel tubular bar is essential in precise traversing with an accuracy of 1/10,000 or greater, but for ordinary control. traverses with an accuracy up to 1/5,000 the wooden bar may be sufficient.     

Mixed Integer-Real Valued Adjustment (IRA) Problems: GPS Initial Cycle Ambiguity Resolution by Means of the LLL Algorithm

In order to achieve to GPS solutions of first-order accuracy and integrity, carrier phase observations as well as pseudorange observations have to be adjusted with respect to a linear/linearized model. Here the problem of mixed integer-real valued parameter adjustment (IRA) is met. Indeed, integer cycle ambiguity unknowns have to be estimated and tested. At first we review the three concepts to deal with IRA: (i) DDD or triple difference observations are produced by a properly chosen difference operator and choice of basis, namely being free of integer-valued unknowns (ii) The real-valued unknown parameters are eliminated by a Gauss elimination step while the remaining integer-valued unknown parameters (initial cycle ambiguities) are determined by Quadratic Programming and (iii) a RA substitute model is firstly implemented (real-valued estimates of initial cycle ambiguities) and secondly a minimum distance map is designed which operates on the real-valued approximation of integers with respect to the integer data in a lattice. This is the place where the integer Gram-Schmidt orthogonalization by means of the LLL algorithm (modified LLL algorithm) is applied being illustrated by four examples. In particular, we prove that in general it is impossible to transform an oblique base of a lattice to an orthogonal base by Gram-Schmidt orthogonalization where its matrix enties are integer. The volume preserving Gram-Schmidt orthogonalization operator constraint to integer entries produces “almost orthogonal” bases which, in turn, can be used to produce the integer-valued unknown parameters (initial cycle ambiguities) from the LLL algorithm (modified LLL algorithm). Systematic errors generated by “almost orthogonal” lattice bases are quantified by A. K. Lenstra et al. (1982) as well as M. Pohst (1987). The solution point of Integer Least Squares generated by the LLL algorithm is = (L')⁻¹[L'◯] ∈ ℤ ^m where L is the lower triangular Gram-Schmidt matrix rounded to nearest integers, [L], and = [L'◯] are the nearest integers of L'◯, ◯ being the real valued approximation of z ∈ ℤ ^m , the m-dimensional lattice space Λ. Indeed due to “almost orthogonality” of the integer Gram-Schmidt procedure, the solution point is only suboptimal, only close to “least squares.” ? 2000 John Wiley & Sons, Inc.     

THE GENERAL THEORY OF TAPE SUSPENSION IN BASE MEASUREMENT

Abstract

The method of accurate linear measurement by means of suspended Invar steel tapes or wires has, since its introduction by Jäderin about the beginning of this century, entirely replaced the older methods of base measurement by bars or rods. It is not surprising, therefore, that the theoretical basis of the method—including a determination of the form of the curved tape and of its horizontal projection—should have received close attention. The most valuable recent contributions to the subject, since Benoit and Guillaume's classic work La Mesure Rapide des Bases Geodesiques, are by Professor and Major Henrici and by the late Mr A. E. Young.     

THE ADJUSTMENT OF A FIRST-ORDER LEVELLING NETWORK

Abstract

In the E.S.R. January and April numbers of 1955, Vol. xiii, Nos. 95 and 96, Mr. Hsuan-Loh Su described the “Adjustment of a Level Net by Successive Approximations and by Electrical Analogy”. It does not seem to be as generally known as it should be that the rigid least square solution can be greatly simplified by utilizing the electrical analogy and solving by Kirchhoff's method. The method as detailed below has been in use for over 40 years.     

A generalisation of the least-squares method for the adjustment of free networks

Summary The system of normal equations for the adjustment of a free network is a singular one. Therefore, a number of coordinates has to be fixed according to the matrix. The mean square errors and the error ellipses of such an adjustment are dependent on this choice. This paper gives a simple, direct method for the adjustment of free networks, where no coordinates need to be fixed. This is done by minimizing not only the sum of the squares of the weighted errorsV ^T PV=minimun but also the Euclidean norm of the vectorX and of the covariance matrixQ X ^T X=minimum trace (Q)=minimum This last condition is crucial for geodetic problems of this type.     

A statistical filter for geodetic observations

A method for filtering of geodetic observationwhich leaves the final result normally distributed, is presented. Furthermore, it is shown that if you sacrifice100.a% of all the observations you may be (1−β).100% sure that a gross error of the size Δ is rejected. Another and, may be intuitively, more appealing method is presented; the two methods are compared and it is shown why Method 1 should be preferred to Method 2 for geodetic purposes. Finally the two methods are demonstrated in some numerical examples.     

PRACTICAL SAG CORRECTION IN CATENARY TAPING

Abstract

When a line is being measured with a steel tape suspended in catenary but standardized on the flat, the correction for sag is usually computed from the weight of the tape. It can, of course, be determined by actual measurements on the ground, if these are made both on the flat and in catenary, but this is not usually done as it is a tedious process in the absence of a proper standardizing base.     

Geospatial Application in the Study of Beach Placer along the Coast of Gulf of Mannar,India

Abstract

Geospatial analysis of marine mineral placer deposits along the Gulf of Mannar is attempted. This study develops a method for the spatial anlaysis of data using geographical information system (GIS). Specifically, creating attribute data base structure, data encoding, data interpolation, and view shed analysis are attempted to delineate the opaque and garnet occurrences in the beach sediments. Data integration including the creation of digital files using TNT Mips software is performed. The interpolation of the spaced data is achieved by inverse distance weighed interpolation to define the zone of heavy mineral enrichment. This study has established the digital elevation model (DEM) capability to identify the potential beach placer zones in the study area.     

MEAN SQUARE ERRORS OF POINT DETERMINATIONS

Abstract

Considering first of all the general case of a triangle ABC with base AB and apex angle C, the assumption is made that at A and at B only one orienting ray has been observed at each point besides the forward rays to C and that at Conly B and A have been observed. In other words, the three angles of the triangle have been observed. The adoption of General Schreiber's rule with regard to the weights of forward and back directions is valid here, since it may easily be shown that, when the weight of a forward ray is one-half of the weight of a back ray, the adjusted angles of a triangle conform to the condition of least squares.     

THE TRIANGULATION OF CULTIVATION OVERLOOKED BY HIGH GROUND

Abstract

14. General. Except for one or two located by an auxiliary triangle or by ray and distance, every point is fixed by a fully observed triangle of which the base is a pair of pillars. To justify the larger and more expensive party required for this method a high rate of observation must be maintained. The two observing periods available each day in the northern Sudan are the 3–4 hours starting just before dawn, and the 2–3 hours which end with sunset. Since moveluent in the cultivation is generally slow and on foot or by donkey, the longer morning period is best used for observing the single angles at each of a series of points there. The shorter and hotter afternoon period may then be used for observing the rounds of angles at each of a pair of pillars, which can normally be reached or at least approached by car. Asfar as possible the points observed to from these pillars will be those occupied on either the preceding or following morning, so that the triangles can be closed as soon as possible. Up to nine triangles have been closed in a day.     

A framework for mixed-use decomposition based on temporal activity signatures extracted from big geo-data

ABSTRACT

Mixed use has been extensively applied as an urban planning principle and hinders the study of single urban functions. To address this problem, it is worth decomposing the mixed use. Inspired by the concept of spectral unmixing in remote sensing applications, this paper proposes a framework for mixed-use decomposition based on big geo-data. Mixed-use decomposition in terms of human activities differs from traditional land use research, and it is more reasonable to infer the actual urban function of land. The framework consists of four steps, namely temporal activity signature extraction, urban function base curve extraction, mixed-use decomposition, and result validation. First, the temporal activity signatures (TASs) of each zone are extracted as the proxy of human activity patterns. Second, the diurnal TASs of routine activities are extracted as urban function base curves (i.e. endmembers). Third, a linear decomposition model is used to decompose the mixed use and obtain multiple results (urban function composition, dynamic activity proportions, and the mixing index). Finally, result validation strategies are concluded. This framework offers method extensibility and has few requirements for the input data. It is validated by means of a case study of Beijing, based on a social media check-in dataset.     

THE CONFORMAL TRANSFORMATION OF A NETWORK OF TRIANGULATION

Abstract

In a recent issue of this Review, an example is given of the conformal transformation of a network of triangulation using Newton's interpolation formula with divided differences. While the application of the method appears to be new, attention should be drawn to the fact that Kruger employed Lagrange's interpolation formula in a discussion and extension of the Schols method in a paper which was published in the Zeitschrift für Vermessungswesen in 1896. A reference to this paper was given at the end of the paper, “Adjustment of the Secondary Triangulation of South Africa”, published in a previous issue of the E.S.R. (iv, 30, 480).     

FURTHER NOTES ON RANGE-FINDING WITH A THEODOLITE

Abstract

Since writing the article which appeared in E.S.R., no. 36, p. 364, the writer has used this method to obtain thousands of spot heights with differences of elevation varying up to 7,500 feet in a single shot. The results of this experience and the modifications introduced in the method may be of some iilterest.